EP3123195B1 - System for protecting people on a worksite through precise positioning - Google Patents

Description

Object of the invention

The present invention relates to a system for collective or individual protection of the human person in places where measures aimed at the safety of persons, in particular at the prevention of falls of workers, are required. The use of the system can thus extend to the protection of any human being confronted with dangerous zones such as for example the protection of pedestrians against collisions with civil engineering machinery, construction site or with respect to any other vehicle confronted by example to a danger of falling or overturning in or around dangerous areas.

State of the art

The state of the art is described below in a series of documents, without this state of the art being considered as exhaustive.

GB200816469 describes a protection of industrial processes by selective authorization of access according to the position and the identity of the bearer of a portable communicator (electronic tag). The user's position can be determined by RTLS.

CA2709171 describes a worker protection on railways based on the detection of the worker wearing a "tag", a central system determining the position of the worker in relation to the approaching train and warning him as soon as he has little time left to take cover. The terminals which litter the route of the train are for example connected to each other using wires.

US200810099 describes a system for protecting people by determining their position vis-à-vis industrial processes. These processes cannot in any case start if an area has not previously been evacuated, for example. The problem posed is very similar to that of GB200816469 .

CN102768352 and CN202770989U describe a mining protection system (underground) based on a joint location in UWB and ultrasound, required by a large number of echoes.

EP2226646 describes a "relative" or "mobile" tracking system. The system consists of wireless transceiver modules connected to a wireless network. Among these is a central "anchor" of known position in the space considered and acting as a base station, the other modules having a position to be determined relative to this base station. However, no means have been put forward to define a border delimiting a dangerous zone.

DE202008005467 describes a system for locating people in a tunnel using anchors in the form of wireless transmitters / receivers whose position is known.

CN101571406 describes a pet tracking system.

IT2004BA0059 describes a system for locating people or animals which transmits the position step by step through a network of fixed transmitters / receivers and which are aware of their absolute position.

US2003122666 describes a system for measuring position by triangulation by playing on the phase of the signals received. The invention describes a positioning method requiring anchors whose positions and orientations are known.

WO200398528 describes a method of measuring the distance between two objects provided with RF tags.

US20030052776 describes a method of measuring distance between two objects based on the UWB.

BR9000368U describes a wristband tracking system with remote and automatic reading.

EP2282106 describes a system for locating workers in an area by laser scanning.

KR101258905 describes a worker protection system with only two RTLS tags (position of a crane and position of a worker) and an access point connected to a server.

KR20110017707 describes a system for locating in a tunnel using fixed terminals (similar to CA2709171 ).

CA2768054 describes a complex tracking system using the received power method in a building. The system requires a calibration phase but checks itself whether there are enough anchors. The system needs a description of the building topology, access points, etc.

US2010017126 describes a positioning system, visibly GPS or SPS satellite, in which an area, visibly circular, is defined with respect to a first localized object. Then a series of alerts are given if other objects approach this first object.

JP2009020847 describes a system for preventing accidents involving the elderly or disabled using anchors placed inside a dwelling. Each beacon receives a strength of a signal emitted by a tag, which makes it possible to determine if a tag is near an anchor and to give an alert if necessary. Communication takes place via the electrical network (such as a lamp supply line for example).

WO2006085280 describes a GPS-based large area animal tracking system using relays.

US2004087314 describes a system for locating a tag relative to a single anchor using distance and angle measurements. Many general ideas are cited in this document such as for example the use of a touch screen but few details are given on how to implement the system or manage obstacles. The desired precision is not mentioned either.

US 2013/0180469 describes a custom wireless fence system for confining one or more dogs in a user-defined containment zone, without the need for a physical fence or underground cable. The system, which is easy to configure and use, includes at least three reference terminals, including a master central terminal and at least two slave terminals, at least one collar and, preferably, a remote control. All these elements communicate with each other in a bidirectional manner. A reference system is configured by the central terminal, in which the coordinates of all reference terminals are assigned.

US 2003/0179140 discloses an electronic pet fence having a plurality of fixed transceivers and a movable collar transceiver attached to the animal. The location of limits and prohibited areas is determined in learning mode and stored in memory. Determination logic responds to signals exchanged between the fixed transceivers and the working collar transceiver to determine if the animal is within defined limits.

US 2013/0324150 discloses a device and a method for estimating position. The position estimation apparatus includes a coordinate system setting unit based on location information. A selection unit selects a target node, the location of which is to be estimated, based on the connection information between nodes received from a plurality of nodes constituting a network. An estimation unit estimates the location information of the target node based on a connection relationship between the target node and reference nodes, the location information of which is known. In particular, when there are two reference nodes, the location information of the target node is based on the comparison between the sum of the distances between the target node and each reference node and the distance between the two reference nodes.

Aims of the invention

The present invention aims to specifically protect minors, drillers, machine operators, workers present as well as occasional visitors in open-pit quarries, mines, sites with or without mining activities, demolition sites. with or without explosives and demining areas.

In particular, the invention aims to provide a solution which no longer requires the manual encoding of the location of the reference terminals and which allows the simple and efficient tracing of a border.

Finally, the object of the invention is to obtain a solution based on the collaboration of people.

Main characteristic elements of the invention

A first aspect of the present invention relates to an individual or collective protection system for people in a potentially dangerous area, comprising the features of claim 5.

• l'unité automatisée d'établissement du repère de référence XY est configurée pour :
  • positionner le premier anchor, de préférence la borne centrale, à l'origine des axes (0, 0) ;
  • positionner le second anchor en (d, 0), où d est la distance mesurée entre les deux anchors précités ;
  • déterminer arbitrairement la position du troisième anchor à partir des positions du premier anchor et du second anchor ainsi que des distances respectives entre le troisième anchor et le premier anchor et entre le troisième anchor et le second anchor ;
• la borne centrale est placée dans une valise munie d'un contrôleur et de moyens d'entrées/sorties comportant des boutons-poussoirs et un écran, de préférence un écran tactile ;
• les bornes de référence et la borne centrale sont équipées de transmetteurs radio UWB et/ou de transducteurs ultrasoniques ;
• les moyens d'avertissement sont des moyens lumineux, acoustiques et/ou vibratoires.

According to preferred embodiments, the system of the invention comprises at least one, or where appropriate an appropriate combination, of the following additional characteristics:

• the automated unit for establishing the XY reference frame is configured for:
  • position the first anchor, preferably the central terminal, at the origin of the axes (0, 0);
  • position the second anchor at (d, 0), where d is the distance measured between the two aforementioned anchors;
  • arbitrarily determining the position of the third anchor from the positions of the first anchor and the second anchor as well as the respective distances between the third anchor and the first anchor and between the third anchor and the second anchor;
• the central terminal is placed in a suitcase provided with a controller and input / output means comprising push buttons and a screen, preferably a touch screen;
• the reference terminals and the central terminal are fitted with UWB radio transmitters and / or ultrasonic transducers;
• the warning means are luminous, acoustic and / or vibratory means.

A second aspect of the invention relates to a method of implementing the aforementioned system for the individual or collective protection of people in a potentially dangerous zone, characterized by at least the steps defined according to claim 1.

• la frontière de la zone rouge est déterminée :
  • soit en utilisant une localisation des bornes de référence dans le repère XY affichée sur un écran tactile associé à la borne centrale et en traçant ladite frontière sur l'écran tactile sous forme du polygone précité ;
  • soit en utilisant un appareil appelé traceur qui communique avec la borne centrale et les bornes de référence, la borne centrale interrogeant périodiquement le traceur lorsqu'il est déplacé dans la zone et lui demandant les distances respectives le séparant des bornes de référence,
  • ce qui permet à la borne centrale de déterminer les positions successives du traceur dans le repère XY et de créer la frontière en joignant ces positions par des segments de droite pour créer le polygone précité ;
  • soit par localisation géométrique en partant des positions d'une pluralité de bornes de référence dans le repère XY et en appliquant une homothétie pour définir une frontière qui englobe le polygone réalisé par les bornes de référence ;
• la frontière de la zone orange est déterminée à partir de la frontière de la zone rouge en créant un polygone intérieur par homothétie, la distance correspondante au retrait étant comprise entre 50 cm et 1 m ;
• le repère XY est établi de la manière suivante par la borne centrale :
  • un premier anchor, de préférence la borne centrale, est assigné arbitrairement à la coordonnée (0, 0) ;
  • un deuxième anchor se trouvant à une distance mesurée d est assigné à la coordonnée (d, 0) ;
  • un troisième anchor est localisé à partir des deux anchors précités en utilisant l'intersection de deux cercles à partir des distances respectives du troisième anchor par rapport aux deux anchors précités, une des deux intersections possibles étant choisie comme position du troisième anchor, la position retenue étant déterminée arbitrairement, par exemple la position de coordonnée Y positive ;
  • les anchors suivants sont localisées à partir des trois premiers anchors en utilisant un algorithme de trilatération, l'algorithme de trilatération étant de préférence l'algorithme décrit ci-dessous pour localiser les tags ;
  • - l'on détermine si le tag se trouve à l'intérieur, respectivement à l'extérieur, du polygone constituant la frontière fermée en traçant une droite horizontale passant par le tag et en vérifiant le nombre de fois que cette droite coupe la frontière à droite du tag, le tag se trouvant à l'intérieur de la frontière si le nombre d'intersections est impair, le tag se trouvant à l'extérieur de la frontière si le nombre d'intersections est pair ;
  • - le filtrage de la frontière fermée de la zone potentiellement dangereuse est réalisé, dont les sommets du polygone sont notés (x0, y0), (x1, y1), etc., selon les étapes suivantes :
    • sélectionner un point (xi, yi), i= 0, 1, 2... ;
    • sélectionner l'ensemble des points (xj, yj), j = 1...Nj, j différent de i, qui sont à l'intérieur d'un cercle de diamètre donné 2d, centré en (xi, yi) ;
    • déterminer un point de la frontière filtrée fi (xfi, yfi) en faisant une moyenne des positions desdits points (xj, yj) ;
    • marquer les Nj point (xj, yj) comme ne pouvant plus servir comme point de départ ;
    • parmi les points restants non marqués, rechercher un nouveau point (xi, yi) comme étant le point le plus proche de (xfi, yfi) ;
    • avec le nouveau point (xi, yi), recommencer à la deuxième étape, et ainsi de suite.

According to preferred embodiments, the method of the invention comprises at least one, or where appropriate an appropriate combination, of the following additional characteristics:

• the border of the red zone is determined:
  • either by using a location of the reference terminals in the XY frame displayed on a touch screen associated with the central terminal and by tracing said border on the touch screen in the form of the aforementioned polygon;
  • either by using a device called a tracer which communicates with the central terminal and the reference terminals, the central terminal periodically interrogating the tracer when it is moved in the zone and asking it for the respective distances separating it from the reference terminals,
  • which allows the central terminal to determine the successive positions of the plotter in the XY coordinate system and to create the border by joining these positions by straight segments to create the aforementioned polygon;
  • either by geometric localization starting from the positions of a plurality of reference terminals in the XY coordinate system and by applying a homothety to define a boundary which encompasses the polygon produced by the reference terminals;
• the border of the orange zone is determined from the border of the red zone by creating an interior polygon by homothety, the distance corresponding to the withdrawal being between 50 cm and 1 m;
• the XY coordinate system is established as follows by the central terminal:
  • a first anchor, preferably the central terminal, is arbitrarily assigned to the coordinate (0, 0);
  • a second anchor located at a measured distance d is assigned to the coordinate (d, 0);
  • a third anchor is located from the two aforementioned anchors by using the intersection of two circles from the respective distances of the third anchor with respect to the two aforementioned anchors, one of the two possible intersections being chosen as the position of the third anchor, the position retained being determined arbitrarily, for example the positive Y coordinate position;
  • the following anchors are located from the first three anchors using a trilateration algorithm, the trilateration algorithm preferably being the algorithm described below for locating the tags;
  • - one determines if the tag is inside, respectively outside, of the polygon constituting the closed border by drawing a horizontal line passing through the tag and by checking the number of times that this line intersects the border at right of the tag, the tag inside the border if the number of intersections is odd, the tag being outside the border if the number of intersections is even;
  • - the closed border of the potentially dangerous zone is filtered, the vertices of the polygon of which are denoted (x0, y0), (x1, y1), etc., according to the following steps:
    • select a point (xi, yi), i = 0, 1, 2 ...;
    • select the set of points (xj, yj), j = 1 ... Nj, j different from i, which are inside a circle of given diameter 2d, centered at (xi, yi);
    • determining a point of the filtered border fi (xfi, yfi) by averaging the positions of said points (xj, yj);
    • mark the Nj points (xj, yj) as no longer being able to serve as a starting point;
    • among the remaining unmarked points, find a new point (xi, yi) as being the point closest to (xfi, yfi);
    • with the new point (xi, yi), start over at the second step, and so on.

A third aspect of the present invention relates to an individual or collective protection system for people in a three-dimensional (3D) potentially dangerous area, comprising the steps defined according to dependent claim 9.

Brief description of the figures

• The figure 1 schematically represents a general and synthetic view of the personal protection system according to the present invention.
• The figure 2 shows schematically how the positioning algorithm according to the invention discriminates between two possible positions of the tag vis-à-vis two anchors, from the position of a third anchor.
• The figure 3 schematically shows the effect that error on the distance between a tag and an anchor can have on the determination of the position of the tag.
• The figure 4 schematically represents the creation of an XY coordinate system according to the invention.
• The figure 5 schematically represents the respective red, orange and green zones defined around a moving vehicle.
• The figure 6 represents an example of a result obtained by means of the border filtering algorithm according to the invention.
• The figure 7 schematically represents the principle of the algorithm for border filtering.
• The figure 8 illustrates how, according to the invention, the relative position of the tag with respect to the boundary is determined, using Jordan's theorem.

Detailed description of the invention and of preferred embodiments

The system according to the present invention makes it possible to warn the minor or any other person located near a dangerous zone. This warning is made by means of a transceiver, or "tag" or beacon, worn by the person directly on the body or on personal protective equipment (PPE). The transceiver or tag signals the danger by means of light, acoustic and vibratory signals, combined or not depending on the dangerousness.

Operation requires that each transceiver can locate itself relative to the danger zone. To do this, several reference markers, also called “anchors”, are placed on the ground. After the installation of the bollards, a configuration step preferably consists in moving a special transceiver called a tracer along the border between the danger zone and the safety zone. This step allows the system to save a set of positions that ultimately define the warning limit. Check-in is done at a central terminal preferably placed in a suitcase.

The location of the transceivers with respect to the terminals is carried out by a trilateration system

A peculiarity of the invention is that the definition of the zone is done during the plotting while the terminals were initially placed in an arbitrary manner and that the position of the reference terminals is unknown during the installation of the device and will remain so throughout. throughout the operation of the device. The resolution of this apparent contradiction is an element of the invention.

A second feature is the protection of the system against measurement errors by the redundancy of measurements and by the redundancy of communication channels between the terminals, the receiver (s) and the case.

The figure 1 schematically shows the various constituent elements of the system of the invention: a person 1 carrying a tag 6 (located here in the green zone), the reference terminals 3, the central terminal (and the case) 4, the tracer 5 and the three security zones 7, 8, 9.

Generic problem to solve

The problem to be solved is to warn one or more people that they are possibly in danger because of their position. This position must be able to be obtained quickly, with precision (+/- 10 cm for example) indoors and outdoors. This last point excludes any solution based on a geolocation system (GPS).

• zone verte : zone dans laquelle il n'y a pas de danger ;
• zone orange : zone dans laquelle il n'y a pas de danger mais qui est proche d'une zone de danger ;
• zone rouge : zone dans laquelle il y a danger effectif.

The danger is defined according to the position occupied by the person (s). More precisely, we want to map, according to the invention, a given space in three zones:

• green zone: zone in which there is no danger;
• orange zone: zone in which there is no danger but which is close to a danger zone;
• red zone: zone in which there is an effective danger.

• fournir une solution pour définir ces trois zones et
• fournir une solution pour déterminer dans quelle zone une personne se trouve avec une précision de localisation souhaitée de +/-10 cm par exemple.

The problem to be solved is then reduced along two axes:

• provide a solution to define these three areas and
• provide a solution to determine which area a person is in with a desired location accuracy of +/- 10cm for example.

Specifics of the problem

• rapidité de mise en œuvre,
• nécessité d'avoir des zones mobiles (autour d'un camion par exemple),
• détermination de l'heure et de la position du système,
• présence d'obstacles,
• protection collaborative,
• principe du feu de signalisation avec un code universel à trois zones (vert, rouge, orange) et
• détermination rapide d'une frontière.

The particularities or requirements of the problem to be solved are as follows:

• speed of implementation,
• need to have mobile areas (around a truck for example),
• determination of the time and position of the system,
• presence of obstacles,
• collaborative protection,
• traffic light principle with a universal three-zone code (green, red, orange) and
• rapid determination of a boundary.

General proposed solution

The proposed solution is thus based on a set of reference terminals which are distributed more or less uniformly in the zone in which it is desired to position people.

These reference terminals communicate with each other and also communicate to a central terminal. It is this central terminal that orchestrates the entire system. In a preferred implementation, it is considered placing this central terminal in a suitcase and providing it with a screen, touchscreen or not, and push buttons.

The reference terminals are also capable of measuring the distance which separates them by means known to those skilled in the art. One solution, for example, is to use UWB radio transmitters or ultrasonic transducers with a TOF ( time of flight ) method.

Note that UWB technology, like other technologies, can assess a degree of reliability over the returned distance as well as the presence of potential obstacles. This information is advantageously used to reject from any calculation the distances considered as unreliable.

Estimation of the position of the tags for a pair of anchors i, j

Suppose the position of anchors (x0, y0), (x1, y1), etc. is known, as well as the respective distances of the tag from these anchors: d0, d1, etc. We aim here to determine the most probable position of the tag (xt, yt).

The idea implemented according to the invention is to consider anchors 2 to 2 and to determine xt and yt from a pair of anchors i and j. Knowing the positions of anchors i, j and the distances between them and the tag, respectively di and dj, it is possible to determine 2 potential positions for the tag, corresponding to the intersection of two circles. The algorithm for calculating these two positions is known to those skilled in the art (see for example

http: // www.ambrsoft.com / TrigoCalc / Circles2 / Circle2.htm ).

According to the invention, the conditions of intersection of the two aforementioned circles will also be imposed by adding a tolerance which represents a possible measurement error over the distances. If these conditions are verified, we continue the calculation, otherwise we consider that there is a measurement error and that the position of the tag cannot be found using this pair of anchors i, j.

At this step, there is thus an uncertainty since 2 possible positions are given. To decide, the algorithm uses the other anchors k (k different from i, j) and determines for each anchor k the distance from the two estimated positions and compare it to dk. This step is illustrated on the figure 2 involving 3 anchors A1, A2 and A3, the two possible positions for the tag with respect to A1 and A2 being denoted T1 and T2 respectively (references 61 and 62).

Then a voting system is applied. We compare each of the distances between the estimated positions 61, 62 and the anchor k with dk. If the smallest difference is that relating to position 61, the score of position 61 is increased by 1 point. Alternatively, if the smallest difference is that relating to position 62, the score of position 62 is increased by 1 point. Once we do this calculation for all the anchors k, the highest score in the end gives the correct position and we get (xt, yt) (ij).

If the two scores are identical, the indeterminacy remains. This indeterminacy can be caused by a measurement error or by the fact that the two tag positions are close. In the latter case, the positions are averaged.

Estimation of the precision of the position of the tag for a pair of anchors i, j

Still according to the invention, the idea is to use the radio information to attach reliability to each distance measurement. The reliability is expressed as an estimate of error itself expressed in meters.

où :

• Δdi_Accuracy est la précision la meilleure à laquelle on peut s'attendre. C'est un paramètre fixé par exemple à : di_Accuracy = 0,10 m ;
• Δdi_Power est lié à la puissance reçue du « first path » FP_Power. Plus la puissance est élevée, plus on a de chances d'être proche et en champ direct et plus la mesure est faible. On considère une perte logarithmique de précision avec la distance, à savoir par exemple une perte de 1 cm de précision avec le doublement de distance (-6 dB) : $$\mathrm{\Delta }{\mathit{di}}_{\mathit{Power}}=\mathrm{0,01}m\ast \frac{-80\mathit{dBm}-\mathit{FP}\_\mathit{<figure-callout\; id="6"\; label="POWER"\; filenames="imgf0001.png"\; state="\{\{state\}\}">POWER</figure-callout>}}{6\mathit{dB}},$$
  
  $$\mathrm{\Delta }{\mathit{di}}_{\mathit{Power}}\in \left[0m,\mathrm{0,05}m\right].$$
  

A heuristic based on measurements of radio statistics is employed and based on the experimental results. For a given distance measurement, the estimated error is at least: $$\mathrm{\Delta }\mathit{di}=\mathrm{\Delta }{\mathit{di}}_{\mathit{Accuracy}}+\mathrm{\Delta }{\mathit{di}}_{\mathit{Power}},$$

or :

• Δ di _Accuracy is the best precision one can expect. This is a parameter set for example at: di _Accuracy = 0.10 m;
• Δ di _Power is linked to the power received from the “first path” FP_Power. The higher the power, the more likely it is to be close and in a direct field and the lower the measurement. We consider a logarithmic loss of precision with distance, i.e. for example a loss of 1 cm of precision with doubling of distance (-6 dB): $$\mathrm{\Delta }{\mathit{di}}_{\mathit{Power}}=0.01m\ast \frac{-80\mathit{dBm}-\mathit{FP}\_\mathit{<figure-callout\; id="6"\; label="POWER"\; filenames="imgf0001.png"\; state="\{\{state\}\}">POWER</figure-callout>}}{6\mathit{dB}},$$
  
  $$\mathrm{\Delta }{\mathit{di}}_{\mathit{Power}}\in \left[0m,0.05m\right].$$
  

After defining the heuristic as above, we will perform a weighting calculation. The objective of this step is to determine if the positions in x and in y are precise or not. To do this, the idea is to “disturb” the measurements with the error values calculated above and to observe the impact of these disturbances on the position found by the algorithm.

An example is shown on figure 3 where the error on the position of the tag (in x and y) is only a function of the error Δd2 (noted error d2 in the figure) on the distance between the tag and the anchor A2.

$$\mathit{dj}\to \mathit{dj}\pm \mathrm{\Delta }\mathit{dj}.$$

The positioning algorithm is therefore implemented four times by disturbing the measurements on di and dj as follows: $$\mathit{di}\to \mathit{di}\pm \mathrm{\Delta }\mathit{di},$$

$$\mathit{dj}\to \mathit{dj}\pm \mathrm{\Delta }\mathit{dj}.$$

$$\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{\Delta }y\left(k\right)\right)}^2}}.$$

After applying the algorithm, we obtain 4 disturbed positions (xt + Δx (k), yt + Δy (k)) (ij) with k varying from 0 to 3 (4 possible disturbances), xt and yt being the positions obtained from the undisturbed distances di and dj. The reliability of the measurements in x and y is then calculated on the basis of the difference that the disturbance creates on the measurement. Position errors on xt (ij) and yt (ij) can be calculated as follows: $$\mathrm{\Delta }\mathit{xt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{\Delta }x\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">k</figure-callout>}\right)\right)}^2}},$$

$$\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{<figure-callout\; id="2"\; label="\Delta \; y\; k"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\Delta </figure-callout>}y\left(k\right)\left(\right)\right)}^2}}.$$

$$\mathit{Pyt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{\Delta }\mathit{yt}{\left(\mathit{ij}\right)}^2}.$$

The following weighting law is then applied: $$\mathit{Pxt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{<figure-callout\; id="2"\; label="\Delta \; xt\; ij"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\Delta </figure-callout>}\mathit{xt}{\left(\mathit{ij}\right)}^{}{\left(\mathit{}\right)}^2},$$

$$\mathit{Pyt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{\Delta }\mathit{yt}{\left(\mathit{<figure-callout\; id="2"\; label="ij"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">ij</figure-callout>}\right)}^2}.$$

1. 1. Copier les Pxt(ij) dans un tableau.
2. 2. Classer les Pxt(ij) dans ce tableau par ordre décroissant.
3. 3. Stocker la valeur du NPTème élément dans une variable locale Threshold. Si NPT est supérieur au dernier indice du tableau, prendre la dernière valeur du tableau.
4. 4. $$\forall \mathit{Pxt}\left(\mathit{ij}\right)<\mathit{Threshold}\Rightarrow \mathit{Pxt}\left(\mathit{ij}\right)=0.$$
   

When many anchors are present and the number of anchor combinations giving little precision is such that these measurements still have a not insignificant weight in the estimation of the precision, this leads to an unnecessary measurement error. We will therefore limit the number of measurements used by canceling certain weights, according to the following procedure:

1. 1. Copy the Pxt (ij) into an array.
2. 2. Sort the Pxt (ij) in this table in descending order.
3. 3. Store the value of the NPTth element in a local variable Threshold. If NPT is greater than the last index in the array, take the last value in the array.
4. 4. $$\forall \mathit{Pxt}\left(\mathit{ij}\right)<\mathit{Threshold}\Rightarrow \mathit{Pxt}\left(\mathit{ij}\right)=0.$$
   

We do the same for Pyt (ij). Thus we will only keep the highest weighting NPTs and even if there is a large number of anchors, the weight of the anchors which create significant position errors will be zero. To start, NPT can be set to 10 for example.

$$\mathit{pyt}\left(\mathit{ij}\right)=\frac{\mathit{Pyt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pyt}\left(\mathit{kl}\right)}}.$$

The reliabilities obtained above can then be normalized so that their sum is equal to 1, that is to say: $$\mathit{pxt}\left(\mathit{ij}\right)=\frac{\mathit{Pxt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pxt}\left(\mathit{kl}\right)}},$$

$$\mathit{pyt}\left(\mathit{ij}\right)=\frac{\mathit{Pyt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pyt}\left(\mathit{kl}\right)}}.$$

If the previous algorithms are applied for all the pairs of anchors (ij) 2 to 2, we obtain a set:
(xt, yt) (ij) and (pxt, pyt) (ij) for all combinations of ij.

positions et les fiabilités associées.For example, if a locate request is executed for 5 anchors, we get ${\mathrm{VS}}_2^5=10$

positions and associated reliability.

$$\mathit{yt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathit{yt}\left(\mathit{ij}\right)}.$$

We therefore have the estimate of the position of the tag (xt, yt): $$\mathit{xt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pxt}\left(\mathit{ij}\right)\mathit{xt}\left(\mathit{ij}\right),}$$

$$\mathit{yt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathit{yt}\left(\mathit{ij}\right)}.$$

$$\mathit{eyt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right).}$$

The estimate of the error on the position of the tag (xt, yt) is then calculated respectively in x and y by: $$\mathit{ext}={\displaystyle \sum _{\mathit{ij}}\mathit{pxt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{xt}\left(\mathit{ij}\right)},$$

$$\mathit{eyt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right).}$$

Creation of an orthonormal "XY" coordinate system

Once the reference markers are installed, the user asks the system to verify the position of the terminals. To do this, the central terminal interrogates the set of reference terminals and asks them for the distance which separates them from each other (see above).

Any location requires a reference mark. According to the prior art, it is always required that this reference mark be defined by assigning known positions to the reference terminals. The proposed invention does not, however, require this heavy constraint for a system which must be installed quickly.

1. 1) Une borne 10, de préférence la borne centrale (se trouvant dans la valise) est assignée arbitrairement à la coordonnée (0, 0).
2. 2) Une seconde borne 20 qui est à une distance d est assignée à la coordonnée (d, 0).
3. 3) Une troisième borne 30 est localisée à partir des deux autres en utilisant l'intersection de deux cercles à partir des informations de distance ( = rayon des cercles). Cela crée une ambiguïté car il existe deux intersections possibles. Une des deux positions est alors choisie arbitrairement. Par exemple, la position de la troisième borne dont la coordonnée y est positive est choisie.
4. 4) A ce stade, étant donné que trois bornes de référence sont localisées, l'ensemble des autres bornes (par ex. borne 40 sur la figure) peuvent être localisées par l'algorithme de localisation des tags décrit ci-dessus.
5. 5) Une étape de raffinement est possible une fois toutes les coordonnées des bornes déterminées. Cette étape a pour but de rendre insensible l'algorithme de localisation au choix initial des bornes aux étapes 1), 2) et 3).

From the distance information collected about the reference markers, the central marker determines an XY marker which will be used for further location. This determination works in several steps (see also figure 4 ):

1. 1) A terminal 10, preferably the central terminal (located in the case) is arbitrarily assigned to the coordinate (0, 0).
2. 2) A second terminal 20 which is at a distance d is assigned to the coordinate (d, 0).
3. 3) A third terminal 30 is located from the other two using the intersection of two circles from the distance information (= radius of the circles). This creates ambiguity because there are two possible intersections. One of the two positions is then chosen arbitrarily. For example, the position of the third terminal whose y coordinate is positive is chosen.
4. 4) At this stage, given that three reference terminals are located, all of the other terminals (eg terminal 40 in the figure) can be located by the tag location algorithm described above.
5. 5) A refinement step is possible once all the coordinates of the limits have been determined. The purpose of this step is to make the localization algorithm insensitive to the initial choice of the limits in steps 1), 2) and 3).

Finally, it will be noted that the choice of the terminals in steps 1), 2) and 3) can be based on the reliability of the distance measurements. Each new terminal whose position is sought to be determined will be chosen as the one with the lowest position error.

Generalization to positioning anchors and tags in 3D space

All the above discussion is based on the assumption that we locate anchors and tags in a two-dimensional or XY reference frame. The present invention is not however limited to a location in a plane and all the concepts presented here can be generalized to a location in a three-dimensional (3D) space.

Thus, the method which consists, in 2D, in considering a pair of anchors, in determining two possible positions by intersection of two circles and in using the other anchors by a mechanism of voting on the distances to select a position among these 2 positions possible is easily generalized in 3D in a method which consists in considering a triplet of anchors, in determining two possible positions by intersection of three spheres and in using the other anchors by a voting mechanism on the distances to select a position among these 2 possible positions.

Likewise, while the disturbance mechanism of the two distances with respect to the pairs of anchors in 2D makes it possible to obtain four disturbed positions, in 3D, the mechanism can be implemented over the three distances with respect to the triplet of anchors. and makes it possible to obtain nine disturbed positions.

As regards the determination of the border in 3D, according to a preferred embodiment, the path which defines the security zone is in fact a projection on the X, Y plane, said zones then being (generalized) cylinders. For example, in the case of a 3D protected building in which the elevator shaft is removed, a security zone would be defined on the ground floor by tracing the border and would automatically carry over to all floors. Thus, in 3D, only during the plotting of the border and during the detection of the inclusion using Jordan's theorem, it suffices to apply the algorithms used in 2D without taking into account the Z coordinate for have the desired operation.

Use of anchors position errors to refine the creation of the orthonormal XY coordinate system

When creating the orthonormal coordinate system, the anchors are placed approximately, as indicated above, and the only known information is the distances between the anchors (dij) and the associated errors (Δdij) - see the method exposed below- above where we replace the notations di and Δdi respectively by dij and Δdij. The distances dij can be measured a large number of times (NMA) and are therefore precise. One can for example limit oneself to making the average of the errors on the four central values of dij.

At this stage, the algorithm therefore has a series of anchors na of which it does not know the positions but only the relative distances dij.

1. 1) La borne centrale est placée au point de coordonnées (0, 0). Celui-ci est noté a0.
2. 2) Parmi les anchors disponibles, on sélectionne avantageusement un anchor an qui est à la distance maximale pour laquelle on a une mesure de distance fiable (la fiablilité est définie sur base de l'erreur estimée Δdij). Cet anchor est alors en position (dn, 0) puisqu'on connaît sa distance à (0, 0).
3. 3) On a donc une base d'anchors positionnés et utilisés pour démarrer la localisation. Comme indiqué ci-dessus, la position du troisième anchor est choisie arbitrairement (parmi deux positions possibles). Par exemple, on choisit la position dont la coordonnée y est positive. On passe ensuite en revue tous les anchors de position inconnue (à partir du quatrième) et on détermine leur position grâce à l'algorithme décrit ci-dessus en considérant les anchors comme des tags dans l'algorithme de positionnement.
4. 4) Parmi les positions déterminées, on choisit un nouvel anchor qui a la somme des erreurs ext + eyt la plus faible.
5. 5) On recommence l'opération en 3) en utilisant l'ensemble des anchors dont on connaît la position.

The algorithm for determining the position of the anchors is as follows:

1. 1) The central terminal is placed at the coordinate point (0, 0). This is denoted a0.
2. 2) Among the available anchors, an anchor an is advantageously selected which is at the maximum distance for which there is a reliable distance measurement (the reliability is defined on the basis of the estimated error Δdij). This anchor is then in position (dn, 0) since we know its distance to (0, 0).
3. 3) We therefore have a base of anchors positioned and used to start the localization. As indicated above, the position of the third anchor is chosen arbitrarily (among two possible positions). For example, we choose the position whose coordinate y is positive. We then review all the anchors of unknown position (from the fourth) and we determine their position using the algorithm described above by considering the anchors as tags in the positioning algorithm.
4. 4) Among the determined positions, we choose a new anchor which has the smallest sum of the errors ext + eyt.
5. 5) We repeat the operation in 3) using all the anchors whose position we know.

Thus, each new anchor is positioned more and more precisely. At the end of this phase, all the anchors are located on an orthonormal grid. Compared to physical reality, because the third anchor is chosen arbitrarily (see above), a mirror effect in x and y is possible but this has no influence on the border.

Methods of determining a border of the red zone

It is envisaged, according to the invention, to determine the border of the red zone in at least three different ways from the position of the reference terminals located in an XY frame.

Localization on touch screen

The reference terminals are located on a touch screen in an XY frame. It is then possible to draw on the touch screen a limit determining the red zone. The border is then defined as a set of closely spaced points joined by line segments.

Localization by a plotter

As already mentioned above, a device called a tracer capable of communicating with the central terminal and the reference terminals is moved along the border by a person, by walking for example. The central terminal periodically interrogates (typically 10x per second) the plotter and asks it for the distances separating it from the reference markers. From this information, the central terminal determines the successive positions of the plotter and thus creates a border by joining these close positions by straight segments. By way of nonlimiting illustration, the plotter could be embodied in the form of a roulette wheel provided with a handle. The roulette wheel could be advantageously used to send the aforementioned periodic signal which would correspond to a given displacement of the latter.

Geometric location

In the case of reference terminals placed at the four "corners" of a vehicle such as a truck for example, the danger zone is defined by connecting the four reference terminals by straight segments and by applying a homothety to define a larger rectangle which delimits the danger zone (red), as shown in the figure 5 .

It is also envisaged to consider the presence of the danger only in the direction of travel of the vehicle in order to limit as much as possible the alerts which prevent the vehicles from moving because of the signaling of false dangers.

It will also be noted that it is also envisaged to locate the mobile reference terminals of the truck with respect to the fixed reference terminals in the same way as the tags are located. Thanks to this, it is possible to have a complete mapping of the location of vehicles and pedestrians.

Border filtering

As explained above, the border is defined by a set of points connected by line segments. In the case of the tracer, if the person equipped with the tracer moves at a speed of 1 m / s and determines a border 1 km long, this represents 10,000 points and segments (if acquisition of 10 points per second). It is therefore advantageously planned to modify this border and replace it with a reduced number of points and segments by “filtering” it. This step is executed only once and makes it possible to reduce the computing power necessary for determining the position of the tags with respect to the border. The figure 6 represents an example of filtering border (raw data obtained from the plotter 50 and border after filtering 51).

More precisely, according to the invention, following the tracing, the border is made up of a list of coordinate points (x0, y0), (x1, y1), ... more or less ordered. This list represents a dense set of points which must be "lightened" to facilitate the determination of the position of the tag relative to the border. The idea implemented by the invention is to go through these points and condense them into a list of points spaced on average by a distance d.

1. 1. Sélectionner le premier point capturé (xi, yi), i = 0 pour ce premier point.
2. 2. Déterminer l'ensemble des points qui sont dans un cercle de diamètre 2d centré autour de ce point, soit : $$\left(\mathit{xj},\mathit{yj}\right)\mathit{tel}\mathit{que}\sqrt{{\left(\mathit{xi}-\mathit{xj}\right)}^2+{\left(\mathit{yi}-\mathit{<figure-callout\; id="2"\; label="yj"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">yj</figure-callout>}\right)}^2}<d$$
   
3. 3. Déterminer le point de la frontière (xfi, yfi), i = 1, 2, ..., en faisant la moyenne de la position des nj points (xj, yj) : $$\mathit{xfi}=\frac{{\displaystyle {\sum }_j\mathit{xj}}}{\mathit{nj}},$$
   
   $$\mathit{yfi}=\frac{{\displaystyle {\sum }_j\mathit{yj}}}{\mathit{nj}}.$$
   
4. 4. Marquer définitivement l'ensemble des points (xj, yj) comme ne pouvant plus servir de point de départ (xi, yi). Sur la figure 7, les points marqués sont hachurés.
5. 5. Parmi les points non marqués, rechercher un nouveau point (xi, yi) comme étant le point le plus proche de (xfi, yfi), c'est-à-dire tel qu'il minimise la distance par rapport à celui-ci. Avec ce nouveau point, recommencer à l'étape 2). On ne considère donc dans cette recherche qu'un nombre limité de points à partir du dernier point marqué. Ainsi, on force l'algorithme à parcourir la liste initiale de points dans un certain ordre, par exemple l'ordre dans lequel elle a été créée.

The algorithm is as follows (see figure 7 ):

1. 1. Select the first point captured (xi, yi), i = 0 for this first point.
2. 2. Determine the set of points which are in a circle of diameter 2d centered around this point, namely: $$\left(\mathit{xj},\mathit{yj}\right)\mathit{Phone}\mathit{than}\sqrt{{\left(\mathit{xi}-\mathit{<figure-callout\; id="2"\; label="xj"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">xj</figure-callout>}\right)}^2+{\left(\mathit{yi}-\mathit{<figure-callout\; id="2"\; label="yj"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">yj</figure-callout>}\right)}^2}<d$$
   
3. 3. Determine the point of the border (xfi, yfi), i = 1, 2, ..., by taking the average of the position of the nj points (xj, yj): $$\mathit{xfi}=\frac{{\displaystyle {\sum }_j\mathit{xj}}}{\mathit{nj}},$$
   
   $$\mathit{yfi}=\frac{{\displaystyle {\sum }_j\mathit{yj}}}{\mathit{nj}}.$$
   
4. 4. Definitively mark the set of points (xj, yj) as no longer being able to serve as a starting point (xi, yi). On the figure 7 , the marked points are hatched.
5. 5. Among the unmarked points, find a new point (xi, yi) as being the point closest to (xfi, yfi), ie such that it minimizes the distance from it. this. With this new point, start over at step 2). In this research, therefore, only a limited number of points are considered from the last point marked. Thus, one forces the algorithm to traverse the initial list of points in a certain order, for example the order in which it was created.

The algorithm ends when there is no more point (xi, yi) to select. The fact of marking the points and starting again on a new point (xi, yi), by excluding the points which have already been used in step 3, makes it possible to avoid local loops and forces the algorithm to progress along the border in a specific direction.

Once the border has been crossed, a very large number of points should be marked. If this is not the case, it will be necessary to generate a warning. Note that very distant points are automatically rejected. The only parameter is d which gives an average spacing between points after filtering.

The set of points (xfi, yfi) constitutes the border named F.

Determining the position of the tag relative to the border

Still according to the invention, we will determine whether the tag is inside or outside the border F by drawing a horizontal line passing through the tag and checking the number of times that this line intersects the border for example. to the right of the tag. If the number of intersections is odd, the tag is initially inside the polygon, otherwise, it is outside of it.

This method is demonstrated by Jordan's (curve) theorem (link: http: // en.wikipedia.org / wiki / Jordan curve theorem).

The figure 8 shows several examples where the number of intersections with the border is either even or odd. In particular, this method is very effective in the case of “noisy” borders which have micro-loops (see lower horizontal line and tag T3).

Determination of an orange zone boundary

The orange zone is defined by a distance parameter from the red zone. For example, we can decide that a tag enters the orange zone if it is less than 80 cm from the red zone. Given a border defined by a set of segments, it is easy for those skilled in the art to find the geometric algorithms necessary to determine whether or not a tag is less than 80 cm from the border.

Safety in operation

In operation, anyone who arrives in a protected area must wear a tag. This tag is a mobile transceiver, capable of communicating with the central terminal and capable of measuring the distances which separate it from the reference terminals.

Once the border corresponding to the red and orange zones is defined with respect to the reference terminals, the central terminal is able to periodically interrogate all the tags for which it provides protection, to determine their position in the XY frame. and to evaluate this position in relation to the borders of the zones previously defined.

The tags are advantageously provided with visual, auditory and / or vibratory signaling means. When a tag enters an orange or red zone, it is notified by the central terminal.

Provision is made, according to a particular embodiment of the invention, to warn the other tags so that several people forming a team can monitor and protect each other.

Thus, if a tag enters a red zone, it can for example start to vibrate, emit a shrill sound and indicate a red light signal. Tags worn by other people will only emit a sound, for example. Thus, the carriers of such a tag know that someone else in the group of people is in danger.

The originality of the present invention lies first of all in the solution provided so as not to have to manually encode the location of the reference terminals. A second originality is the way in which the border is defined using a plotter and then filtered. The idea of making the system based on the collaboration of people is also innovative.

Glossary

• UWB (ultra-wideband signal): wideband signal (more than 100 MHz standardized by IEEE 802.15.4a - 2007).
• RTLS: real-time location system.
• anchor (anchor point, reference terminal): fixed or mobile object used as a reference to locate another object.
• tag: mobile transceiver intended to be located in relation to anchors.

Benchmarks

• 1 person to protect
• 2 border of the danger zone (red zone)
• 3 reference terminal or anchor
• 4 central terminal (with case)
• 5 border plotter
• 6 tag worn by the person
• 7 green zone
• 8 orange zone
• 9 red zone
• 10 terminal N ° 1 in the XY coordinate system
• 20 terminal N ° 2 in the XY coordinate system
• 30 terminal N ° 3 in reference XY
• 40 terminal N ° 4 in the XY coordinate system
• 50 rough border
• 51 filtered border
• 61 ^1st intersection of the two circles centered on A1 and A2 (T1)
• 62 ^2nd intersection of the two circles centered on A1 and A2 (T2)

Claims (9)

1. A method for implementing a system for protecting persons individually or collectively (1) in a potentially dangerous area, comprising the following steps:

   - the plurality of reference markers (3) are installed arbitrarily in the potentially dangerous area;

   - the central marker (4) queries the plurality of reference markers (3) and determines the distances separating them from one another as well as the distance separating them from the central marker (4);

   - the central marker establishes a two-dimensional or XY frame of reference that will be used to locate the persons (1);

   - a closed border (2) of the potentially dangerous area, called red area (9), is determined and filtered, said closed border (2) being defined as a polygon, that is to say a set of points or apices connected by line segments or sides;

   - a border of an area located inside the red area (9) is determined, defining a so-called orange area (8), the area located inside the border delimiting the orange area being defined as the safe area for the persons, or green area (7), the preceding steps being configuration steps;

   - during operation, each person (1) that will be located in the potentially dangerous area is equipped with a tag (6);

   - the central marker (4) periodically queries all of the tags (6), determines their position in the XY frame of reference to assign each of these positions a location either in the green area (7), in the orange area (8), or in the red area (9);

   - if one of the tags (6) is located in the orange (8) or red (9) area, the central marker (4) actuates the warning means associated with said tag (6) and optionally actuates one of the warning means associated with the other tags (6);

   - in the step for determining the position of the tags (6) in the XY frame of reference, in order to assign each of these positions a location either in the green area (7), in the orange area (8), or in the red area (9), each tag (6) is positioned relative to at least one pair of anchors (i, j; i, j = 1, 2, ...), which gives two possible positions T1, T2 (61, 62) for the tag (6), the selected position being determined owing to a vote based on the use of the other anchors k (k different from i, j), a score being assigned to each possible position T1, T2 (61, 62), by calculating the difference between the tag-anchor distance k, or dk, and each of the distances of the anchor k and the possible positions T1, T2 (61, 62), the smallest difference causing the incrementation of the score for the corresponding possible position T1, T2 (61, 62), the ultimate highest score giving the selected position among the two possible positions;

   - it is determined whether the tag (6) is located inside, respectively outside, the polygon making up the closed border (2) by drawing a horizontal straight line passing through the tag and verifying the number of times that this line intersects the border (2) on the right-hand side of the tag (6), the tag (6) being located inside the border if the number of intersections is odd, the tag (6) being located outside the border if the number of intersections is even;

   characterized in that the position and the position error of a tag (xt, yt)(ij) relative to a plurality of pairs of anchors i, j (i, j = 1, 2, ...) are estimated according to the following steps:

   - a heuristic based on distance-measuring statistics between tag and anchors i and j, respectively denoted di and dj, is used so as to estimate an error Δdi and an error Δdj, Δd being at least equal to Δd_Accuracy + Δd_Power, where Δd_Accuracy is the best precision that can be expected and Δd_Power is related to the power received from the "first path";

   - the calculation of the position of the tag relative to the anchors i, j is carried out four times, disrupting the measurements on di and dj as follows: $$\mathit{di}\to \mathit{di}\pm \mathrm{\Delta }\mathit{di},$$

   

   $$\mathit{dj}\to \mathit{dj}\pm \mathrm{\Delta }\mathit{dj};$$

   

   - 4 disrupted positions are obtained (xt+Δx(k), yt+Δy(k))(ij) with k varying from 0 to 3;

   - the position errors on xt(ij) and yt(ij) are calculated as follows: $$\mathrm{\Delta }\mathit{xt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{\Delta }x\left(k\right)\right)}^2}},$$

   

   $$\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{\Delta }y\left(k\right)\right)}^2}};$$

   

   - a weighting law is applied as follows to obtain reliabilities; $$\mathit{Pxt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{\Delta }\mathit{xt}{\left(\mathit{ij}\right)}^2},$$

   

   $$\mathit{Pyt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{\Delta }\mathit{yt}{\left(\mathit{ij}\right)}^2};$$

   

   - the weights are ranked by decreasing order and a predetermined number of the highest weights are retained, in order to remove the anchors that create significant errors;

   - the aforementioned reliabilities are normalized so that their sum is equal to 1, that is to say: $$\mathit{pxt}\left(\mathit{ij}\right)=\frac{\mathit{Pxt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pxt}\left(\mathit{kl}\right)}},$$

   

   $$\mathit{pyt}\left(\mathit{ij}\right)=\frac{\mathit{Pyt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pyt}\left(\mathit{kl}\right)}};$$

   

   - the estimate of the position of the tag (xt, yt) is: $$\begin{array}{ll}\mathit{xt}& ={\displaystyle {\sum }_{\mathit{ij}}\mathit{pxt}\left(\mathit{ij}\right)\mathit{xt}\left(\mathit{ij}\right),}\\ \mathit{yt}& ={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathit{yt}\left(\mathit{ij}\right);}\end{array}$$

   

   - the estimate of the error on the position of the tag (xt, yt) is then respectively calculated in x and y by: $$\mathit{ext}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pxt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{xt}\left(\mathit{ij}\right)},$$

   

   $$\mathit{eyt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right)};$$

   

   and in that, during the establishment of the XY frame of reference, the first anchor (10) and the second anchor (20) are arbitrarily assigned to the respective coordinates (0, 0), and (d, 0), d being the distance measured between the two anchors, the third anchor (30) is located based on the two aforementioned anchors (10, 20) by using the intersection of two circles based on the respective distances of the third anchor (30) relative to the two aforementioned anchors (10, 20), one of the two possible intersections being chosen as position of the third anchor (30), the selected position being determined arbitrarily, the following anchors (40, ...) are located based on the first three anchors (10, 20, 30) by using a trilateration algorithm, the third anchor (30) being chosen among all of the remaining anchors of unknown position, such that the sum of the errors ext + eyt is lowest for this anchor, the position of the following anchors then being determined by selecting the anchor each time such that the sum of the errors ext + eyt is lowest for this anchor.
2. The method according to claim 1, characterized in that the border (2, 50) of the red area (9) is determined:

   - either by using a location of the reference markers (3) in the XY frame of reference displayed on a touch-sensitive screen associated with the central marker (4) and by drawing said border (2, 50) on the touch-sensitive screen in the form of the aforementioned polygon;

   - or by using an apparatus called tracer (5) that communicates with the central marker (4) and the reference markers (3), the central marker (4) periodically querying the tracer (5) when it is moved in the area and asking it for the respective distances separating it from the reference markers (3), which allows the central marker (4) to determine the successive positions of the tracer in the XY frame of reference and to create the border (2, 50) by joining these positions by line segments in order to create the aforementioned polygon;

   - or by geometric location starting from positions of a plurality of reference markers (3) in the XY frame of reference and by applying an homothetic transformation to define a border (2, 50) that encompasses the polygon made by the reference markers.
3. The method according to claim 1, characterized in that the border of the orange area (8) is determined based on the border (2) of the red area (9) by creating an inner polygon through homothetic transformation, the distance corresponding to the pullback being between 50 cm and 1 m.
4. The method according to claim 1, characterized in that the filtering of the closed border (2) of the potentially dangerous area, whereof the apices of the polygon are denoted (x0, y0), (x1, y1), etc., is done, according to the following steps:

   - selecting a point (xi, yi), i= 0, 1, 2...;

   - selecting all of the points (xj, yj), j = 1... Nj, j different from i, which are inside a circle of given diameter 2d, centered on (xi, yi);

   - determining a point of the filtered border fi (xfi, yfi) by obtaining an average of the positions of said points (xj, yj);

   - marking the Nj point (xj, yj) as no longer being able to serve as starting point;

   - among the remaining unmarked points, looking for a new point (xi, yi) as being the closest to (xfi, yfi);

   - with the new point (xi, yi), starting again in the second step, and so forth.
5. A system for protecting persons individually or collectively (1) located in a potentially dangerous area, comprising at least the following devices:

   - a plurality of reference markers or anchors (3) including a central marker (4), distributed in said area, said anchors (3, 4) communicating by two-way communication with one another, and being capable of measuring the distance that separates them from one another with a precision at least equal to a predetermined value;

   - an automated unit for establishing a two-dimensional or XY frame of reference configured in order, based on the distances measured between the anchors (3, 4), to first assign a position in the XY frame of reference, to three anchors (10, 20, 30), such that the position of the third anchor (30) is determined arbitrarily based on positions of the first anchor (10) and the second anchor (20), as well as the respective distances between the third anchor (30) and the first anchor (10) and the second anchor (20), and to next locate the other anchors (40, ...) in this XY frame of reference through a trilateration method;

   - at least one mobile transceiver, called tag or beacon (6), worn by a person (1) and capable of communicating by two-way communication at least with the central marker (4) and with other tags (6), said tag (6) being provided with danger-warning means that can be actuated by the central marker (4);

   - a unit (5) for drawing a polygon making up a closed border (2) of the potentially dangerous area based on the position of the anchors (3) once located in the aforementioned XY frame of reference, said border (2) being intended to define at least one area in which the presence of a person (1) causes the central marker (4) to actuate the danger-warning means associated with the tag (6);

   - an automated unit for positioning the tags in the XY frame of reference and relative to the closed border (2), configured to position each tag (6) relative to at least one pair of anchors (i, j; i, j = 1, 2, ...), which gives two possible positions T1, T2 (61, 62) for the tag (6), the selected position being determined owing to a vote based on the use of the other anchors k (k different from i, j), a score being assigned to each possible position T1, T2 (61, 62), by calculating the difference between the tag-anchor k distance, or dk, and each of the distances between the anchor k and the possible positions T1, T2 (61, 62), the smallest difference causing the incrementation of the score for the corresponding possible position T1, T2 (61, 62), the ultimate highest score giving the selected position among the two possible positions T1, T2 (61, 62); said aforementioned automated unit being also configured to determine whether the tag (6) is located inside, respectively outside, the polygon making up the closed border (2) by drawing a horizontal straight line passing through the tag and by verifying the number of times this line intersects the border (2) on the right-hand side of the tag (6), the tag (6) being located inside the border if the number of intersections is odd, the tag (6) being located outside the border if the number of intersections is even,

   characterized in that the automated unit for positioning the tags in the XY frame of reference and relative to the closed border (2) is configured to estimate the position and the position error of a tag (xt, yt)(ij) relative to a plurality of pairs of anchors i, j (i, j = 1, 2, ...) according to the following steps:

   - a heuristic based on distance-measuring statistics between tag and anchors i and j, respectively denoted di and dj, is used so as to estimate an error Δdi and an error Δdj;

   - the calculation of the position of the tag is carried out four times, by disrupting the measurements on di and dj as follows: $$\mathit{di}\to \mathit{di}\pm \mathrm{\Delta }\mathit{di},$$

   

   $$\mathit{dj}\to \mathit{dj}\pm \mathrm{\Delta }\mathit{dj};$$

   

   - 4 disrupted positions (xt+Δx(k), yt+Δy(k))(ij) are obtained with k varying from 0 to 3;

   - the position errors on xt(ij) and yt(ij) are calculated as follows: $$\mathrm{\Delta }\mathit{xt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{\Delta }x\left(k\right)\right)}^2}},$$

   

   $$\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right)=\sqrt{{\displaystyle {\sum }_{k=0}^3{\left(\mathrm{\Delta }y\left(k\right)\right)}^2}};$$

   

   - a weighting law is applied as follows to obtain reliabilities: $$\mathit{Pxt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{\Delta }\mathit{xt}{\left(\mathit{ij}\right)}^2},$$

   

   $$\mathit{Pyt}\left(\mathit{ij}\right)=\frac{1}{\mathrm{\Delta }\mathit{yt}{\left(\mathit{ij}\right)}^2};$$

   

   - the aforementioned reliabilities are normalized so that their sum is equal to 1, that is to say: $$\mathit{pxt}\left(\mathit{ij}\right)=\frac{\mathit{Pxt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pxt}\left(\mathit{kl}\right)}},$$

   

   $$\mathit{pyt}\left(\mathit{ij}\right)=\frac{\mathit{Pyt}\left(\mathit{ij}\right)}{{\displaystyle {\sum }_{\mathit{kl}}\mathit{Pyt}\left(\mathit{kl}\right)}};$$

   

   - the estimate of the position of the tag (xt, yt) is: $$\begin{array}{ll}\mathit{xt}& ={\displaystyle {\sum }_{\mathit{ij}}\mathit{pxt}\left(\mathit{ij}\right)\mathit{xt}\left(\mathit{ij}\right),}\\ \mathit{yt}& ={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathit{yt}\left(\mathit{ij}\right);}\end{array}$$

   

   - the estimate of the error on the position of the tag (xt, yt) is then respectively calculated in x and y by: $$\mathit{ext}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pxt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{xt}\left(\mathit{ij}\right)},$$

   

   $$\mathit{eyt}={\displaystyle {\sum }_{\mathit{ij}}\mathit{pyt}\left(\mathit{ij}\right)\mathrm{\Delta }\mathit{yt}\left(\mathit{ij}\right)};$$

   

   and said automated unit is also configured so that, during the establishment of the XY frame of reference, the first anchor (10) and the second anchor (20) are assigned to the respective coordinates (0, 0), arbitrarily, and (d, 0), d being the distance measured between the two anchors, the third anchor (30) being located based on the two aforementioned anchors (10, 20) by using the intersection of two circles based on the respective distances of the third anchor (30) relative to the two aforementioned anchors (10, 20), one of the two possible intersections being chosen as position of the third anchor (30), the selected position being arbitrarily determined, the following anchors (40, ...) being located based on the first three anchors (10, 20, 30) by using a trilateration algorithm, the third anchor (30) being chosen among all of the remaining anchors of unknown position, such that the sum of the errors ext + eyt is lowest for this anchor, the position of the following anchors being then determined by selecting the anchor each time such that the sum of the errors ext + eyt is lowest for this anchor.
6. The system according to claim 5, characterized in that the central marker (4) is placed in a case provided with a controller and input/output means comprising pushbuttons and a screen, preferably a touch-sensitive screen.
7. The system according to claim 5, characterized in that the reference markers (3) and the central marker (4) are equipped with UWB radio transmitters and/or ultrasonic transducers.
8. The system according to claim 5, characterized in that the warning means are light, audio and/or vibrating means.
9. The system for protecting individually or collectively persons (1) according to claim 5, the potentially dangerous area comprising three dimensions (3D):

   - the plurality of reference markers or anchors (3) including a central marker (4), distributed in said area, said anchors (3, 4) communicating with one another by two-way communication, and being able to measure the distance that separates them from one another with a precision at least equal to a predetermined value;

   - the automated establishing unit being suitable for setting a three-dimensional or XYZ frame of reference, configured in order, based on the distances measured between the anchors (3, 4), to first assign a position in the XYZ frame of reference, at least partially arbitrarily, to four anchors (10, 20, 30, 40) and next to locate the other anchors (40, ...) in this XY frame of reference through a trilateration method;

   - the automated unit for positioning the tags in the XYZ frame of reference, being configured to position each tag (6) relative to at least one triplet of anchors (i, j; k; i, j, k = 1, 2, ...), which gives two possible positions T1, T2 (61, 62) for the tag (6) by intersection of three spheres, the selected position being determined owing to a vote based on the use of the other anchors I (I different from i, j, k), a score being assigned to each possible position T1, T2 (61, 62), by calculating the difference between the tag-anchor distance I, or dl, and each of the distances between the anchor I and the possible positions T1, T2 (61, 62), the smallest difference causing the incrementation of the score for the corresponding possible position T1, T2 (61, 62), the ultimate highest score giving the selected position among the two possible positions T1, T2 (61, 62);

   - the unit (5) for drawing a border (2) of the potentially dangerous area being suitable for drawing the border based on the position of the anchors (3) once located in the aforementioned XYZ frame of reference, said border (2) being intended to define at least one area in which the presence of a person (1) causes the central marker (4) to actuate the danger-warning means associated with the tag (6).

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