RU2716495C1 - Method and system for multi-purpose tracking in two-position radar systems - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to radar ranging and can be used in development of advanced multi-position radar systems and their modernization. Essence of the method consists in that for each incoming measurement from all air objects from any information position indirect measurements are made on the leading (first) position, based on which for each trajectory tracked to perform certain conditions for the received coordinates of the aerial object (entry into the gate of identification) for the path for which these conditions are met, the forecast is corrected, wherein the prediction (extrapolation) itself is carried out according to corresponding rules. Multipurpose tracking system for two-position radar system is intended for method implementation and is implemented in certain way.

EFFECT: technical result is higher reliability and accuracy of identification of aerial objects in multi-purpose tracking mode for two-position radar systems.

2 cl, 9 dwg, 2 tbl

Description

The invention relates to radar and can be used in the development of promising multi-position radar systems and their modernization. Technical result achieved: increasing the reliability, accuracy and stability of multi-purpose tracking.

One of the directions ensuring the improvement of all systemic indicators of aviation information management systems (IMS) [1] - efficiency, survivability, dynamism and informational content - is the use of the multi-position principle of their construction, within which coordinated sustainable formation of the necessary data from spatially separated sources is carried out [1].

However, the use of this principle, giving certain advantages, also requires significant complications of the IMS, caused, first of all, by the emergence of another higher managerial level designed to control the spatial position of positions within the trajectory control of observation [2] and control information flows of information extraction and sharing it between positions.

The influence of these complications is enhanced by the construction of aviation multi-position radar systems (MP radar) [3]. Especially these complications are manifested when the multi-purpose tracking mode is used in the MP radar, since in the process of its implementation it is necessary to identify the incoming signals not only by the tracked air objects, but also by position.

It should be emphasized that in solving the problems of identification of measurements in the MP radar it is necessary to take into account the following features:

каждая позиция измеряет координаты воздушных объектов в своей, как правило, полярной системе координат, начало которой связано с центром массы носителя [4, 5];

each position measures the coordinates of airborne objects in its, as a rule, polar coordinate system, the beginning of which is associated with the center of mass of the carrier [4, 5];

время прихода сигналов, отраженных от одного воздушного объекта, на различные позиции в общем случае разное;

the time of arrival of signals reflected from one airborne object at different positions is generally different;

точность измерения одних и тех же координат на различных позициях может существенно различаться;

the accuracy of measuring the same coordinates at different positions can vary significantly;

законы изменения координат одних и тех же воздушных объектов для различных позиций могут отличаться друг от друга;

the laws of changing the coordinates of the same airborne objects for different positions may differ from each other;

пространственное и взаимное расположение позиций изменяются во времени;

spatial and relative position of positions change over time;

для управления пространственным положением позиций информация о местоположении воздушных объектов должна формироваться непрерывно.

To control the spatial position of positions, information about the location of air objects should be formed continuously.

The first feature predetermines the need to bring all measurements formed at each position to a single coordinate system with a common origin.

Other features predetermine the need to use analog-discrete filtering algorithms [6, 7].

After the identification procedure is completed, the remaining stages of multi-purpose tracking (MSC) can be performed on the basis of algorithms for tracking single airborne targets in the MP radar, taking into account the increasing number of measurements coming from other positions. In this regard, further in the framework of the general procedure of the MDC, the main attention will be paid to the consideration of identification algorithms.

In the general case, the problem of identifying measurements in MDCs, in which the general forecast is corrected by residuals formed from measurements of all positions, can be solved in the MP radar in various ways using different coordinate systems and different decision criteria [5] with different types of information exchange (active passive and semi-active).

As a prototype, a method of multi-purpose tracking in single-position pulse-Doppler radars with identification of measurements in identification gates and α, β-filtering [3], which operates as follows, was taken.

, скорости сближения

и бортового пеленга

.The radar forms measurements of the distance D to the airborne object, the approach speed V _c with it and the directional bearings in the horizontal ϕ plane. The on-board computer system extrapolates them, forms identification gates and identifies the measurement results of the next review cycle in them, forming range estimates

approach speeds

and airborne bearing

.

At the time intervals between the arrivals of measurements, the previously traced paths are extrapolated based on the hypothesis of a change in the state coordinates (hereinafter referred to as x _i ∈ [D, V _c , ϕ]) with constant speed [3]. The current extrapolated value of the pth coordinate of the state x _{e, pi is} sent to information consumers for implementing trajectory control and to missiles as target designation commands.

Simultaneously with the extrapolation for each escorted air object and measured state coordinates, identification gates Δx _{i are formed} , which, as a rule, are chosen constant [4].

If at the time moment of (k + 1) -th measurements z _i for some trajectory with number p ^* for extrapolated values of the coordinates of the state x _{e, p * i} (k + 1) the conditions are satisfied

where k∈ [1, ∞) is the time discrete number, then the obtained measurements are considered to correspond to this trajectory and are used for subsequent correction in α, β-filtering algorithms [4].

Correction of the forecast results of the identified trajectory by the obtained measurements is performed according to the α, β-filtering algorithms:

определяются путем экстраполяции по гипотезе движения с постоянной скоростью на момент прихода измерений; Т - интервал времени между приходом измерений; α_i, β_i - соответствующие постоянные коэффициенты усиления невязок измерений. После вычисления оценок (2), (3) начинается новый этап экстраполяции.Here

determined by extrapolation according to the hypothesis of movement with a constant speed at the time of arrival of measurements; T is the time interval between the arrival of measurements; α _i , β _i - the corresponding constant gain of the residuals of the measurements. After calculating estimates (2), (3), a new stage of extrapolation begins.

This method of MCC, being one of the most common, does not have the accuracy and stability of tracking air objects required for target designation. The low accuracy of coordinate estimation when using the considered method of the MSC is due to the following reasons: a large time of access to an air object when using antennas with mechanical scanning; using fairly simple state models for forecasting; low reliability of identification of airborne objects in wide identification gates and low accuracy of estimating using α, β-filtering algorithms.

The proposed MDC method for a two-position radar (DP radar) differs from the prototype primarily in the use of measurements from a second spatially separated position, and in the use of more advanced analog-discrete filtering algorithms, which improves the survivability, dynamism, and information content of the information system as a whole. When developing the regime of the MDC in the radar station it was assumed that:

1. Each radar has its own spatial coordinates x ₁ , y ₁ and the coordinates of another position

и бортовые пеленги в горизонтальной ϕ_ij плоскости. Здесь i=1, 2 - номер позиции, j - номер воздушного объекта.2. At each position, the active location mode is used and the ranges D _ij to the air object, the speed of their changes are measured

and side bearings in the horizontal ϕ _ij plane. Here i = 1, 2 is the position number, j is the number of the air object.

3. Measurements from the same airborne object are formed at positions at different points in time.

4. Between positions, measurements are exchanged in the process of tracking air objects.

5. The rectangular coordinate system associated with the center of mass of the radar carrier 1 is used as a common one.

6. For the current estimation of the coordinates of airborne objects, instead of an α, β-filter, an analog-discrete second-order filter is used [6], which allows for a linear process of the form

in the presence of measurements

form estimates by the rule

provided that Δt >> T _i , where T _i is the smallest interval of access to the airborne radar object of the i-th position; x _q1 (k), y _q1 (k) and x _q2 (k), y _q2 (k) are measurements formed from observations of the first and second positions, and Q ₁ and Q ₂ are signs of the arrival of measurements:

и

вычисляются по общему правилуgain coefficients K _xij and K _{yij of the} corresponding residuals

and

calculated as a general rule

- a priori D _{(x, y) i} (k, k-1) and a posteriori D _{(x, y) i} (k-1) matrices of filtering errors for the corresponding filters; Ф _{(x, y) i} is the transition matrix; H _{(x, y) j} - matrix of measurements of the corresponding coordinate for the j-th position; ξ _{(x, y) i} is the vector of Gaussian random perturbations with the dispersion matrix D _{(x, y) and} ; ξ _{(x, y) and} is the vector of Gaussian measurement errors, characterized by the dispersion matrix D _{(x, y) and} , E is the identity matrix; T is the transpose operation.

The geometric relationships of positions and air objects are shown in FIG. 1.

Based on the measurements obtained, the rectangular coordinates of the airborne object are calculated (* - unknown target number) from which the reflected signal is received, at the first position of radar station 1 (Fig. 1):

and in the second position (radar2):

When forming (12), (13), the side bearings ϕ _{i *} are considered positive for airborne objects located to the right of the longitudinal axis of the aircraft. If aerial objects are located on the left, then bearings are considered negative.

Based on representations (12), (13), indirect measurements are formed in radar1

where ξ _ii , ξ and _yi are the measurement noise determined by the errors of the primary radar measurements of the positions and the conversion rules (12), (13), which make it possible to calculate their variances D and _xij , D and _yij , which are used in (6).

If in the process of enumerating the generated measurements for all the results of the forecast (2) for the i-th air object, the conditions are met

then a decision is made on whether the studied measurements belong to it, after which they enter the filtering algorithm (6) of the coordinates of this air object to correct the extrapolated values. Here x _ic , y _ic are the results of measurements (14) or (15), and Δx _i and Δy _i are the size of the identification gates.

The dimensions of the gates built relative to the extrapolated coordinates O _ce1 , O _ce2 (Fig. 1) are determined by the relations [4]

и

- дисперсии производных x_i и y_i; D_иximax, D_иyimax - максимально возможные дисперсии ошибок измерений одной из позиций.in which T ₁ and T ₂ are the intervals between the radar station 1 and radar station 2 to the air object;

and

- variances of derivatives x _i and y _i ; D _andximax , D and _yimax - the maximum possible variances of measurement errors of one of the positions.

The structural diagram of a system that implements the proposed method of multi-purpose tracking is shown in FIG. 2.

The system is multi-channel, the number of identical channels is determined by the number p of tracked air objects. In general, the system includes:

• first information item 1 (IP1), consisting of:

• on-board navigation system 2, forming measurements of the own position of the first information position 1;

• radar system 3 (RLS1), which forms the measurement of ranges and airborne bearings of airborne objects relative to the first information position 1;

• a complex of communication equipment 4, receiving measurements of ranges and airborne bearings of airborne objects and own coordinates from the second information position 5;

• second information item 5 (IP2), consisting of:

• on-board navigation system 6, forming measurements of the own position of the second information position 5;

• radar system 7 (RLS2), which forms the measurements of ranges and airborne bearings of airborne objects relative to the second information position 5;

• a complex of communication facilities 8, transmitting measurements of ranges and airborne bearings of airborne objects and own coordinates to the first information position 1;

• a unit for recalculating measurements from IP1 9, converting measurements from radar 3 of the first information position 1 to Cartesian coordinates (12) and generating signs of the arrival of measurements (8) from radar1;

• a unit for recalculating measurements from IP2 10, converting measurements from radar 7 of the second information position 5 into Cartesian coordinates (13) of the first information position 1 and generating signs of the arrival of measurements (8) from radar2;

• logical adder 11, forming a continuous sequence of measurements (14), (15) and signs of the arrival of measurements;

• p channels for tracking air objects 12-1, ..., 12-p, each of which consists of:

• residual formation block 13-1, ..., 13-p

• a key 14-1, ..., 14-p, transmitting the calculated residuals to the tracking channel of the airborne object for further forecast correction;

по правилу (6);• forecast correction block 15-1, ... 15-p, forming estimates

by rule (6);

• the extrapolation block 16-1, ..., 16-p, which forms the forecast x _e1 , ..., x _er , _e1 , ..., _er according to rule (5);

до прихода новых измерений от воздушного объекта;• delay devices estimates 17-1, ..., 17-p, delay estimates

before the arrival of new measurements from an air object;

• a block for calculating a priori variances 18-1, ..., 18-p, performing calculations according to rule (10);

• a block for calculating the gain of residuals 19-1, ..., 19-p, performing calculations according to rule (9);

• a unit for calculating posterior dispersions 20-1, ..., 20-r, which performs calculations according to rule (11);

• devices for delaying dispersions 21-1, ..., 21-p, delaying posterior dispersions until new measurements come from an air object;

• block calculation gates 22-1, ..., 22-p, according to the rules (17) determining the size of the gates to identify incoming measurements;

• a threshold device 23-1, ..., 23-r, comparing the resulting discrepancies with the size of the gates according to the rules (16);

• search devices 24, which sequentially searches by the serial number for that air object for which the conditions are satisfied first (16).

Navigation system 2 is connected to conversion units 9 and 10; Radar 3 is connected to the conversion unit 9; the complex of communication equipment 4 is connected to the conversion unit 10; a navigation system 6 is connected to a complex of communications 8; Radar 7 is connected to a complex of communications 8; the complex of communications 8 is connected to the complex of communications 4; the conversion unit 9 is connected to the logical adder 11; the conversion unit 10 is connected to the logical adder 11; the logical adder 11 is connected to blocks of residual formation 13-1, ..., 13-p and blocks of calculation of a priori dispersions 18-1, ..., 18-p; residual formation blocks 13-1, ..., 13-p are connected to the keys 14-1, ..., 14-p and threshold devices 23-1, ..., 23-p; the keys 14-1, ..., 14-p are connected to the forecast correction blocks 15-1, ..., 15-p; forecast correction blocks 15-1, ..., 15-p are connected to extrapolation blocks 16-1, ..., 16-p; extrapolation units 16-1, ..., 16-p are connected to delay devices 17-1, ..., 17-p and end users; delay devices 17-1, ..., 17-p are connected to blocks of residual formation 13-1, ..., 13-p and forecast correction blocks 15-1, ..., 15-p; blocks for calculating a priori dispersions 18-1, ..., 18-p are connected to blocks for calculating the gain of residuals 19-1, ..., 19-p; blocks for calculating the gain of residuals 19-1, ..., 19-p are connected to blocks for calculating posterior dispersions 20-1, ..., 20-p; blocks for calculating posterior dispersions are connected to delay devices 21-1, ..., 21-p and blocks for calculating gates 22-1, ..., 22-p; delay devices 21-1, ..., 21-p are connected to the blocks for calculating a priori dispersions 18-1, ..., 18-p; blocks for calculating gates 22-1, ..., 22-p are connected to threshold devices 23-1, ..., 23-p; threshold devices are connected to a busting device 24; busting device 24 is connected to the keys 14-1, ..., 14-p.

The functioning of the system in dynamics includes the following steps.

ϕ_г1j, ϕ_в1j по формулам (12), (14) пересчитываются в декартовы координаты воздушного объекта х_ц1, у_ц1 в блоке пересчета измерений 9 и вместе с сформированным признаком прихода измерений (8) от РЛС1 передаются на логический сумматор 11. Если измерение пришло на вторую информационную позицию ИП2 (блок 5), то полученные от ее РЛС (блок 7) измерения координат воздушного объекта Д_2j,

ϕ_г2j, ϕ_в2j и полученные от бортовой навигационной системы (блок 6) собственные координаты передаются на комплекс средств связи 8 и далее на комплекс средств связи 4 первой информационной позиции (блок 1). Полученные измерение и собственные координаты второй информационной позиции передаются на блок пересчета измерений 10, где вместе с собственными координатами первой информационной позиции (блок 1), полученными от бортовой навигационной системы 2, пересчитываются по формулам (13), (15) в декартовы координаты воздушного объекта х_иц2, у_иц2 и передаются на логический сумматор 11 вместе с сформированным признаком прихода измерений (8). Сформированная на логическом сумматоре 11 единая последовательность измерений х_иц*, у_иц* вместе с признаками прихода измерений Q_1,2 на блоки формирования невязок 13-1, …, 13-p каждого канала сопровождения воздушных объектов 12-1, …, 12-p и блоки расчета априорных дисперсий 18-1, …, 18-p. В блоках 18-1, …, 18-p по формуле (10) рассчитываются значения D_(x,y)i(k,k-1) априорных дисперсий, по которым в блоках 19-1, …, 19-р по формула (9) рассчитываются коэффициенты усиления невязок K_(x,y)ij. Полученные коэффициенты K_(x,y)ij передаются в блоки коррекции прогнозов 12-1, …, 12-p и в блоки 20-1, …, 20-р, где по формуле (11) рассчитываются апостериорные дисперсии D_(x,y)i(k). Рассчитанные апостериорные дисперсии D_(x,y)i(k) передаются на устройства задержки 21-1, …, 21-р и блоки расчета стробов 22-1, …, 22-р. Задержанные на блоках 21-1, …, 21-p апостериорные дисперсии D_(x,y)i(k-1) передаются в блоки 18-1, …, 18-p для расчета априорных дисперсий в следующий момент времени. Поступившие на блоки 22-1, …, 22-р значения D_(x,y)i(k) используются для расчета стробов по формулам (17). Рассчитанные стробы Δx_i и Δy_i передаются на пороговые устройства 23-1, …, 23-р. Полученные в блоках 13-1, …, 13-p невязки передаются на ключи 14-1, …, 14-p и пороговые устройства 23-1, …, 23-р. В пороговых устройствах 23-1, …, 23-р выполняется проверка условия (16), результаты передаются с каждого канала в устройство перебора 24. В устройстве перебора 24 производится последовательная проверка результатов выполнения условия (16) и при нахождении канала с наименьшим номером (*), для которого данное условие выполняется, на ключ 14-* соответствующего канала передается сигнал замыкания. При замыкании ключа 14-* находящееся на нем значение невязки передается на блок коррекции невязок 15-*, где по формуле (6) производится коррекция текущего прогноза и получаются оценки

,

. Результаты коррекции (для контура слежения 12-*) или оригинальный прогноз (для остальных контуров, а также в случае, если измерений не было) передаются на блоки экстраполяции 16-1, …, 16-p, где они используются для расчета по формулам (7) прогнозов на следующий момент времени x_эj(k+1), y_эj(k+1), передаваемых конечным пользователям и на устройство задержки 17-1, …, 17-р. Задержанные значения прогнозов x_эj(k), y_эj(k) передаются на блоки 13-1, …, 13-p для расчета невязок измерений и на блоки 15-1, …, 15-p для коррекции и экстраполяции в последующие моменты времени.If the measurement came to the first informational position IP1 (block 1), then received from its radar (block 3) measurements of the coordinates of the airborne object D _1j ,

ϕ _g1j , ϕ _b1j according to formulas (12), (14) are converted to the Cartesian coordinates of the air object x _c1 , at _c1 in the measurement conversion unit 9 and, together with the generated sign of arrival of measurements (8), are transmitted from radar 1 to the logical adder 11. If the measurement came to the second information position IP2 (block 5), then received from its radar (block 7) measurements of the coordinates of the airborne object D _2j ,

ϕ _g2j , ϕ _b2j and received from the on-board navigation system (block 6) own coordinates are transmitted to the complex of communications 8 and then to the complex of communications 4 of the first information position (block 1). The obtained measurement and the own coordinates of the second information position are transferred to the measurement conversion unit 10, where, together with the own coordinates of the first information position (block 1), received from the on-board navigation system 2, are converted according to formulas (13), (15) into the Cartesian coordinates of the airborne object x _IC2 , _IC2 and transmitted to the logical adder 11 together with the generated sign of the arrival of measurements (8). Formed on a logical adder 11, a single measurement sequence x _{y *} , y _{* *} along with signs of the arrival of measurements Q _1.2 to the blocks of formation of residuals 13-1, ..., 13-p of each channel tracking aircraft objects 12-1, ..., 12- p and the blocks for calculating a priori variances 18-1, ..., 18-p. In blocks 18-1, ..., 18-p, according to formula (10), the values D _{(x, y) i} (k, k-1) of a priori variances are calculated, according to which in blocks 19-1, ..., 19-p, according to the formula (9) the residual gain gains K _{(x, y) ij are} calculated. The obtained coefficients K _{(x, y) ij} are transmitted to forecast correction blocks 12-1, ..., 12-p and to blocks 20-1, ..., 20-p, where a posteriori variances D _{(x, y are} calculated by formula (11) _{) i} (k). The calculated posterior variances D _{(x, y) i} (k) are transmitted to delay devices 21-1, ..., 21-p and gate calculation blocks 22-1, ..., 22-p. The posterior dispersions D _{(x, y) i} (k-1) detained on blocks 21-1, ..., 21-p are transferred to blocks 18-1, ..., 18-p for calculating a priori dispersions at the next moment in time. The values of D _{(x, y) i} (k) received at blocks 22-1, ..., 22-p are used to calculate the gates according to formulas (17). The calculated gates Δx _i and Δy _i are transmitted to the threshold devices 23-1, ..., 23-p. The residuals obtained in blocks 13-1, ..., 13-p are transmitted to the keys 14-1, ..., 14-p and threshold devices 23-1, ..., 23-p. In threshold devices 23-1, ..., 23-p, condition (16) is checked, the results are transmitted from each channel to the search device 24. In the search device 24, the results of condition (16) are checked sequentially and when the channel with the lowest number is found ( *), for which this condition is fulfilled, a closure signal is transmitted to the key 14- * of the corresponding channel. When the key 14- * is closed, the residual value located on it is transmitted to the residual correction block 15- *, where according to formula (6), the current forecast is corrected and estimates are obtained

,

. Correction results (for the tracking loop 12- *) or the original forecast (for the remaining loops, as well as if there were no measurements) are transmitted to the extrapolation units 16-1, ..., 16-p, where they are used for calculation using formulas ( 7) forecasts for the next time x _ej (k + 1), y _ej (k + 1) transmitted to end users and to the delay device 17-1, ..., 17-p. The _delayed forecast values x _ej (k), y _ej (k) are transmitted to blocks 13-1, ..., 13-p for calculating the measurement discrepancies and to blocks 15-1, ..., 15-p for correction and extrapolation at subsequent times .

For the proposed multi-purpose tracking system, an efficiency assessment was carried out based on the results of simulation modeling:

полета двух носителей РЛС и двух воздушных объектов по пересекающимся траекториям в горизонтальной плоскости;

the flight of two radar carriers and two air objects along intersecting paths in the horizontal plane;

измерений координат; их отождествления с траекториями и алгоритмов фильтрации.

coordinate measurements; their identification with trajectories and filtering algorithms.

The study evaluated:

возможность осуществления МЦС в МП РЛС со стробовой идентификацией и поле условий применения для эффективного функционирования системы;

the possibility of implementing the MSC in the MP radar with strobe identification and the field of application conditions for the effective functioning of the system;

влияние второй позиции на показатели эффективности МП РЛС при МЦС;

the influence of the second position on the performance indicators of MP radar at the MDC;

зависимость показателей эффективности от соотношения периодов и времени обращения РЛС-позиций к воздушному объекту.

the dependence of performance indicators on the ratio of periods and time of the radar position to the air object.

Moreover, to assess the health of the investigated variant of the MDC, a combination of qualitative and quantitative indicators was used. Qualitative indicators were characterized by the type of trajectories of air objects, the shape of the areas of uncertainty, and quantitative - by the errors of estimates of the position of air objects in a rectangular coordinate system.

The initial coordinates, speeds and courses of positions and airborne objects are shown in table 1, and the dispersion of radar meters 1 and 2 in table 2.

In FIG. 3 shows the trajectories of air objects relative to the first position, and in FIG. 4 - received standard deviation of filtering errors. The bar plots in FIG. Figure 3 shows the boundaries of the identification gate for the trajectory corresponding to the air object 1, and the dashed lines for the air object 2. As can be seen from the illustration, as the distance to the air objects increases, the size of the gate increases significantly (more than two orders of magnitude in area), which leads to a decrease in the reliability of identification , accuracy of tracking and resolution deterioration.

In the general case, the errors of the MCC are determined both by identification errors leading to entanglement of the trajectories or failure of tracking, and directly by errors in the estimation of filtering algorithms (6).

Points A, B, C, D in FIG. 3, a zone of uncertainty is noted in which the identification gates for the trajectories of air objects 1 and 2 coincide, which under certain conditions can lead to a breakdown in tracking or confusion of the trajectories of a part of air objects (Fig. 5).

In FIG. 4, a period of time from 500 to 580 s corresponds to the penetration of airborne objects into this zone (Fig. 1). As can be seen from FIG. 3 and 4, after air object 2 fell into the zone of uncertainty, some of the measurements coming from it were assigned to air object 1, which led to an increase in filtering errors not only of air object 2 due to the long period of absence of extrapolation corrections, but also of air object 1 Also from FIG. 6 shows that the reliability and accuracy of the filtering also depends on the angle of the air object.

It should be noted that the size of the ABCD zone depends on the mutual geometry of the location of both the air objects themselves and the radar positions. The smallest size of the zone of uncertainty is for orthogonal paths, while the worst options are for closely spaced parallel paths, which are typical for the flight of aircraft in formation.

In FIG. 5, situations of disruption of tracking of an airborne object 2 and an increase in errors of escorting of airborne object 1 at the moment of intersecting the trajectories due to the assignment to it of measurements coming from airborne object 2 are clearly visible.

In order to clarify the effect of radar station 2 on the performance of the MDC, two types of studies were generally conducted. The first included a qualitative assessment by comparing accuracy indicators in one- and two-position versions. The study showed that the on-off option has the best indicators of accuracy and stability of tracking. However, quantitative indicators largely depend on the geometry of the relative positions and trajectories of airborne objects (Fig. 6).

In addition, it is worth noting that in the case of a multi-position radar, the loss of measurements from airborne objects in connection with its presence in the areas of tail shading or Doppler rejection is almost impossible.

The second type of research was devoted to the analysis of the influence of radar accuracy indicators 2 on the accuracy indices of the system as a whole. A variant of the mutual arrangement of positions and air objects, reducing the influence of the geometry of the relative positions of air objects and positions, is shown in FIG. 7.

The study showed that in the General case, the influence of the rangefinder (Fig. 8) channel on the accuracy of the MSC system as a whole is significantly less than the influence of the goniometric (Fig. 9) channel.

The obtained simulation results confirm the possibility of using this variant of multi-purpose tracking for on-off systems. When escorting easily identifiable remote air objects (without crossing the identification gates), use allows the MP radar at the MCC to increase the stability and accuracy of tracking. For individual priority airborne objects, it is possible to improve tracking indicators when using trajectory control of information positions.

An important advantage of the resulting system is the absence of restrictions on the possibility of its implementation, which allows it to be implemented on existing radar systems.

Literature

1. Verba V.S. Aviation complexes of radar patrol and guidance. The principles of construction, development problems and features of functioning. - M .: Radio engineering. - 2014 .-- 526 s.

2. Merkulov V.I. Improving the system performance of an airborne radar station due to the trajectory control of observation // Journal of Radio Electronics, 2012, No. 1 http://jre.cpire.ru/jre/jan/12/index.html.

3. Chernyak B.C. Multiposition radar - M .: Radio and communications. 1998.

4. Merkulov V.I., Drogalin V.V., Kanaschenkov A.I. et al. Aviation systems of radio control. T. 2. Radio-electronic homing systems. / Ed. A.I. Kanaschenkova and V.I. Merkulova. - M.: Radio Engineering, 2003 .-- 390 p.

5. Yarlykov M.S., Bogachev A.S., Merkulov V.I., Drogalin V.V. Radio-electronic systems for navigation, aiming and weapon control. T. 2. The use of aircraft electronic systems in solving combat and navigation tasks. / Ed. M.S. Yarlykova. - M .: Radio engineering, 2012 .-- 254 p.

6. Merkulov V.I., Sadovsky P.A. Non-simultaneous measurement filtering algorithms for a two-position radar // Radio engineering. - 2014. - No. 7. - S. 28-32.

7. Merkulov V.I., Verba V.S., Ilchuk A.R. Automatic tracking of air objects in the radar of integrated aircraft systems. T. 1. Theoretical foundations. Radar as part of an integrated complex / Ed. V.S. Pussy-willow - M.: Radio Engineering, 2018 .-- 360 p.

8. Merkulov V.I. Linear estimation algorithm with current forecast correction for non-simultaneous incoming measurements. // Information-measuring and control systems. - 2009. - No. 8.

Claims (43)

1. A multi-purpose tracking method for a two-position radar system, in which for each incoming measurement from all air objects from any information position indirect measurements are formed at the leading position, which is the first information position,

where k∈ [1, ∞) is the time discrete number, on the basis of which, for each tracked trajectory, the conditions for the obtained coordinates of the air object are checked

and for the trajectory for which the conditions are satisfied, the forecast is adjusted

while extrapolation is carried out according to the rules

where x _its1 (k), y _its1 (k) and x _its2 (k), y _its2 (k) - measurement, formed from the observations of the first and second positions, Q ₁ and Q ₂ - signs measurements arrival, ξ _ih1, ξ _ih2 , ξ _иу1 , ξ _иу2 - measurement noise, determined by the errors of the primary radar measurements of positions and conversion rules, x _ei , _ei - extrapolated values of the coordinates of the air object, which are the forecast,

- an estimate of the coordinates of the airborne object and their derivatives, x its _* , for its _* - measurement results, Δх _i , Δy _i - the size of the identification gates, determined by the formulas

in which T ₁ and T ₂ are the intervals between the radar systems of the first and second information positions, respectively, to the airborne object, D _x1 , D _x2 and D _y1 , D _y2 are the variances of the derivatives x _i and for _i , D their _max , D and _{y max} are the maximum possible variance of measurement errors at one of the positions, and K _x11 , K _x12 , K _x21 , K _x22 , K _y11 , K _y12 , K _y21 , K _y22 are the gain of residuals calculated by the formulas

in which D _{(x, y) i} (k, k-1) and D _{(x, y) i} (k-1) are the a priori and posterior filtering error matrices for the corresponding filters, H _{(x, y) j} is the measurement matrix corresponding coordinate for the jth position, ξ _{(x, y) i} is the vector of Gaussian random perturbations with the dispersion matrix D _{(x, y) and} , ξ _{(x, y) and} is the vector of Gaussian measurement errors, characterized by the dispersion matrix D _{(x , y) and} , E is the identity matrix, T is the transpose operation. 2. Multipurpose tracking system for a two-position radar system, consisting of the following parts: • first information position (IP1), consisting of: • on-board navigation system, • radar system (radar1), • a complex of communication facilities, • second information position (IP2), consisting of: • on-board navigation system, • radar system (radar2), • a complex of communication facilities,             • unit for recalculation of measurements from IP1, • unit for recalculation of measurements from IP2, • logical adder, • p channels for tracking airborne objects, each of which consists of: • residual formation block, • key • forecast correction block, • extrapolation unit, • evaluation delay devices, • a block for calculating a priori variances, • unit for calculating the residual gain, • a block for calculating posterior variances, • dispersion delay devices, • block calculation gates, • threshold device, • busting devices, which are connected as follows: IP1 navigation system is connected to measurement conversion units from IP1 and IP2, RLS1 is connected to measurement conversion unit from IP1, communication IP1 complex is connected to measurement conversion unit from IP2, IP2 navigation system is connected to IP2, radar2 communication system connected to a set of communication tools IP2, a set of communication tools IP2 connected to a complex of communication tools IP1, the unit for recalculating measurements from IP1 is connected to a logical adder, the unit for recalculating measurements for IP2 is connected to a logical sum Orom, the logical adder is connected to the residual formation blocks and the a priori dispersion calculation blocks, the residual generation blocks are connected to the keys and threshold devices, the keys are connected to the forecast correction blocks, the forecast correction blocks are connected to the extrapolation blocks, the extrapolation blocks are connected to the evaluation delay devices and end users , evaluation delay devices are connected to residual formation units and forecast correction blocks, a priori variance calculation blocks are connected to residual enhancement factors, residual gain calculation blocks are connected to a posteriori dispersion calculation blocks, posterior dispersion calculation blocks are connected to dispersion delay devices and strobe calculation blocks, dispersion delay devices are connected to a priori dispersion calculation blocks, strobe calculation blocks are connected to threshold devices, threshold devices connected to the search device, the search device is connected to the keys.

Images