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WO2019179882A1 - Réglage automatique d'un estimateur - Google Patents

Réglage automatique d'un estimateur Download PDF

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Publication number
WO2019179882A1
WO2019179882A1 PCT/EP2019/056497 EP2019056497W WO2019179882A1 WO 2019179882 A1 WO2019179882 A1 WO 2019179882A1 EP 2019056497 W EP2019056497 W EP 2019056497W WO 2019179882 A1 WO2019179882 A1 WO 2019179882A1
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tuning
estimator
error
physical properties
modelling
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Magdalena DROZDZ
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FNV IP BV
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FNV IP BV
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G05B13/045—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance using a perturbation signal
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

Definitions

  • the present invention relates to a method for calibrating one or more sensor arrangements by means of an automated tuning of an estimator for estimating calibration parameters for the one or more sensor arrangements.
  • the estimator is tuned based on different sets of error modelling coefficients in a parallel computing architecture.
  • the invention also relates to a computer system performing the method and a machine-readable medium.
  • Integrated navigation systems are widely used for positioning purposes within many different applications i.e. aircraft applications, onshore positioning and subsea positioning of Remotely Operated Vehicles (ROV).
  • ROV Remotely Operated Vehicles
  • data from multiple sensors are integrated with IMU by applying Kalman filtering.
  • This approach allows to combine advantages of different positioning techniques such as long-term absolute accuracy of Global Navigation Satellite System (GNSS) position and high short-term relative accuracy of inertial sensors. Because each sensor/technique has its limitations, the combined approach allows to mitigate them and provide a robust positioning solution.
  • GNSS Global Navigation Satellite System
  • INS inertial navigation systems
  • MEMS Microelectromechanical
  • integrating IMU sensors carries also challenges.
  • Each IMU sensor is influenced by errors that needs to be corrected by determining calibration parameters. These errors are usually modelled when designing the Kalman filter for data integration.
  • the mathematical function of modelling the errors is the same.
  • the parameters of the function are different for each type of IMU and application.
  • the real challenge is to select proper values of error modelling coefficients such that the mathematical function describes the real behavior of an error in an accurate way.
  • a priori estimates of statistical parameters within the Kalman filter need to be adjusted for individual system to achieve optimal performance. This process is referred to as Kalman filter tuning.
  • Kalman filters are usually manually tuned by a method referred to as serial tuning procedure.
  • the initial parameters are provided by a manufacturer or calculated using Allan Variance Analysis. Next, they are manually changed until the optimal performance of the filter is reached.
  • the optimum performance indicators can vary. Residuals between IMU based estimate and an aiding should be minimized. Modelled errors to be compensated in calibration parameters such as biases and scale factors should behave according to expected characteristics of a sensor provided by a manufacturer.
  • a common approach to tune Kalman filters is to introduce a condition such as position gaps in position aiding and minimize the free inertial drift during the gaps. Depending of the application, the condition indicating optimal tuning can vary - not all applications focus on trajectory or have position aiding.
  • a cost function is modelled based on a statistical analysis of at least a part of the IMU based estimates such that a yield of the cost function relates to an accuracy of the IMU based estimates.
  • the tuning process is a time consuming and tedious procedure. In practice, tuning is finished when the filter performance is "good enough", because it is not possible to check all possible combinations of parameters. Because of the rapid development of inertial sensors, there is a high demand in optimizing the filter for specific applications in relatively short amount of time.
  • the invented method is building on the patent document WO2015138024A2. Further, the graduation project: "Implementation of a protocol for acquisition and processing of strapdown gravity data from airborne inertial navigation system to compute geoid models in coastal areas" by Hamza Mazih, August 2017, ENSTA Bretagne, is an example of practical application of the invented method of parallelizing recursive problems.
  • WO2015138024A2 covers a concept of airborne gravimetry in combination with Lidar data for extraction of gravity anomalies. It states the need of navigation data, gravity data and Lidar data.
  • the navigation data are considered to be attitude and position, which allow to combine mentioned data to generate orthometric heights and gravity field information.
  • This method allows for the search for hydrocarbon or other commodity deposits, whereby gravimetry can be used to locate such deposits.
  • anomalies in the gravity field can be detected by carrying exploration flights during which the gravity field is estimated.
  • INS/GNSS integration There is no remark on INS/GNSS integration.
  • W002103398A1 covers procedure of airborne gravimetry with specific sensors as laser scanner, gravity gradiometer. It focuses on detailed procedure to combine different data to generate DTM. It mentions inertial data but considering attitude which is used to relate all data streams.
  • US631 1 129B1 describes the concept of integrated navigation using Kalman filter. It focuses on tightly coupled integration of raw GNSS observations. It mentions the aspect of filter tuning - it states that measurement residuals can be used to assess the quality of filter tuning. It does not expand on that and it does not describe how the tuning should be performed.
  • US2004133346A1 describes the concept of inertial navigation with different aiding sources using Kalman filter. It focuses on using attitude change measurements to estimate gyro biases better and at the end improve performance of Kalman filter. It does not mention tuning of adjusting Kalman filter parameters.
  • US2009308157A1 describes a method of constructing IMU. The are no relations to data integration.
  • US9772186B1 describes the concept of integrated navigation with INS sensor as a base and other data types used as an aiding sources. It describes a concept of software platform with GUI that houses algorithms for data integration. The concept focuses on building a hardware/software platform that enables efficient testing and validation of different types of IMU, as well as algorithms for data integration. The platform with GUI is used to verify the results of Kalman filter solution. There is no direct concept of tuning as "adjusting" the algorithm parameters to obtain better performance of the algorithm.
  • W00063646A1 describes an autonomous navigation system for an orbital platform incorporating a global positioning system based navigation device optimized for low- Earth orbit and medium-Earth orbit applications including a 12 channel, GPS tracking application-specific integrated circuit operating in concert with a microprocessor implementing an extended Kalman filter and orbit propagator which autonomously generates estimates of position, velocity, and time to enable planning, prediction and execution of event-based commanding of mission operations.
  • W00063646A1 is an example for another type of determining continuous real time earth-sun vector data from a GPS constellation by means of a Kalman filter. Parameters of such a Kalman filter could be potentially tuned by applying the method according to the present invention.
  • US9772186B1 describes a miniaturized inertial measurement and navigation sensor device and a flexible, simplified GUI operating in real time to create an optimum
  • the IMU/INS includes multiple angle rate sensors, accelerometers, and temperature sensors to provide stability device.
  • a navigation GUI tests algorithms prior to embedding them in real-time IMU hardware.
  • MATLAB code is converted to C++ code tailored for real-time operation. Any point in the algorithm suite structure can be brought out as a data channel to investigate the pattern of operation.
  • the data channels permit zooming in on the algorithm's operation for the open-loop angle, velocity and position drift measurements for bias-compensated channels.
  • the GUI can be used to verify results of an extended Kalman filter solution as well as the implementation of the real-time attitude and heading reference system. When the code has been verified, it is compiled and downloaded into a target processor.
  • US631 1 129B1 describes a positioning method and a system for measuring a position of a vehicle on land, air, and space, using measurements from a global positioning system receiver and an inertial measurement unit.
  • An integrated Kalman filter processes the all-available measurements of the global positioning system: pseudo- range, delta range, carrier phase, and the solution of an inertial navigation system.
  • the integrated Kalman filter is a multi-mode, robust Kalman filter, in which optimal integrated mode is selected based on the measurement availability and filter stability.
  • the high accurate solution of the inertial navigation system which is corrected by the Kalman filter, is used to aid on-the-fly resolution of the carrier phase integer ambiguity of global positioning system in order to incorporate the carrier phase measurements into the Kalman filter, and to aid the carrier phase and code tracking loops of the receiver of the global positioning system to improve the receiver jamming and high dynamic resistance.
  • US20040133346A1 describes a navigation system including a Kalman filter to compensate for bias errors in inertial sensing elements.
  • An observed pitch, roll or heading change is input to the Kalman filter either from an aiding source or when the navigation system is in a known condition.
  • the Kalman filter generates a correction signal that is provided to the navigation computation system.
  • US20090308157A1 describes an inertial measurement system having a triangular cupola shaped base structure with three mutually orthogonal sides and a bottom surface surrounding a hollow core.
  • the bottom surface includes an aperture providing access to the hollow core.
  • An inertial module is mounted on each of the sides and includes a gyroscopic rotational rate sensor and a linear accelerometer connected to a circuit board.
  • the inertial measurement system also includes a motherboard and a plurality of metallization elements. The metallization elements extend from the bottom surface to the sides of the base structure and conductively connect the inertial module to the motherboard.
  • the inertial measurement system may also include a
  • accelerometer and gyroscope biases and scale factor should behave according to sensor characteristics.
  • An estimator is configured to process a time series of measurements containing errors like statistical noise and determines estimates of unknown variables by considering feedback from an aiding source.
  • Widely known estimators are for example Kalman filters. Consequently, the optimizing of the tuning process as discussed in the background section is not only an issue when applying a Kalman filter, but for all kinds of estimators.
  • An estimator may be applied to any kind of time series analysis, for example in signal processing, robotics, trajectory optimization, and econometrics, in applications where the current state of a system needs to be estimated.
  • the present invention is based on the idea that an estimator and a cost function are executed in multiple instances using different error modelling coefficients, preferably in a parallel computing architecture like a cloud framework.
  • the execution of the estimator and the cost function over the multiple instances in parallel is referred to as "tuning run”.
  • tuning run As each cost function outputs its corresponding yield, the performance of a plurality of different settings for modelling the error can be monitored.
  • further tuning runs with further different settings for modelling the error might be required to identify the settings corresponding to the cost function that provides an optimum yield.
  • the entire process is referred to as “auto-tuning” or “automated tuning”.
  • the present invention allows a system requiring tuning of an estimator to be:
  • the auto-tuning procedure is implemented using parallel computing architecture. This allows to significantly reduce tuning time (from one month of manual tuning to a few days of auto-tuning) preserving the significant amount of candidates for tuning parameters.
  • auto- tuning allows to increase the amount by efficient processing. Thanks to that the risk of missing a parameter combination or estimating a local minimum is limited.
  • the auto-tuning procedure concerns a full tuning cycle comprising of one or more tuning runs, starting from a preparation of a data set requiring time series analysis, defining the system for a specific application, and finishing at the final settings for modelling the error of the system.
  • an automated tuning procedure of an estimator for estimating calibration parameters for one or more sensor arrangements As a result of the automated tuning, the one or more sensor arrangements are calibrated.
  • a data set to be processed by the estimator is provided.
  • the data set comprises (i) a first time series of first measurement data obtained from the one or more sensor arrangements to measure first physical properties and (ii) a second time series of second measurement data obtained from a reference sensor arrangement to measure second physical properties.
  • the first time series and the second time series share a common time interval.
  • At least a part of the first physical properties are time derivates of the second physical properties to establish a fusion of interrelated sensors in a combined system that allows minimizing of errors through a calculated redundancy of information.
  • the estimator is modelled.
  • dynamics equations are modelled that link the first physical properties and their corresponding first measurement data with the second physical properties and their corresponding second measurement data.
  • error dynamics equations are modelled by perturbing the dynamics equations.
  • Time-dependent errors incurred by the one or more sensor arrangements are modelled with the calibration parameters depending on error modelling coefficients.
  • the estimator is modelled.
  • the estimator is configured to estimate the calibration parameters and the values of the second physical properties over the common time interval by processing the first time series of first measurement data and the second time series of second measurement data in a processing loop.
  • the processing loop of the estimator is initialized with an input value set of error modelling coefficients on which the calibration parameters depend.
  • one or more cost functions are modelled based on a statistical analysis of at least a part of the estimated values of the second physical properties over the common time interval such that a yield of a cost function relates to an accuracy of the estimated values of the second physical properties.
  • Different value sets of the error modelling coefficients are generated and used to initialize the estimator for performing a tuning run.
  • the one or more cost functions for each of the processed sets of error modelling coefficients are calculated to provide a
  • the output of the tuning run is a list of yields associated with a value set of the error modelling coefficients that caused the yield. Further tuning runs are performed with further different value sets of the error modelling coefficients until a value set of error modelling coefficients is identified having an associated yield in a determined optimum range.
  • multiple instances of the estimator are executed in a parallel computing architecture, each of the multiple instances with a different value set of the error modelling coefficients. After having processed an instance of the estimator, corresponding one or more cost functions are calculated in the parallel computing architecture. It is determining whether one of the multiple instances of the cost function already provides a yield in a determined optimum range. If not, the step of executing multiple instances of the estimator based on a new plurality of different input value sets of the error modelling coefficients is performed again until one or more of the calculated cost functions provides the optimum yield.
  • At least a part of the error modelling coefficients defined in a plurality of different input value sets is within a limited value range or is a value from a limited list.
  • At least a part of the error modelling coefficients defined in a plurality of different input value sets is constant.
  • determining the new plurality of different input value sets for a new iteration in the tuning process comprises a selecting of a subset of input value sets from the different input value sets where the corresponding cost functions are within a particular yield.
  • the values of the error modelling parameters of this subset are used to identify smaller boundaries for one or more error modelling parameters in another tuning run, thereby further limiting the value range of at least one of the error modelling coefficients.
  • the estimator may be configured to produce estimates of unknown variables by estimating a joint probability distribution over the variables for each timeframe of the time series.
  • the estimator is a Kalman filter.
  • a first type of one or more cost functions is modelled based on a statistical analysis of a comparison of at least a part of the estimated values of the second physical properties and at least a part of reference values of the second physical properties over the common time interval determined from the second time series of second measurement data.
  • a first type of cost functions is a position based cost function using a position calculated by the estimator and a reference position provided by a reference measurement system like as GNSS.
  • the yield of the cost function is based on the differences between position values over the entire trajectory.
  • a first type of cost functions calculates free inertial drift during the gaps in aiding data.
  • gaps in aiding data are introduced during each run of the estimator (the same gaps - location, length) for each run of the estimator.
  • the differences between the reference position and those estimated by the estimator are computed only during the gaps as the drift during the gaps is clearly observable.
  • Free inertial drift is present when there is no aiding data.
  • the mean value of all differences during the gaps is computed to express the mean drift. The smaller the mean drift the better are the parameters.
  • a first type of cost functions is a gravity based cost function.
  • Reference gravity is provided from gravimetric measurements or a very accurate local geoid model. Furthermore, it can be known over some area as gridded values or along lines or at specific points only. Once the reference gravity data is known, the estimated gravity data and the reference gravity data are compared. The measure of the yield of the gravity based cost function would be a mean of differences. How to compute the differences (perform the statistical analysis) is related to available reference data and the data set used for the estimation. In general, the statistics needs to include interpolation such that compared gravity values relate to exactly the same location. The statistic can be computed for absolute gravity values or gravity anomalies so that appropriate reductions on geoid need to be applied first.
  • a first type of cost functions is a rotation based cost function.
  • the measurement system comprising the one or more sensor arrangements is mounted in a setting which is able to measure in a very accurate way changes of rotation angles so that the changes of rotation angles between the measurement system and the setting can be compared.
  • a setting could be a turn table.
  • the differences between the reference values delivered from turn table servomotors or attitude changes estimated from camera observations by applying computer vision (or any other technique) and the estimated values extracted from the estimator can be calculated.
  • the mean value of the differences can express a yield of this cost function.
  • a second type of one or more cost functions is modelled based on a condition that must be fulfilled for at least a part of the estimated values of the second physical properties according to the laws of physics.
  • the condition is used to define a measure which indicates when the second type of cost function provides the best yield.
  • the statistical analysis is used to extract and compute the measure.
  • the condition can directly act on the estimated physical properties. If the condition is indirect, the estimated physical properties are used as input for another measuring technique.
  • the cost function acts on the outcome of the fusion of estimated physical properties and the other measuring technique.
  • a second type of cost functions is a gravity based cost function where reference gravity is not known. However, the condition is used that gravity is the same at the same location.
  • a data set is available where a specific location is covered multiple times over the common time interval, multiple values of gravity are available for an analyzed location. The differences between the values can be computed (in statistics: standard deviation) to express the
  • the resemblance is the measure expressing the yield of cost function.
  • the condition can be applied at specific points (e.g. line crossings) or along a part of a trajectory (covered multiple times). In that case more points are available so the final measure is the mean of the standard deviation at many points (e.g. along a line).
  • a line (called a repeat line) is used and multiple points with reasonable for gravity analysis spacing are generated to calculate the average resemblance.
  • the resemblance can be calculated for absolute gravity or gravity anomaly; if calculated for gravity anomaly, appropriate reductions need to be applied.
  • a second type of cost functions is a position based cost function where a reference position is not known.
  • the measurement system comprising the one or more sensor arrangements is mounted and moved in a such a way that the position follows the same path (e.g. a circle).
  • the position follows the same path (e.g. a circle).
  • the resemblance of the estimated position with the assumed trajectory could be calculated and act as measure of a yield of this cost function.
  • the examples from above refer to cost functions which act directly on the estimated physical properties.
  • the cost functions act indirectly on the estimated physical properties:
  • the measurement system comprising one or more sensor arrangements is coupled with another technique - the estimator provides georeferencing for another measurement technique, e.g. coupling of inertial navigation system for georeferencing a camera or a scanner.
  • the point clouds e.g. from a camera or a scanner, are combined between each other along the trajectory using position from IMU/GNSS position trajectory.
  • the cost function can act on the point cloud directly i.e. if a specific feature is scanned multiple times within the whole trajectory (and respectively one tuning run), the location and orientation and shape of the feature detected from the point cloud should be the same.
  • the measure of the cost function yield is the resemblance of location and orientation and shape of the feature extracted from the georeferenced point cloud.
  • the one or more cost functions comprise a plurality of cost functions.
  • the calibration parameters associated with that input value set of the error modelling coefficients are retrieved that provide an optimum yield over the entire plurality of cost functions.
  • multiple cost functions are combined to a combination of cost functions defining measures that either express the yield of each of the multiple cost function separately or express a combined yield of the combination of cost functions.
  • the plurality of cost functions comprise at least one cost function of the first type and at least one cost function of the second type.
  • the one or more sensor arrangements comprises IMU sensors.
  • the IMU sensors may comprise three accelerometers and three gyroscopes.
  • the one or more sensor arrangements comprises further sensors to integrate IMU data like position and velocity with other types of data like depth, acoustic ranges, and speeds.
  • the IMU sensors may be extended by additional sets of accelerometers and gyroscopes besides three accelerometers and gyroscopes comprising the base measurement sensors of IMU.
  • the sensor related errors can be divided into three main groups:
  • Bias it concerns initial bias which can be usually removed during calibration; bias instability which cannot be removed before integration and needs to be modeled; and bias noise that leads to effect described as Rate Random Walk (RRW) but this effect may be very small and can be neglectable for the majority of applications.
  • RRW Rate Random Walk
  • Scale factor it is a scaling effect of the raw readings which directly influences raw sensor readings together with bias error according to formula:
  • Noise it is mainly related to electrical noise. If integrated, it causes errors which are described, in case of sensors like accelerometers and gyroscopes, as Velocity Random Walk or Angle Random Walk. This effect cannot be removed prior to integration, it needs to be modeled with error modelling coefficients.
  • Initial bias may be removed by an initial sensor calibration. Biases and scale factors are modelled as calibration parameters within an estimator like a Kalman filter.
  • IMU sensors it should be noted that prior to raw sensor data integration gravity needs to be removed from accelerometer readings as well. As gravity can be only approximated by mathematical model, the remaining gravity bias may also be modelled as Gauss- Markov process.
  • the parallel computing architecture is provided by a cloud service, for example Azure Cloud.
  • Azure Cloud provides a service of renting machines for computation purposes. Usage of computers (number of them and processor speed) is determined automatically. It also supports users with a framework which simplifies implementing desired actions. It provides build in elements such as functions, tables and requests. Functions are triggered by requests which are used to navigate through big amount of data. Results or parameters can be provided or stored within tables which are easily to import/export. Azure fully supports the .NET
  • more than one cost function is calculated to validate a set of error modelling coefficients during each run. Selection of the best set of error modelling coefficients is done by minimizing the yield of the involved cost functions.
  • the inventive method utilizes a parallel computing architecture for recursive
  • the auto-tuning process can be divided into the following steps:
  • each tuning run performed with a plurality of different value sets of the error modelling coefficients until a yield of the cost function is in an optimum range.
  • the results of the final tuning run are validated using a different dataset.
  • a first tuning run is performed with relatively wide parameter boundaries for selected error modelling coefficients while keeping the remaining error modelling coefficients constant.
  • a second tuning run is performed with wide parameter boundaries for all error modelling coefficients.
  • a fine tuning run is performed with small parameter boundaries for all error modelling coefficients.
  • a fine tuning is performed with small parameter boundaries for selected error modelling coefficients while keeping the remaining error modelling coefficients constant or with wide parameter boundaries.
  • the processing platform is a software platform implemented in parallel computing architecture.
  • the platform consists of set of methods allowing to execute steps of the auto-tuning procedure in efficient manner.
  • a machine-readable medium having suitable program instructions to realize the inventive method, for example, on a general-purpose computer or in a programmable integrated circuit.
  • the machine-readable medium may be any kind of physical or non- physical data carrier like, for example, a computer disk, computer tape, CD, DVD, Bluray, a semiconductor memory, or a signal transmitted over a computer network.
  • Fig. 1 shows a sample auto-tuning process for calibrating IMU sensors by means of a Kalman filter according to an embodiment of the present invention
  • Fig. 2 shows free inertial drift versus different combinations of tuning parameters representing the yield of a cost function of an auto-tuning process for calibrating IMU sensors according to an embodiment of the present invention
  • FIG. 3 shows processing results with initial parameters before performing an auto- tuning process according to an embodiment of the present invention
  • Fig. 4 shows processing results with optimal parameters after having performed an auto-tuning process according to an embodiment of the present invention
  • Fig. 5 shows an example application of a Kalman filter for calibrating IMU sensors and a GPS aiding.
  • the invention is using measured sets of data and a set of constraints or parameters in order to optimize a model based on said constraints by means determining the yield of cost functions. Said optimizations, while recursive in nature, can be executed in parallel.
  • a method is described in detail in which one or more IMU sensors are integrated with GNSS position within a Kalman filter and parameters of the Kalman filter are calibrated.
  • the following method steps are performed as shown in Fig. 1 in order to use the present method for optimizing INS based navigation system for gravimetric applications such as locating of hydrocarbon deposits, mineral deposits or ore deposits and determining of geoid models:
  • Kalman filter parameters comprising the error modelling coefficients.
  • Kalman filter parameters are strictly related to the type of IMU. For each type of IMU a manufacturer usually provides a specification which can be used to define rough set of initial parameters. 3.
  • First auto-tuning run - wide parameter boundaries for selected error modelling coefficients. During the first tuning run, a selected set of error modelling coefficients from the initial parameters is tuned.
  • Second auto-tuning run wide parameter boundaries for all error modelling coefficients.
  • the second tuning run aims to examine all error modelling coefficients. At this stage, their boundaries are well defined by outcome of the first tuning run.
  • the last tuning run is the actual fine tuning. After the optimal local minimum is selected by the second tuning run, all error modelling coefficients are tuned within a small boundary and with a small step.
  • the set of Kalman filter parameters consists of around 20 different parameters comprising the error modelling coefficients. For each parameter, a specific value needs to be selected. The tuning aims to find a specific combination of parameter values such that the performance of Kalman filter is maximized. Each auto-tuning run provides the set of the best parameter combinations as an outcome.
  • the measure of Kalman filter performance is mathematically expressed by cost functions. Minimizing a cost function allows to find a combination of parameters providing the best performance of Kalman filter.
  • the type of cost function is related to the type of application.
  • the commonly used cost function is based on the concept of minimizing free inertial drift.
  • the GNSS position is selected as a reference position, thereby determining a reference trajectory.
  • the reference trajectory is used to compute the free inertial drift.
  • couple of position gaps of different length are introduced to compute the average free inertial drift.
  • the method uses a repeat line (a line that a vehicle follows a few times within one data set) - the gravity profile along a repeat line should be the same at different moments of time.
  • the gravity profiles resulting from a few passages along the repeat line are compared.
  • standard deviation is computed.
  • the standard deviation is minimized - the better tuned Kalman filter the smaller spread among gravity profiles.
  • SD standard deviation
  • the gravity profile is linked with position "profile” using time stamps - gravity vs. 3D position datum is created. Using this datum gravity values for every discrete point are interpolated. As this procedure is repeated for all repeat line passages, there are a few gravity values (the amount of gravity values is equal to number of passages along a repeat line) for each discrete point.
  • Gravity SD profile is generated along the average repeat line by computing SD of gravity values for each discrete point. There are couple of statistical measures computed from the gravity SD profile, the mean value is the most important one as represents the final consistency of gravity for a specific set of parameters and it is used as indicator of the best set of parameters.
  • the auto-tuning method uses a combination of two types of cost functions to find the best set of parameters. For each cost function set of best combinations of parameters is selected. Parameters common for both cost function specific sets are selected as the final tuning parameters.
  • Initial parameters may be defined based on sensor specifications. Additionally, Allan Variance analysis may be performed. But these methods allow to initialize only a couple of parameters (spectral densities of attitude, velocity and biases). Scale factors are initialized with a value the same as corresponding bias. Time constants are set to 1000 seconds. The initial boundaries for each parameter are defined based on experience. In the first tuning run they are wide e.g. attitude spectral density changes by step of two in power within 10 4 to 10 15 . To simplify the process, not much attention is paid to exact numbers or the size of boundaries. Usually a few manual runs are done to define edges of boundaries - after crossing the edges the filter does not coverage or coverages very poorly.
  • a selected set of parameters is tuned. Scale factors are usually fixed with one value. Time constants are represented by three widely speed values (500, 1000, 2000 seconds). This run aims to find the potential areas of local minimum. Spectral densities of velocity, attitude, accelerometer and gyroscope biases are examined because these parameters have the strongest influence on the filter performance.
  • the second tuning run aims to examine all parameters. At this stage, their boundaries are well defined by outcome of the first tuning run. The values of spectral densities usually differs by 2-3 orders of magnitude. For time constants, the step is usually around 500 seconds.
  • the last tuning run is the actual fine tuning. After the optimal local minimum is selected by the second tuning run, all parameters are tuned within a small boundary and with a small step.
  • the complete tuning procedure is an extensive task. To make the process efficient all tuning steps are performed with Azure environment. The processing is scaled such that multiple runs with different set of parameters can be processed at the same time. Processing 160,000 combinations of parameters using 1 5h data set would take one year for one processor (PC). When using Azure set up it can be done within four days.
  • the process is also automated to limit the user work load.
  • the data set is uploaded to the Azure server, and parameters boundaries typed in, set of three functions needs to be triggered to start the process.
  • Majority of tuning time is the processing time by the Azure framework when user interaction is not needed.
  • the processing results are organized within a table; then they can be easily sorted to select the best set of parameters.
  • the described auto-tuning procedure was used to tune multiple different IMU sensors with a success. As an example, a gravimetric application was selected when high grade IMU was coupled with GNSS position to provide gravity anomaly estimation for geodetic application such as: geoid or orthometric height estimation without need of gravimeter sensor.
  • Figure 5 presents the concept of data integration.
  • FIG. 2 shows the result of tuning done with a high grade IMU.
  • the tuning was performed using a data set where IMU and GNSS position were integrated, and with a few GNSS gaps introduced.
  • the selected data was processed 160,000 times, each time with different a priori Kalman filter parameters. For each set of parameters, the averaged drift per minute was computed.
  • Figure 2 is the graphical representation of correlation between free inertial drift and different a priori parameters of the Kalman filter. Free inertial drift (average, in meters per one minute) are shown versus different combinations of tuning parameters (each combination has its own specific number - file number). The chart shows that there are three local minima. Further analysis could reveal which minimum is the best by analyzing the behavior of biases and residuals.
  • Figures 3 and 4 present the quality of the tuning before and after tuning. It is visible that before tuning position was rejected at many turns, additionally the free inertial drift was in order of a few meters. After tuning the position residuals stay within a few centimeters and the maximum free inertial drift is around 2m.
  • the presented auto-tuning method aims to define a straightforward and efficient tuning procedure.
  • the process can be speeded up by incorporating into Cloud services such as Azure, AWS, Google.
  • the tuning time is limited to one week (for one specific IMU type). That is significantly shorter considering that manual tuning can last even one or two months.
  • many combinations of parameters are examined.
  • the selection of the optimal set of parameters is based on minimizing of a couple of cost functions.
  • the implemented framework is flexible - incorporation of a new cost function or introducing different filters is straightforward.
  • the set of cost functions can be extended by a cost function specific for an application such as gravity repeatability cost function for gravimetric applications. This approach enables to achieve more robust result with comparison to using one cost function.
  • the auto-tuning is finalized when the best possible performance of an IMU is reached. Thanks to that the process of selecting an optimal IMU for a particular application can be more efficient. Multiple types of IMU can be evaluated at the same time. Moreover the selection of the most suitable IMU can be based not only on sensor specification but also on the final performance under real conditions.
  • the method according to the present invention shall be understood to be suitable for any system allowing to estimate physical properties that vary with time.
  • Such system has to be observable i.e. the input data allow to calculate the physical properties by applying the mathematical relations containing the links between the input data and physical properties where the mathematical relations are captured within a system model.
  • the three components: input data, system model and physical parameters are the key components of a majority of applications. As the applications are created to answer variety of questions in a best possible and reliable way, the optimization of one of the three components are involved. With the growing demand of solving problems within a very complex system the optimization can be challenging. With increasing complexity the risk of converging to a local but not appropriate minimum is higher. Moreover the complexity makes the capturing of the optimization problem in a mathematical way simply not feasible.
  • An automated tuning does not require defining an optimization method. It requires only providing the three key components of every application and indicating the one which needs to optimized by providing multiple candidates of the component.
  • the optimization is performed in a parallel computing architecture where each instance of a tuning run is executed with a different candidate.
  • the method assumes defining of a cost function and a measure corresponding to the cost function that expresses the yield of the cost function.
  • the candidates providing the best yield of the cost faction are the optimal candidates for the system.
  • each of the three components of the system can be optimized: the input data, the system model, and the physical properties.
  • the system model links the sensors data and the detection outcome; the set of parameters within the system needs to be tuned to provide the reliable detection of oil, gas, minerals.
  • the input data are sensor data; the system model contains relations between sensor data and calculated physical properties (e.g. gravity); the set of parameters related to sensor errors needs to be tuned to optimize gravity estimation.
  • LiDAR surveys an optimization of survey conditions which influence the survey outcome (i.e. wind perturbations cause vibration and influence quality of data); the physical properties are the expected quality of measured parameters; the system model describes links between conditions and measured parameters; the coefficients related to varying conditions are altered in order to provide the best quality of measured parameters.
  • measurements collected in a specific pattern e.g. measurements following parallel lines with a specific spacing
  • a model i.e. a set of mathematical equations or a grid model
  • the parameters related to varying patterns of trajectories are alternated to provide the optimum model outcome.
  • the measuring sensor set needs to be aligned/prepared for a survey in order to provide the optimum measurements.
  • the relations between multiple sensors needs to get constrained and defined.
  • the parameters describing the varying aligning scenarios are varied in order to provide the best alignment.
  • Subsea navigation (ROV, AUV) containing multiple sensors; how long and in which pattern move to secure a good quality of the outcome from the whole survey.
  • parameters related to weights of different data sets dependent on data availability, quality etc. can be altered in order to provide the optimum model.
  • GNSS measurements PPP, RTK
  • corrections need to be estimated (tropospheric, ionospheric etc.) to secure high accuracy measurements.
  • the corrections are estimated based on many observations from reference stations. Parameters related to quality, availability of a station and geometrical relations of stations can be varied to provide the best quality of coefficients.
  • the measurement network layout In preparation of measurement campaigns where e.g. the locations beacons, the measurement network layout, type of used sensors/technologies needs to predefined to secure a required accuracy.
  • LBL beacons In subsea navigation (ROV, AUV), different layouts of networks (e.g. of LBL beacons) can be alternated to provide the optimum accuracy of LBL measurements.
  • parameters related to usage of different sensors can be varied to achieve a required accuracy with minimum cost.
  • parameters reflecting the influence of environment temperature, salinity, pressure, currents etc
  • Monitoring of vibration, movements of buildings, dams, civil engineering structures vary parameters relating to different configuration of measuring sensors in order to successfully monitor a specific feature (e.g. detect vibrations of a pillar, possible cracks).
  • Indoor navigation vary parameters describing configuration of many beacons (WiFi, radio-navigation) and their configuration to optimize the accuracy of navigation within the whole area of an indoor structures (e.g. shopping malls, storage
  • Varying parameters describing operating condition of accelerometers, inclinometers, gravimeters to achieve desired accuracy in a specific range e.g. 2g, 10g.
  • Varying parameters describing operating conditions for interferometers for distance measurements Calibration of strain sensors as used in CPT (cone penetration testing) or SPT (standard penetration testing) and the like. e) Traffic control and optimization of trajectories:
  • Air security and reliability in systems utilizing different techniques (ILS, GNSS, LAAS) for plane trajectory estimation; vary parameters referring to these techniques to obtain accurate and secure trajectory determination.
  • ILS in systems utilizing different techniques
  • GNSS GNSS
  • LAAS LAAS
  • Air traffic control vary parameters describing different configurations of lanes, potential trajectories, amount of planes etc. to optimize the aircraft traffic.
  • Sea traffic control vary parameters referring to layout, depth, type of water ways to optimize sea traffic in ports or TSS (traffic separation scheme).
  • Roads (highways, motorways etc.) traffic control vary parameters related to conditions of the road (number of lanes opened, condition of the road), number and type of cars to optimize the vehicle flow.
  • the amount and type of necessary auxiliary power stations may be optimized based on availability of natural resources, such as wind or sunshine to a certain power consumption load.
  • System optimization e.g. related to drilling, applying pressure, product flow optimization in refineries.
  • laser scanning optimization of laser system parameters (density of points, intensity, angle of view) with respect to scanned structures in order to provide the reliable point cloud interpretation; e.g. optimizing airborne LiDAR system parameters to detect ground points in presence of thick greenery, optimizing land laser systems to detect different building surfaces.
  • laser system parameters density of points, intensity, angle of view

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Abstract

La présente invention porte sur un procédé d'étalonnage d'un ou plusieurs agencements de capteurs à l'aide d'un réglage automatique d'un estimateur de façon à estimer des paramètres d'étalonnage desdits agencements de capteurs. L'estimateur est réglé sur la base de différents ensembles de coefficients de modélisation d'erreur dans une architecture informatique parallèle. L'invention porte également sur un système informatique mettant en œuvre le procédé et un support lisible par machine.
PCT/EP2019/056497 2018-03-23 2019-03-14 Réglage automatique d'un estimateur Ceased WO2019179882A1 (fr)

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CN113848721A (zh) * 2021-10-09 2021-12-28 九江学院 基于高增益观测器滑模控制的冷原子重力仪主动隔振方法
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EP4060614A1 (fr) * 2021-03-19 2022-09-21 Aptiv Technologies Limited Procédé de détermination des statistiques de bruit des capteurs d'objets

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CN112749470A (zh) * 2019-10-31 2021-05-04 北京华航无线电测量研究所 一种结构形变传感器布局优化拟合方法
US11268813B2 (en) * 2020-01-13 2022-03-08 Honeywell International Inc. Integrated inertial gravitational anomaly navigation system
EP4060614A1 (fr) * 2021-03-19 2022-09-21 Aptiv Technologies Limited Procédé de détermination des statistiques de bruit des capteurs d'objets
CN113848721A (zh) * 2021-10-09 2021-12-28 九江学院 基于高增益观测器滑模控制的冷原子重力仪主动隔振方法

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