Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
  • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
  • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
  • G01S19/393—Trajectory determination or predictive tracking, e.g. Kalman filtering

Definitions

• the present invention relates to the field of satellite positioning and more particularly concerns a geolocation method and device.
• GNSS Global Navigation Satellite Systems
• satellite positioning and navigation are important tools for security, including maritime security, ballistic guidance systems or vehicle and personnel tracking.
• various phases of flight, circulation of ships, en route, approach or landing are carried out by satellite positioning given that global satellite navigation systems have planetary coverage and do not require assistance with navigation.
• ground-based navigation enabling optimal route planning, improved air and ocean space, and reduced operational costs.
• Satellite positioning algorithms are now designed and evaluated using an important performance metric called integrity to prevent malfunctions and ensure reliability - a measure of trust placed in a system. This is achieved by issuing alerts when the use of the satellite positioning system is unsafe.
• satellites transmit signals that allow receivers to calculate their position. These signals are obtained by phase modulation of a carrier with coded messages and are available on several frequencies.
• the receiver for example present in a smartphone or an on-board location system in a vehicle, includes a low-cost chip which allows the reception of a single frequency and ensures positioning on code measurements only, without including an algorithm correction measurement.
• This positioning method makes it possible to obtain control accuracy of around five meters in open areas.
• a measurement correction algorithm for example based on a Kalman filter, it is possible to obtain a precision of the order of a meter.
• this precision is insufficient for certain applications that require centimeter precision such as, for example, autonomous and semi-autonomous vehicles, regardless of the environment (highway, urban, etc.) in which they operate.
• centimeter precision in geolocation proves complicated when the signal is disturbed, particularly in an urban environment with the presence of obstacles which can block or reflect the signals coming from the satellites.
• This precision already obtained in an open environment thanks to the use of a merging filter, can be obtained in urban areas by combining the measurements obtained using satellite signals with data from several sensors and with an appropriate choice of filter. associated with a dynamic model.
• multi-sensor systems are complex and expensive.
• the satellite positioning algorithm based on the extended Kalman filter is recognized as the most powerful and widely used tool for processing satellite signals to ensure reliable position estimation.
• the reason is that the Kalman filter is recursive in time and takes into account the contribution of all measurements optimally, processing only current measurements without the need to memorize all past data.
• the Kalman filter is the best linear estimator in the minimum mean square error (MMSE) sense provided that the process and measurement covariances are known exactly.
• MMSE minimum mean square error
• One of the aims of the invention is to propose a simple, effective and precise geolocation solution.
• Another aim of the invention is to propose an alternative filter solution adapted to geolocation.
• Another aim of the invention is to propose a technical solution making it possible to improve the precision of geolocation compared to a solution using a Kalman filter, particularly in the presence of obstacles which make the processing non-linear.
• Another aim of the invention is to propose a solution for early detection of the degradation in the quality of geolocation signals.
• the invention firstly relates to a method for measuring the geographical position of a device from a network of satellites in a forecasting (i.e. predictive) system with a variable gain filter, said gain being represented by a vector of variable gain coefficients, said method, implemented by the device, comprising, for an iteration at a time t+1, the steps of:
• the method according to the invention allows significant geolocation precision thanks to the use of a stable adaptive filter.
• the minimization of the expectation of the square of the innovation of the filter at time t+1 calculated from the gain parameters corresponds to the minimization of the mathematical expectation of the square of the distance between the observation at time t and its calculated prediction, which makes the calculations simple and therefore requiring less computing power than for a Kalman filter.
• the gain coefficient vector is a vector of parameters to be set at each step (control parameters) in the filter gain. Under a condition called ergodicity, the minimization of the mathematical expectation of the square of the innovation norm of the filter in the probability space is equivalent to the minimization of the temporal average of the square of the innovation norm of the filter.
• the original minimization problem can be replaced by time-averaged minimization, which is not the case in a Kalman filter.
• the method according to the invention does not require specification of input statistics of random variables (in particular, model error, observation error, etc.).
• the method according to the invention approaches the optimal regime as the filtering process progresses.
• averaging the gain over time allows smoothing which stabilizes the filter and therefore reduces the error.
• the Kalman filter is theoretically optimal only when the statistics of the measurement and model errors are known with exact precision and, moreover, the model is linear, which is rarely the case in practice.
• the method according to the invention is not constrained by this restriction, the use of AF thus allows very precise geolocation, particularly in the presence of obstacles around the device which cause knowledge of the error statistics to be lost and would make nonlinear Kalman filtering.
• the Kalman filter is only optimal for linear filtering problems.
• the extended Kalman filter (EKF) an extension of the KF for nonlinear systems, is not optimal. Due to the iterative temporal minimization of the mathematical expectation of the square of the innovation norm, the method according to the invention does not require linearization for non-linear systems, it maintains optimality of the non-linear filters.
• the method according to the invention learns model uncertainties and observation error statistics through filter innovation achievements and is capable of keeping estimation errors at a low level, synonymous with robustness.
• the filter used in the method according to the invention is stable, in particular because it is not constrained by the solution of the Riccati equations for the error covariance matrices as is the case with a Kalman filter.
• the method according to the invention constitutes a method that is both simple and effective for satellite positioning, under low conditions of knowledge of noise statistics.
• the method according to the invention allows in particular a more precise estimation in the context of satellite positioning, with a limited calculation load and storage requirement.
• a variant is to use, as an observation vector, no longer the speeds and positions, but the list of pseudoranges associated with each satellite visible to the receiver, that is to say, for each of these satellites, the speed of light in a vacuum multiplied by the delay between transmission and reception.
• the method further comprises, at each iteration, a step of bounding the variable gain coefficients between a minimum and a maximum in order to improve smoothing while being simpler than an obvious solution using a Hessian.
• the gain coefficients are limited between a minimum value equal to a limiting variable ⁇ (small and positive) and a maximum value equal to (2 - ⁇ ).
• the calculations, in particular on the gain coefficients are carried out by a neural network from a predetermined sample.
• the measurement module is configured to limit the variable gain coefficients between a minimum and a maximum.
• the measuring module is configured to limit between a minimum equal to a limiting variable ⁇ and a maximum equal to a limiting variable (2 - ⁇ ).
• the measurement module comprises a neural network configured to carry out the calculations while being optimized from a predetermined sample.
• the measurement module is configured to store and use a model, representative of the system, devoid of the “acceleration” parameter.
• the invention also relates to a device, in particular mobile, comprising a measuring module as presented previously.
• the invention also relates to a satellite geolocation system, said system comprising a plurality of satellites, configured to emit each geolocation signals, and at least one module as presented previously and/or at least one device as presented previously.
• System 1 comprises a constellation of satellites S1, S2, S3, S4 and a device 10 according to the invention.
• system 1 can include more than four satellites S1, S2, S3, S4, in particular dozens of satellites to be able to geolocate a device 10 in most regions of the globe, or even in all regions of the globe.
• Each satellite S1, S2, S3, S4 is configured to transmit geolocation signals S10, S20, S30, S40.
• the device 10 for example a smartphone or a vehicle, comprises a measurement module 100 configured to measure the position of said device 10 from the signals S10, S20, S30, S40 transmitted by the satellites S1, S2, S3, S4.
• the measurement module 100 embedded in the device 10, is configured to receive signals S10, S20, S30, S40 transmitted by a plurality of satellites S1, S2, S3, S4 of the set of satellites S1, S2, S3, S4.
• the measurement module 100 is configured to determine the position and/or speed of the device 10 at a time (t+1) from the signals S10, S20, S30, S40 received, called “observation at time (t+ 1)”.
• the position and/or speed can be measured directly or from other preliminary measurements, such as "pseudoranges", known per se.
• the measurement module 100 is configured to determine the position p(t+1) and/or the speed v(t+1) of the device 10 at time (t+1) using measurements and a predictive model based on a specific filter.
• the predictive model makes it possible to determine the state of the system through successive iterations.
• the measurement module 100 is configured to determine an estimate
• the gain K is parameterized by a vector of variable gain coefficients ⁇ 1, ⁇ 2, ..., ⁇ n.
• a possible gain structure, used in the present implementation, is given by the equations [Math 36] and following below.
• the measurement module 100 is configured to calculate the best prediction of the state of the system at time t+1, denoted
• the measurement module 100 is configured to calculate the prediction of the observation at time t+1, denoted
• H and ⁇ could be non-linear operators rather than matrices.
• the measurement module 100 is configured to calculate the prediction error of the filter, called “innovation”, noted
• the ⁇ model is a matrix which describes the transition of the state of the system from time t to time (t+1).
• the model ⁇ is used to calculate the position and/or the speed, preferably both the position and the speed, in the state vector x(t+1) but is devoid of acceleration parameter, this which increases the precision of predictions and therefore localization.
• the acceleration present in the model is calculated using the estimated speed. It is possible to add other parameters (associated or not with additional sensors). If the model is non-linear, this matrix is obtained by linearization. It can be calculated once in the first iteration and then kept for subsequent iterations.
• the measurement module 100 is configured to determine the estimate of the state of the system at time (t+1), denoted
• the measurement module 100 is configured to determine the position of the device 10 at time (t+1) from the estimate of the state of the system at time (t+1), denoted
• the state of the system x(t+1) is a column vector comprising the position coordinates of the device 10 at time (t+1) and the speed coordinates of the device 10 at time (t+1):
• the measurement module 100 is configured to determine the estimate of the position coordinates at time (t+1) by projecting the estimate of the state of the system
• ⁇ ⁇ . x(t) + A(t) + W(t), where the noise W(t) is the column vector (w(t), w'(t)), and where A(t) is a function which does not depends only on the acceleration.
• This matrix ⁇ is the model involved in the algorithm and is preferably defined only once before or during the first iteration.
• the measurement module 100 comprises at least one processor capable of implementing a set of instructions allowing these functions to be performed.
• the device receives the signals S10, S20, S30, S40 transmitted by the satellites S1, S2, S3, S4 then the measuring module 100 determines, in a step E2 the position and speed of the device at the instant (t+1) from the received signals, called “observation at instant (t+1)” denoted
• the measurement module 100 then calculates, in a step E3, the best prediction of the state of the system at the instant (t+1), denoted
• the measurement module 100 then calculates, in a step E4, the prediction
• step E3
• the device then calculates, in a step E6, the coefficients
• the measurement module 100 minimizes the expectation of the square of the innovation norm
• This equation can for example be solved numerically using the known method SPSA (Simultaneous Perturbation Stochastic Approximation), this known method requiring the calculation of the gradient of the squared norm of the innovation at time (t+1) to determine minimum.
• SPSA Simultaneous Perturbation Stochastic Approximation
• the measurement module 100 then calculates, in a step E7, the gain K( ⁇ (t+1)) at time t+1 preferably from the vector ⁇ calculated in step E6 according to the following formula:
• P 0 can be the initial covariance matrix used in a known manner in a Kalman filter of the prior art
• the device then calculates, in a step E8, the estimate of the state of the system at time (t+1), denoted
• the state of the system x(t+1) is a column vector comprising the position coordinates of the device 10 at time (t+1) and the speed coordinates of the device 10 at time (t+1):
• the estimate of the position coordinates at time (t+1) is obtained by projecting the estimate of the state of the system
• the calculations, in particular on the gain coefficients can be carried out by a neural network from a predetermined sample.
• the parameters of the cost function to be minimized are the weights W of the neural network which minimizes the difference between the learning data and the outputs of said neural network.
• ⁇ is the parameter matrix defined previously, chosen as previously to minimize innovation, and NN the neural network.
• the abscissa axis represents the number of iterations of the process.
• the y-axis represents the squared error (in meters), i.e. the square of the difference between the estimated trajectory and the reference trajectory.
• the abscissa axis represents a distance (in meters) in a first direction.
• the y axis represents a distance (in meters) in a second direction.
• the black line represents the real REAL trajectory followed by the mobile device 10 (set of real positions).
• the light line represents the positions measured in the absence of MEAS filtering.
• the intermediate gray line represents the positions measured with prior art Kalman filtering AA.
• the abscissa axis represents a distance (in meters) in a first direction.
• the y axis represents a distance (in meters) in a second direction.
• the black line represents the real REAL trajectory followed by the mobile device 10 (set of real positions).
• the light line represents the positions measured in the absence of MEAS filtering.
• the intermediate gray line represents the positions measured with filtering according to the INV invention.
• Figures 6 to 9 illustrate another comparison between a Kalman filter of the prior art and a method according to the invention for a trajectory of a vehicle type mobile. It can be seen that the absolute error along the three dimensional axes X, Y and Z is always on average lower with the method according to the invention compared to a solution based on a Kalman filter and that the average absolute error is approximately 50% lower on average with the method according to the invention compared to a solution based on a Kalman filter, which is particularly advantageous.

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• Engineering & Computer Science (AREA)
• Radar, Positioning & Navigation (AREA)
• Remote Sensing (AREA)
• Computer Networks & Wireless Communication (AREA)
• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Position Fixing By Use Of Radio Waves (AREA)

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• 2022
  • 2022-06-29 FR FR2206514A patent/FR3137450A1/fr not_active Ceased
• 2023
  • 2023-06-28 FR FR2306816A patent/FR3137460B1/fr active Active
  • 2023-06-28 WO PCT/EP2023/067730 patent/WO2024003187A1/fr not_active Ceased
  • 2023-06-28 EP EP23735330.5A patent/EP4548129A1/de active Pending

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