Method for determining at least one protection radius associated with at least one navigation parameter, and associated electronic determination device

Abstract

The present invention relates to a method for determining at least one protection radius associated with at least one navigation parameter of a wearer. The method comprises receiving (110) a measurement from a sensor, an error bound and an inertial measurement. The method further comprises, for each successive reception time, determining (130) an estimated state vector on the basis of the measurement from the sensor and the inertial measurement. The method further comprises computing (140) an estimate error propagation matrix and a bounded error influence matrix, and computing transfer matrices on the basis of the calculated matrices. The method further comprises determining (170) navigation parameters from the estimated state vector and the associated protection radius on the basis of the calculated transfer matrices.

Description

[0001]DESCRIPTION TITLE: Method for determining at least one protection radius associated with at least one navigation parameter, the method being implemented by an electronic determination device. The present invention relates to a method for determining a protection radius associated with at least one navigation parameter of a carrier, such as the position, speed, attitudes, and / or heading of the carrier. The present invention also relates to an electronic determination device configured to implement such a determination method. The present invention also relates to a computer program product capable of implementing such a determination method. The invention relates to the field of integrated localization of a carrier, for example a mobile carrier. The term "integrated localization" means an estimation of navigation parameter(s), such as the position, speed, attitudes,and / or the heading of a carrier and the provision of a protection radius associated with the navigation parameter(s) considered. Thus, it is guaranteed that an estimation error of the navigation parameter remains within the protection radius, according to a predefined probability. It is known to estimate navigation parameters such as the position, speed, attitudes and heading of the carrier by performing a hybridization from a GNSS (Global Navigation Satellite System) position estimated by a satellite positioning system and inertial measurements from an inertial measurement unit (IMU). When implementing such an estimation, errors are likely to disrupt the estimation of the navigation parameters of the carrier. These errors can be broken down into two types of error: on the one hand, modeled errors, called rare and normal,and on the other hand, unmodeled but bounded errors. The first type of error is generally modeled by a random variable that follows a continuous probability distribution. It is often assumed that the distribution of errors of the first type follows a normal distribution. By definition, the normal distribution is a probability distribution, often called Gaussian. In this case, it is clear that the values ​​of errors of the first type are not bounded. However, since the distribution of errors of the first type is known, it is possible to determine a bound that guarantees, for a predefined probability, that errors of the first type remain included in said bound. Errors of the first type are subsequently called "rare and normal errors". Physically,Rare and normal errors most often come from intrinsic characteristics of the sensors used and which have an impact on the estimation of the carrier's navigation parameters. Examples include the thermal noise of the GNSS receiver or the residual noise of inertial measurements. For rare and normal errors, it is already known to determine a respective protection radius of at least one carrier navigation parameter, such as position, speed, attitudes and / or heading. The second type of error concerns bounded but unmodeled errors. Errors of the second type are included in an interval, formed by two bounds, but for which the distribution model is unknown. Errors of the second type are called "bounded errors" in the rest of the description. Physically, bounded errors correspond, for example, to errors linked to the use of erroneous ephemerides for calculating the GNSS position,or a satellite clock failure in one of the satellites needed to calculate the GNSS position. It is not possible to know or predict the distribution or temporal evolution of errors of the second type. Only the error evolution interval is known with a probability that guarantees that the error remains between the limits of this interval with a confidence level characterized by this probability. Document US9341718B2, for example, attempted to provide a model of bounded errors. Similarly, in the article “Merging Kalman Filtering and Zonotopic - State Bounding for Robust Fault Detection under Noisy Environment” by C. Combastel, a mathematically more rigorous approach to modeling bounded errors was proposed. However, in the aforementioned documents, the determination of the protection radius is not optimal. Thus,an object of the invention is to improve the determination of the protection radius associated with a navigation parameter. To this end, the invention relates to a determination method intended to limit an error induced on at least one navigation parameter of a carrier, in particular a position, a speed, attitudes, and / or a heading of the carrier, the error being induced by a measurement error whose temporal evolution is unknown but whose limit is known and the probability of not exceeding this limit is also known; the limit and the probability being known for a plurality of times at which the method is implemented, the fact of limiting the induced error being obtained by the determination of at least one protection radius associated with the navigation parameter(s) of the carrier, the method being implemented by an electronic determination device and comprising the following steps: - reception, at successive reception times,of a measurement from a sensor, such as a GNSS receiver, in particular a GNSS position, of at least one error bound associated with the measurement from the sensor and inertial measurement(s): - for each successive reception instant: - determination of an estimated state vector of the carrier by applying to the measurement from the sensor and to the inertial measurement an estimation filter, the estimation filter comprising for each reception instant, a gain, an observation matrix and a propagation matrix of the state vector; - calculation of a propagation error matrix for estimating the state from the propagation matrix of the state vector, the gain of the estimation filter and the observation matrix, and calculation of an influence matrix of the bounded error from the propagation matrix of the state vector and the gain; - calculation of N transfer matrices, from the N-1 transfer matrices calculated at the instant preceding the reception instant,of the estimation error propagation matrix at said reception time and of the bounded error influence matrix at said reception time, N being the number of successive reception times; and - determination of the navigation parameter from the estimated state vector and determination of the protection radius associated with the navigation parameter, by summing unit contributions calculated for at least part of the reception times, the unit contribution associated with each of said times being calculated from the transfer matrix calculated for this time and the error bound received at this reception time. The steps of calculating N transfer matrices and determining the protection radius from these N transfer matrices make it possible to take into account, in a simple and rapid manner, the bounded errors in the determination of the protection radius. Thus,the risk that the error on the navigation parameter of the carrier is greater than the protection radius is minimized without a significant computational load being necessary. In particular, the method has the effect of limiting the error induced on navigation parameters of a carrier, such as the position, speed, attitudes and / or heading of the carrier. The induced error is generated by a measurement error whose temporal model is not known but whose limit is known deterministically or with a given probability of not exceeding this limit. According to other advantageous aspects of the invention, the determination method comprises one or more of the following characteristics, taken individually or in all technically possible combinations: - for each reception time, the measurement from the sensor comprises M components, and the method further comprises for each reception time,between the reception step and the step of determining an estimated state vector, an evaluation step comprising: - for each component of the measurement from the sensor, calculation of a unit gain of the filter; and - evaluation of a gain from the M unit gains, during the step of determining the estimated state vector and the step of calculating the error propagation matrix and the bounded error influence matrix, the gain of the estimation filter being the evaluated gain; - for each reception time, during the first calculation step, the estimation error propagation matrix at said reception time is equal to:^^( ^^ ^^)( ^^ − ^^ ^^( ^^ ^^) ^^( ^^ ^^)),where: - F(T, N ) is the propagation matrix of the state vector at said reception time; - I is the identity matrix; - K R (T N ) is the gain of the estimation filter at said reception time; and - H(T N) is the observation matrix at said reception time, the error influence matrix bounded at said reception time being equal to:^^( ^^ ^^) ^^ ^^( ^^ ^^)- the method further comprising, for each reception time, a step of writing each transfer matrix in a transfer shift register and each received error bound in a threshold shift register, during the calculation step, the Nth transfer matrix being equal to the error influence matrix bounded at said reception time, and each of the other first transfer matrices being calculated by multiplying the estimation error propagation matrix of said time with each transfer matrix calculated at the preceding reception time; - if during the reception step, at a loss time the measurement from the sensor is not received, then the step of writing the loss time comprises: - freezing the threshold shift register,and - writing each transfer matrix into the transfer shift register without performing a shift in the transfer shift register; - for the loss instant, during the first calculation step, the estimation error propagation matrix at said loss instant is equal to the state vector propagation matrix at said loss instant and the bounded error influence matrix at said resetting instant is equal to the zero matrix; - for each reception instant, during the protection radius determination step, each unit contribution is determined from at least one sub-matrix extracted from the transfer matrix calculated at the reception instant for the previous reception instant, the calculation of each unit contribution preferably comprising a calculation of the eigenvalue(s) of one of the sub-matrices; - during the reception step,a contribution of rare and normal error(s) to the protection radius is received for at least one reception instant; and the step of determining the protection radius comprising calculating the sum between the contribution of rare and normal error(s) and the sum of the unit contributions. The invention also relates to an electronic device for determining at least one protection radius associated with a navigation parameter of a carrier, the electronic determination device comprising technical means capable of implementing a determination method as described above. The invention also relates to a computer program product comprising software instructions which, when executed by a computer, are capable of implementing such a determination method. These characteristics and advantages of the invention will appear on reading the description which follows, given by way of non-limiting example,and made with reference to the appended drawings, in which: - [Fig. 1] Figure 1 is a schematic view of an electronic determination device according to the invention, on board a carrier; - [Fig. 2] Figure 2 is a flowchart of a determination method according to the invention, implemented by the determination device of Figure 1; and - [Fig. 3] Figure 3 is an explanatory diagram of a registration step of the method of Figure 2, illustrated in an example. With reference to Figure 2, a carrier 5 is mobile in an environment. The carrier 5 carries a sensor capable of providing measurements, such as a GNSS receiver 10 capable of receiving GNSS signals, an inertial positioning device 11 capable of providing inertial measurements and an electronic determination device 15 configured to determine at least one protection radius associated with at least one navigation parameter of the carrier 5. The expression "GNSS" is understood to mean,a satellite positioning system (Global Navigation Satellite System). Alternatively, the receiver 10 is a barometric sensor, a Loch sensor, an odometer, a vision sensor, a LIDAR (Laser Imagining Detection And Ranging) sensor, a SONAR (Sound Navigation And Ranging) sensor, a RADAR (Radio Detection And Ranging) sensor, a Doppler Velocity Log (DVL) speed sensor, or a Pitot tube. The carrier 5 is for example an aircraft, such as a drone, an airplane or a helicopter, moving in space in three dimensions, or a land or sea vehicle moving in a plane in two dimensions, or for example a railway vehicle moving in a single direction following a railway track. The GNSS receiver 10 is configured to receive GNSS signals from satellite(s) belonging to the same GNSS system,such as for example the GPS system. The GNSS receiver 10 comprises for example a reception antenna 12 known per se and a calculation module 13. The antenna 12 is configured to receive GNSS signals from a plurality of satellites and transmit them in the form of electrical signals to the calculation module 13. Without loss of generality, it will be considered in the remainder of the description that the measurement from the sensor is a GNSS position. It is clear that what will be described subsequently is also generalizable to other types of measurements from other sensors. The calculation module 13 is for example capable of determining a GNSS position of the receiver 10 from the GNSS signals received by the antenna 12, using techniques known per se. The GNSS position has for example the form of a vector comprising three components: a GNSS longitude,a GNSS latitude and a GNSS altitude. The GNSS position includes rare and normal errors on the one hand and bounded errors on the other hand. The bounded errors are included in a finite interval but the probability that they take certain values ​​in this interval is indeterminable. More specifically, the bounded errors related to the horizontal position of the carrier 5 are included in the interval [-HIL ; HIL], where HIL is a value of a horizontal error threshold likely to evolve over time. Similarly, the bounded error related to the vertical position of the carrier 5 is included in the interval [-VIL ; VIL],where VIL is a value of a vertical error threshold capable of evolving over time. These thresholds are for example directly supplied at the output of the receiver 10 and are for example calculated in accordance with the RAIM (Receiver Autonomous Integrity Monitoring) algorithm defined by the RTCA DO-229 standard. The calculation module 13 is configured to form an error bound S from the horizontal HIL and vertical VIL threshold values. For example, the error bound S comprises three components, the first two of which are equal to the horizontal error threshold HIL. The third component is then equal to the vertical error threshold value VIL. The calculation module 13 is further configured to send, to the determination device 15,the calculated GNSS position as well as the error bound S. The inertial positioning device 11 comprises for example an inertial measurement unit or IMU (from the English Inertial Measurement Unit) configured to measure linear accelerations and angular velocities of the carrier 5 in three mutually orthogonal directions. The inertial positioning device 11 is configured to determine, from these accelerations and these angular velocities, the inertial position of the carrier 5, according to a technique known per se, by applying for example a triple integration. In particular, this technique comprises for example a first integration of the attitude of the carrier 5 and then, a projection of the orientation of different axes of the sensors and a double integration of the results. This technique therefore makes it possible to successively obtain speed and position information. Thus,the inertial position has for example the form of a vector of three components: an inertial longitude, an inertial latitude and an inertial altitude. The inertial positioning device 11 is configured to further transmit to the determination device 15, the determined inertial position. The determination device 15 comprises an input module 17, a processing module 20 and an output module 25. According to a preferred embodiment, the input module 17, the processing module 20 and the output module 25 are each produced in the form of software stored in one or more storage means (such as a hard disk or a flash disk) and implemented by one or more processors, memory (RAM) and other computer components known per se. These components are then included in the same computer or in different computers / servers. In the latter case,the computers / servers are connected by a local or global network. In addition or alternatively, at least part of these modules 17, 20 and 25 takes the form, at least partially, of an independent electronic component, such as for example a programmable logic circuit of the FPGA (field-programmable gate array) type or other. The input module 17 is configured to receive, at a plurality of reception times T, N , the GNSS position and the error bound S(T N ) from the GNSS receiver 10, and the inertial position from the inertial positioning device 11. The input module 17 is configured to transmit to the processing module 20, the information received, namely: the GNSS position, the error boundary S(T N ) and the inertial position received at the reception time T N . In the rest of the description, for any quantity “W”, the formulation “W(T N) » designates the value of the quantity “W” at the time of reception T N. In addition, the formulation “(Ti)i=1,…,N” designates the set of reception times between a first reception time “T1” and a current reception time “TN”. By analogy, the formulation “(W(Ti))i=1,…,N” designates the set of values ​​of the quantity “W” at each of the reception times “(Ti)i=1,…,N”. The processing module 20 is configured to process the information received to determine the protection radius RP(TN) associated with a navigation parameter of the carrier 5. “Navigation parameter” means a location parameter of the carrier 5, such as the horizontal position, the vertical position, the horizontal speed, the vertical speed, the horizontal acceleration or the vertical acceleration or even the roll, the pitch or the heading, this list being non-exhaustive.For this, the processing module 20 is configured to process the information received as described below in relation to the determination method according to the invention. The processing module 20 includes an estimation filter, comprising a gain KR, an observation matrix H and a propagation matrix F of an estimated state vector X. The gain KR, the observation matrix H, the propagation matrix F and the estimated state vector X are capable of evolving over time. For this reason, they will subsequently be respectively denoted by the references KR(TN), H(TN), F(TN), and X(TN). The estimation filter is for example a Kalman filter in one of its forms such as for example an extended Kalman filter (from the English, Extended Kalman Filter).The processing module is notably configured to carry out, for each reception instant TN, a data fusion between the GNSS position and the inertial position, from the estimation filter and according to a technique known per se. This data fusion makes it possible to estimate the estimated state vector X(T. N ). The observation matrix H(T N ) is the matrix determining the observable components of the estimated state vector X(T N ). "Observable components" are the measured components of the estimated state vector. In the example presented, the observable components correspond to the positions of the carrier 5. The propagation matrix F(T N ) is the matrix connecting the estimated state vector X(T N ) at the time of reception T N to the estimated state vector X(T N+1 ) at the next reception time T N+1The classical formulation of the Kalman filter makes it possible to recalibrate the estimate of a state vector at each reception instant T N using a measurement vector z(T N ) for example equal to the difference between the GNSS position and the inertial position received at the reception time T N . It is known to recalibrate all the components of the estimated state vector X(T N ) simultaneously from the gain KR(TN) of the estimation filter, for example according to the equations: [ MATH 1] where P(TN) is the covariance matrix associated with the estimation error of the estimated state vector X(TN) at the reception time TN. A person skilled in the art knows that the covariance matrix is ​​symmetric positive definite. Equations 1 are recursive, i.e., knowledge of the state variables X(TN), the gain KR(TN), the measurement vector z(TN), the observation matrix H(TN) and the covariance matrix P(TN) for the reception time TN are necessary to calculate the estimated state vector X(T N+1 ) and to the covariance matrix P(T N+1 ) for the next reception time T N+1. In addition, the processing module preferably includes in its memory a transfer matrix shift register and a threshold shift register whose utility will be detailed below. The output module 25 is connected to the processing module 20. The output module 25 is configured to transmit to a user or to another electronic device not shown, the protection radius RP(T N ) determined and optionally the navigation parameter to which the protection radius RP(T) is associated N). If the output module 25 is configured to communicate with a user, this communication is carried out, for example, using a screen not shown. The determination method implemented by the electronic determination device 15 according to the invention will now be explained with reference to FIG. 2 showing a flowchart of this method and to FIG. 3 illustrating a step of this method. Initially, the wearer 5 moves in an environment and the GNSS receiver 10 receives, via its antenna 12, GNSS signals from a plurality of satellites. The calculation module 13 calculates the information mentioned above and transmits it to the determination device 15. Similarly, the inertial positioning device 11 calculates the inertial position and transmits it to the input module 17. During a reception step 110, the input module 17 receives at a plurality of successive reception times (T i ) i=1,…,N, the GNSS position of carrier 5, the inertial position of carrier 5 and the error bound S(T N ). N is the number of reception times T i . Then, for each successive reception instant TN, the method comprises the following steps. During an optional evaluation step 120, the processing module 20 comprises the evaluation of a gain KR(TN) of the estimation filter. The evaluation step 120 is advantageously a calculation of the gain KR(TN) of the estimation filter, from the unit gains (Kj(TN))j=1,…,M. The unit gains correspond to the gains used during the successive component-by-component recalibrations of the measurement vector received at the reception instant TN. The processing module 20 determines the gain KR(TN) from the unit gains (Kj(TN))j=1,…,M. For this, the processing module applies for example the following equation, recursive on the number of measurements: [ MATH 2] where: - I is the identity matrix, - ∗ denotes the matrix product, - (TN) is the gain calculated at the reception time TN for a measurement vector z(TN) comprising “M” component(s), and^^ ^^+1( ^^ ^^) is the observation matrix associated with the unit gain Kj+1(TN) calculated at the reception time T N for the j+1-th component of the measurement vector z(T N ). Equation 2 originates from the fact that the gain K R (T N ) must respect the following equation: where: - for all j, ^^ ^^, ^^ ( ^^ ^^ ) is the j-th column of the gain K R (T N), and - for all j, Hj(TN) is the j-th row of the observation matrix H(TN). In the proposed example in which the GNSS and inertial positions are received during the reception step 110, the measurement vector z(TN) comprises three components since the GNSS position and the inertial position respectively comprise three components. Thus, the application of equation 2 to this case gives a gain K R (T N ) equal to: [ MATH 4] Then, during a first determination step 130, according to a technique known per se, the estimated state vector (X(T N )) of carrier 5 is determined from the gain K R (T N ) evaluated during evaluation step 120, the observation matrix H(T N ) and the propagation matrix F(T N), for example according to equation 1 by initializing the estimated state vector X(T1) to zero for the first reception time T1. Then, during a first calculation step 140, the processing module 20 calculates an estimation error propagation matrix A(TN) of the state from the propagation matrix of the state vector F(TN), the gain KR(TN) of the estimation filter and the observation matrix H(TN). For example, the estimation error propagation matrix A(TN) is calculated according to the following equation: [ MATH 5] ^^( ^^ ^^) = ^^( ^^ ^^)( ^^ − ^^ ^^( ^^ ^^) ^^( ^^ ^^))The estimation error propagation matrix A(T N ) is calculated from the gain K R (T N ) of the estimation filter. Still during the first calculation step 130, the processing module 20 calculates an influence matrix of the bounded error B(T N ) for example according to the following equation: [ MATH 6]^^( ^^ ^^) = ^^( ^^ ^^) ^^ ^^( ^^ ^^) The estimation error propagation matrices A(T N ) and bounded error influence B(T N ) come from the following equation for the evolution of the estimated state vector X(T N ) : [ MATH 7] ^^( ^^ ^^) = ^^( ^^ ^^)( ^^ − ^^ ^^( ^^ ^^) ^^( ^^ ^^)) ^^( ^^ ^^−1) + ^^( ^^ ^^) ^^ ^^( ^^ ^^) ^^ ^^ ^^( ^^ ^^)where ^^ ^^ ^^( ^^ ^^ ) is a bounded error vector comprising the bounded error values ​​at time TN. It is clear that the bounded error vector ^^ ^^ ^^( ^^ ^^ ) is unknown since only the error bound S(T N ) is known. Thus, each bounded error in the bounded error vector ^^ ^^ ^^( ^^ ^^) has an unknown value, between the value HIL; VIL of the associated component in the error bound S(TN) and the opposite of the value –HIL; -VIL of the associated component in the error bound S(TN). Those skilled in the art will note that using equations 5 and 6, equation 7 is written in the form: [ MATH 8]^^( ^^ ^^) = ^^( ^^ ^^) ^^( ^^ ^^−1) + ^^( ^^ ^^) ^^ ^^ ^^( ^^ ^^)Then, during a second calculation step 150, the processing module 20 calculates N transfer matrices (V(N,i))i=1..,N. For this purpose, the processing module 20 calculates the transfer matrices (V(N,i))i=1,…,N from the N-1 transfer matrices (V(N-1, i))i=1,…,N-1 calculated at the previous reception time TN-1, from the estimation error propagation matrix A(TN) at said reception time TN and from the bounded error influence matrix B(TN) at said reception time TN. For example, the processing module 20 calculates the transfer matrices (V(N,i))i=1,…,N according to the following equation: [ MATH 9] ∀ ^^ < ^^, ^^( ^^, ^^) = ^^( ^^ ^^) ∗ ^^( ^^ − 1, ^^)^^( ^^, ^^) = ^^( ^^ ^^)It is clear that for the first reception time T1, i.e. if N is equal to 1, the processing module 20 only calculates the transfer matrix V(1,1) as being equal to the bounded error influence matrix B(T1). For example, at the second reception time T2, the processing module calculates the following transfer matrices V(2,2) and V(2,1) according to the following equations: [ MATH 10] ^^(2,2) = ^^( ^^2)^^(2,1) = ^^( ^^2) ∗ ^^(1,1) = ^^( ^^2) ∗ ^^( ^^1) Similarly, at the third reception time T3, the processing module 20 calculates the transfer matrices V(3,3), V(3,2), and V(3,1) according to the following equations: [ MATH 11] ^^(3,3) = ^^( ^^3)^ ^ ( 3,2 ) = ^^ ( ^^3 ) ∗ ^^ ( 2,2 ) = ^^ ( ^^3 ) ∗ ^^ ( ^^2 )^^(3,1) = ^^( ^^3) ∗ ^^(2,1) = ^^( ^^3) ∗ ^^( ^^2) ∗ ^^( ^^1)Then, during an optional registration step 160, the processing module registers each transfer matrix (V(N,i)) i=1,…,N in the transfer shift register and each error terminal (S(T i )) i=1,…,N in the threshold shift register(s). Thus, according to the optional addition in which the method comprises the registration step 160, the second calculation step 150 and the registration step 160 are preferably implemented simultaneously. Indeed, with reference to the left part of Figure 3, during these steps 150, 160, the transfer shift register is initially filled with the values ​​of the calculated transfer matrices (V(N-1,i)) i=1,…N-1 at the previous reception time TN-1 and the threshold shift register(s) is filled with the threshold vector(s) (S(T i )) i=1,…,N-1received between the first reception time T1 and the previous reception time T N-1. Then, the processing module 20 shifts each shift register to free a memory location in each shift register. Finally, and as visible on the right-hand side of Figure 3, the processing module 20 multiplies each of the first N-1 values ​​of the transfer shift register by the error propagation matrix A(TN) calculated at the reception time TN and writes in the freed location of this register the bounded error influence matrix B(TN) calculated at said reception time TN. In accordance with equation 9, the transfer shift register then comprises the values ​​of the transfer matrices (V(N,i))i=1,…,N calculated at the reception time TN and for each reception time (Ti)i=1,…,N preceding or equal to said reception time TN. In parallel with this writing, the processing module 20 writes, in the freed location of the threshold register, the error bound S(TN) received at the reception time TN.Alternatively, each shift register comprises a predetermined number of memory locations. This predetermined number of memory locations is also called the “depth of the shift register”. Thus, when the processing module 20 performs the shift of each shift register, the transfer matrix V(N-1,L) calculated at the previous instant TN-1 and for the oldest instant TL present in the transfer shift register, is expelled from the transfer shift register. Similarly, during this shift, the error bound S(T. L ) received at the same time the oldest T L , is expelled from the threshold shift register(s). The depth of the shift register is therefore equal to N-L+1. For example, according to the previous variant, the depth of each shift register is for example equal to 100, 50 or 10. If the depth is equal to 10, the transfer shift register includes, for each reception time T N, only the transfer matrices (V(N,i) i=N-9,…,N calculated between the reception times T N-9 and T N . Similarly, the threshold shift register(s) includes the threshold vectors (S(T i )) i=N-9,…,N received between these same reception times. During a second determination step 170, the processing module 20 determines the navigation parameter of the carrier 5 from the estimated state vector X(T N). For example, the navigation parameter is the horizontal position of the carrier 5, i.e. its longitude and latitude. According to another example, the navigation parameter is the vertical position of the carrier 5, i.e. its altitude. The processing module 20 determines the navigation parameter as being equal to one or more of the components of the estimated state vector X(TN), or to a combination of one or more of the components of the estimated state vector X(TN), such as a linear combination. During the second determination step 170 still, the processing module 20 determines the protection radius RP(TN) associated with the determined navigation parameter, from the calculated transfer matrices (V(N,i))i=1,…,N. For this, if the navigation parameter is the horizontal position, the processing module 20 performs the following actions.The processing module 20 extracts from each transfer matrix (V(N,i))i=1,…,N, a horizontal-horizontal transfer sub-matrix ^^. ℎ,ℎ ( ^^, ^^) comprising the coefficients of the transfer matrix V(N,i) whose rows correspond to the rows of the components associated with the horizontal position in the estimated state vector X(TN), and whose columns correspond to the rows associated with the horizontal position in the error bound S(TN). Each horizontal-horizontal transfer submatrix ^^ ℎ,ℎ ( ^^, ^^) is therefore a matrix of dimensions 2-2. Similarly, the processing module extracted from each transfer matrix (V(N,i)) i=1,…,N , a horizontal-vertical transfer submatrix ^^ ℎ, ^^ ( ^^, ^^) comprising the coefficients of the transfer matrix V(N,i) whose rows correspond to the rows of the components associated with the horizontal position in the estimated state vector X(T N), and whose column corresponds to the row associated with the vertical position in the error bound S(TN). Each horizontal-vertical transfer sub-matrix ^^ ℎ, ^^ ( ^^, ^^) is therefore a matrix of dimensions 2-1. Then, the processing module 20 calculates a unit contribution PL(T i ) for at least part of the reception times (T i ) i=j,…,N , for example for each moment of reception (Ti ) i=1,…,Nou for the reception times (Ti ) i= L,…,N for which a transfer matrix V(N,i) is present in the transfer shift register. The variable ^^ in index is either equal to 1 if the depth of the shift register is greater than the number of values ​​stored in said register, or to L if the shift register is already full and the depth of the register is equal to N-L+1. The processing module 20 calculates for example each unit contribution PL(Ti) from the following equation: Or : - √ − is the square root function, - ^^ ^^ ^^(−) is the function for calculating the eigenvalue(s), - max(−) is the maximum function, and - − ^^ is the matrix transpose. Alternatively, if the navigation parameter is the vertical position, the processing module 20 performs the following actions. The processing module 20 extracts from each transfer matrix (V(N,i))i=j,…,N, a vertical-horizontal transfer sub-matrix ^^ ^^,ℎ ( ^^, ^^) comprising the coefficients of the transfer matrix V(N,i) whose row corresponds to the row of the component associated with the vertical position in the estimated state vector X(T N ), and whose columns correspond to the rows associated with the horizontal position in the error bound S(T N ). Each vertical-horizontal transfer sub-matrix ^^ ^^,ℎ( ^^, ^^) is therefore a matrix of dimensions 1-2. Similarly, the processing module extracts from each transfer matrix (V(N,i))i=j,…,N, a vertical-vertical transfer sub-matrix ^^ ^^, ^^ ( ^^, ^^) comprising the coefficient of the transfer matrix V(N,i) whose row corresponds to the row of the component associated with the vertical position in the state vector X(TN), and whose column corresponds to the row associated with the vertical position in the error bound S(TN). Each vertical-vertical transfer sub-matrix ^^ ^^, ^^ ( ^^, ^^) is therefore a 1-1 dimension matrix. In other words, each vertical-vertical transfer matrix ^^ ^^, ^^( ^^, ^^) is a scalar number. Then, the processing module 20 calculates a unit contribution PL(Ti) for at least a part of the reception times (Ti)i=j,…,N, for example for each reception time (Ti)i=1,…,N or for the reception times (Ti)i=L,…,N for which a transfer matrix V(N,i) is present in the transfer shift register. The processing module calculates for example each unit contribution PL(Ti) from the following equation: where |−| is the absolute value function. Then, still during the second determination step 170, the processing module 20 determines the protection radius RP(T N ) from each unit contribution (PL(T i )) j=1,…,N calculated, regardless of how the unit contributions were calculated. For this purpose, the processing module 20 determines the protection radius RP(T N ) for example according to the following equation: [ MATH 14] where: - ^^ is the first index for which a unit contribution PL(T i ) is calculated, - ∑ ^ ^ ^ ^ = ^^ − is the sum over the index ^^ evolving between ^^ and N, and Then, during a transmission step 180, the output module 25 transmits to the user or to the other electronic device not shown, the determined protection radius RP(TN) and optionally the navigation parameter with which the protection radius is associated. According to a first variant embodiment, during the reception step 110, the input module 17 also receives the contribution to the protection radius PL FF (T N) resulting from rare and normal errors. According to this first embodiment variant, during the second determination step 170, the protection radius RP(TN) is then for example calculated by the following equation: [MATH 15] A second embodiment variant, for example combinable with the first embodiment variant is now presented. This variant can for example be used for each loss instant T P for which the GNSS position and / or the error bound S(T P ) is lost or invalidated. For these instants, the method does not include the evaluation step 120. According to this second variant, during the first determination step 130, the estimated state vector X(T P ) is determined only by prediction, that is to say without recalibration. This amounts to putting the gain K R (T N) to zero for these instants. According to this second variant still, during the calculation step 140, the estimation error propagation matrix A(T N ) and the bounded error influence matrix B(T N ) are calculated for example according to the following equation: [ MATH 16] ^^( ^^ ^^) = ^^( ^^ ^^)^^( ^^ ^^) = 0Then, during the calculation step 150, each transfer matrix (V(P,i))i=j,…,P-1 is calculated for example according to the following equation: [ MATH 17]∀^^ ≤ ^^ − 1, ^^( ^^, ^^) = ^^( ^^ ^^) ^^( ^^ − 1, ^^)It is clear that during the second calculation step 150, at most P-1 transfer matrices V(P,i) are calculated. Then, during the writing step 160, the processing module 20 freezes the threshold shift register. In other words, the processing module does not perform any shifting of the threshold shift register. During this writing step 160, the processing module 20 writes each calculated transfer matrix (V(P,i))i=j,…P-1, into the transfer shift register without performing any prior shifting of this register. With the method according to the invention, the determination of the protection radius RP(TN) is improved. With the protection radius RP(TN) determined by the method according to the invention, the probability that the error on the navigation parameter is greater than the protection radius RP(TN) is, for example, less than 10 -7 / h. With the method according to the invention, the calculation of the protection radius RP(TN) is simple and quick to implement. It is thus possible to implement the method according to the invention on the electronic determination device 10 on board the carrier 5. The optional evaluation step 120 allows real-time recalibration using the gain K R (T N ) of the estimation filter by limiting the risk that numerical approximations affect the characteristic(s) of the estimation filter matrix(s). With the method according to the first embodiment variant, the determination of the protection radius RP(T N) is further improved since it takes into account bounded errors on the one hand and rare and normal errors on the other. With the method according to the third embodiment variant, the determination method is more robust since it allows the protection radius to continue to be determined even when the GNSS position is lost.

Claims

CLAIMS 1. Method for limiting an error induced on at least one navigation parameter of a carrier (5), in particular a position, a speed, attitudes, and / or a heading of the carrier (5), the error being induced by a measurement error whose temporal evolution is unknown but whose limit is known and the probability of not exceeding this limit is also known; the limit and the probability being known for a plurality of times at which the method is implemented, the fact of limiting the induced error being obtained by the determination of at least one protection radius associated with the navigation parameter(s) of the carrier (5), the method being implemented by an electronic determination device (15) and comprising the following steps: - reception (110), at successive reception times (TN), of a measurement from a sensor, such as a GNSS receiver, in particular a GNSS position, of at least one error limit ( ^^( ^^ ^^)) associated with the measurement from the sensor and inertial measurement(s): - for each reception time (T N ) successive: - determination (130) of an estimated state vector (X(T N )) of the carrier by applying to the measurement from the sensor and to the inertial measurement an estimation filter, the estimation filter comprising for each reception instant ((T i ) i=1,…,N ), a gain (K R (T i )), an observation matrix (H(T i )) and a propagation matrix of the state vector (F(T i )) ; - calculation (140) of an estimation error propagation matrix (A(T N )) of the state from the propagation matrix of the state vector (F(T N )), of the gain (K R (T N )) of the estimation filter and the observation matrix (H(T N )), and calculation of a bounded error influence matrix (B(T N )) from the propagation matrix of the state vector (F(TN )) and the gain (K R (T N )); - calculation (150) of N transfer matrices (V(N,i) i=1..,N ), from the N-1 transfer matrices (V(N-1, i)i=1,…,N-1) calculated at the instant preceding (TN-1) the reception instant (TN), from the estimation error propagation matrix (A(N)) at said reception instant (TN) and from the bounded error influence matrix (B(N)) at said reception instant (TN), N being the number of successive reception instants ((Ti)i=1,…,N); - determination (170) of the navigation parameter from the estimated state vector (X(TN)) and determination of the protection radius (RP(TN)) associated with the navigation parameter, by summation of unit contributions ((PL(T i )) i=j,….,N ) calculated for at least part of the reception times ((T i ) i=j,…,N ), the unit contribution (PL(T i )) associated with each of said instants ((T i ) i=j,…,N) being calculated from the transfer matrix (V(N,i)) calculated for this instant (T i ) and the error bound (S(T i )) received at this time of reception (T i ).

2. Method according to the preceding claim, in which for each reception time (T N ), the measurement from the sensor comprises M components, and in which the method comprises for each reception time (T N ) furthermore, between the receiving step (110) and the determining step (130) of an estimated state vector (X(T N)), an evaluation step (120) comprising: - for each component of the measurement from the sensor, calculation of a unit gain (Kj(TN)) of the filter; and - evaluation of a gain (KR(TN)) from the M unit gains ((Kj(TN))j=1,…,M), during the step of determining the estimated state vector (X(TN)) and the step of calculating the error propagation matrix (A(TN)) and the bounded error influence matrix (B(TN)), the gain (KR(TN)) of the estimation filter being the evaluated gain.

3. Method according to claim 2, in which for each reception time (TN), during the first calculation step (140), the estimation error propagation matrix (A(TN)) at said reception time (TN) is equal to: ^^( ^^ ^^)( ^^ − ^^ ^^( ^^ ^^) ^^( ^^ ^^)), where: - F(T N ) is the propagation matrix of the state vector at said reception time (T N); - I is the identity matrix; - KR(TN) is the gain of the estimation filter at said reception time (TN); and - H(TN) is the observation matrix at said reception time (TN), the influence matrix of the bounded error (B(T N )) at the time of receipt (T N ) being equal à : ^^( ^^ ^^) ^^ ^^( ^^ ^^).

4. Method according to any one of the preceding claims, further comprising, for each reception time (T N ), a registration step (160) of each transfer matrix (V(N,i) i=1,…,N ) in a transfer shift register and each received error terminal (S(T N )) in a threshold shift register(s), during the calculation step, the Nth transfer matrix (V(N,N)) being equal to the influence matrix of the bounded error (B(T N )) at the time of receipt (T N ), and each of the other first transfer matrices ((V(N,i) i=j,…,N-1) being calculated by multiplying the estimation error propagation matrix (A(T N )) of said instant (T N ) to each transfer matrix (V(N-1, j) j=1,…,N-1 ) calculated at the reception time preceding (T N-1 ).

5. Method according to the preceding claim, in which if, during the reception step (110), at a loss time (T P ) the measurement from the sensor is not received, then the step of recording (160) the instant of loss (T P) comprises: - freezing the threshold shift register, and - writing each transfer matrix (V(P,i)j=1,…,P-1) in the transfer shift register without performing a shift in the transfer shift register.

6. Method according to the preceding claim, in which, for the loss instant (TP), during the first calculation step (140), the estimation error propagation matrix (A(TP)) at said loss instant (TP) is equal to the state vector propagation matrix (F(TP)) at said loss instant (TP) and the bounded error influence matrix (B(TP)) at said loss instant (TP) is equal to the zero matrix.

7. Method according to any one of the preceding claims, in which for each reception time (TN), during the step of determining (170) the protection radius (RP(TN)), each unit contribution is determined from at least one sub-matrix ( ^^ ℎ,ℎ ( ^^, ^^), ^^ ℎ, ^^ ( ^^, ^^) ; ^^ ^^,ℎ( ^^, ^^), ^^ ^^, ^^ ( ^^, ^^)) extracted from the transfer matrix (V(N,i)) calculated at the reception time (TN) for the previous reception time (Ti), the calculation of each unit contribution (PLi(TN)) preferably comprising a calculation of the eigenvalue(s) of one of the sub-matrices ( ^^ ℎ,ℎ ( ^^, ^^)).

8. Method according to any one of the preceding claims, in which during the reception step (110), a contribution (PL FF (T N )) of rare and normal error(s) at the protection radius (RP(TN)) is received for at least one reception instant (TN), the step of determining (170) the protection radius (RP(T N )) including the calculation of the sum between the contribution (PL FF (T N )) of rare and normal error(s) and the sum of the unit contributions (PL i (T N)).

9. Electronic device (15) for determining at least one protection radius (RP(TN)) associated with a navigation parameter of a wearer (5), the electronic determination device (15) comprising technical means suitable for implementing a determination method according to any one of the preceding claims.

10. Computer program comprising software instructions which, when executed by a computer, are capable of implementing a determination method according to any one of claims 1 to 8.

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