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

Abstract

The present application relates to a method for determining at least one protection radius associated with at least one navigation parameter of a carrier. The method comprises receiving (110) measurements from sensors, error boundaries, and inertial measurements. The method further comprises determining (130), for each consecutive reception time, an estimated state vector based on measurements from the sensor and inertial measurements. The method further comprises calculating (140) an estimated error propagation matrix and an influence matrix of the boundary errors, and calculating a transfer matrix based on the calculated matrices. The method further comprises determining (170) a navigation parameter from the estimated state vector and an associated protection radius based on the calculated transfer matrix.

Description

[0001] The present application relates to a method for determining a protection radius associated with at least one navigation parameter of a vehicle, such as the vehicle's position, speed, attitude and / or heading.

[0002] The application also relates to an electronic determination device configured to implement such a determination method.

[0003] Another subject matter of the present application relates to a computer program product suitable for implementing such a determination method.

[0004] The present invention relates to the field of integrated positioning of a carrier, for example a mobile carrier. "Integrated positioning" refers to the estimation of navigation parameters, such as the position, speed, attitude and / or heading of the carrier, and the provision of a protection radius associated with the considered navigation parameters. Thus, according to a predefined probability, it is ensured that the error in estimating the navigation parameters remains within the protection radius.

[0005] It is known to estimate navigation parameters such as position, velocity, attitude and heading of the vehicle by performing a combination of a GNSS (Global Navigation Satellite System) position estimated from a satellite positioning system and inertial measurements from an Inertial Measurement Unit (IMU).

[0006] In the process of performing this estimation, errors may perturb the estimation of the navigation parameters of the vehicle. Such errors can be divided into two categories: modeled errors, called rare and normal errors, and unmodeled but called boundary errors.

[0007] The first type of errors are usually modeled by random variables that follow continuous probability laws. It is usually assumed that the distribution of the first type of errors follows a normal distribution. By definition, the normal distribution is a probability distribution, often called a Gaussian distribution. In this case, it is obvious that the values ​​of the first type of errors are unbounded. However, since the distribution of the first type of errors is known, a bound can be determined that guarantees that the first type of errors remain within said bounds for a predetermined probability. The first type of errors are then referred to as "rare and normal errors". In practice, rare and normal errors are usually caused by intrinsic characteristics of the sensors used, which affect the estimation of the navigation parameters of the carrier. Examples include thermal noise from the GNSS receiver or residual noise from inertial measurements.

[0008] For rare and normal errors, respective protection radii are known for determining at least one navigation parameter of the vehicle, such as position, velocity, attitude and / or heading.

[0009] The second type of errors involves bounded but unmodeled errors. The second type of errors are contained in the interval formed by the two bounds, but their distribution model is unknown. In the following description, the second type of errors are called "boundary errors". In practice, the boundary errors correspond, for example, to errors related to the calculation of the GNSS position using an erroneous ephemeris, or to a satellite clock failure in one of the satellites required to calculate the GNSS position.

[0010] It is not possible to know or predict the distribution or time evolution of the Type II error. Only the interval of the error evolution is known, along with the probability that the error will remain within the interval, and the confidence level characterized by the probability.

[0011] For example, document US9341718B2 attempts to provide a model of boundary error. Similarly, in C. Combastel's article "Merging Kalman Filtering and Zonotopic-State Bounding for Robust Fault Detection under Noisy Environment", a more mathematically rigorous method for modeling boundary error is proposed.

[0012] However, in the above-mentioned literature, the determination of the protection radius is not optimal.

[0013] The subject matter of the present application is therefore to improve the determination of a protection radius associated with a navigation parameter.

[0014] To this end, the present application relates to a determination method aimed at limiting a sensed error on at least one navigation parameter of a carrier, in particular the position, velocity, attitude and / or heading of the carrier, said error being caused by a measurement error whose temporal evolution is unknown but whose one limit is known and whose probability of not exceeding said limit is also known; said limit and said probability being known at a plurality of moments in the implementation of said method, the fact of limiting said sensed error being obtained by determining at least one protection radius associated with a navigation parameter of the carrier, said method being implemented by an electronic determination device and comprising the following steps:

[0015] - receiving at successive reception moments measurements from a sensor, such as a GNSS receiver, in particular GNSS positions, and at least one error bound associated with the measurements from the sensor and with inertial measurements:

[0016] -For each consecutive reception moment:

[0017] - determining an estimated state vector of the vehicle by applying the measurements from the sensors and the inertial measurements to an estimation filter comprising, for each reception instant, a gain, an observation matrix and a propagation matrix of the state vector;

[0018] - calculating the estimated error propagation matrix of the state based on the propagation matrix of the state vector, the gain of the estimation filter and the observation matrix, and calculating the influence matrix of the boundary error based on the propagation matrix and the gain of the state vector;

[0019] - calculating N transfer matrices based on N-1 transfer matrices calculated at a time instant before the receiving time instant, from the estimated error propagation matrix at the receiving time instant and from the influence matrix of the boundary error at the receiving time instant, N being the number of consecutive receiving time instants; and

[0020] - determining navigation parameters from the estimated state vector by summing unit contributions calculated for at least some of the reception moments, and determining a protection radius associated with the navigation parameters, wherein said unit contribution associated with each of said moments is calculated based on a transfer matrix calculated for said moment and an error bound received at said reception moment.

[0021] By these steps of calculating N transfer matrices and determining the protection radius from said N transfer matrices, the boundary error can be easily and quickly taken into account when determining the protection radius. Thus, the risk of the carrier navigation parameter error being larger than the protection radius is minimized without requiring a large computational load.

[0022] More specifically, the method has the effect of limiting the sensed errors on navigation parameters of the vehicle, such as position, velocity, attitude and / or heading of the vehicle, which are caused by measurement errors whose temporal pattern is unknown but whose bounds are known or have a given probability of not exceeding the bounds.

[0023] According to other advantageous aspects of the present application, the determination method includes one or more of the following features, taken individually or in all technically possible combinations:

[0024] - for each reception instant, the measurement result from the sensor comprises M components, and wherein for each reception instant, between the receiving step and the step of determining an estimated state vector, the method further comprises an evaluation step comprising:

[0025] - for each component of the measurement from the sensor, calculating the unity gain of the filter; and

[0026] - Evaluate the gain from M unity gains,

[0027] In the step of determining the estimated state vector and the step of calculating the error propagation matrix and the influence matrix of the boundary error, the gain of the estimated filter is the estimated gain

[0028] - For each reception instant, in a first calculation step, the estimated error propagation matrix for said reception instant is equal to:

[0029] F(T N )(IK R (T N )H(T N ))

[0030] in:

[0031] -F(T N ) is the propagation matrix of the state vector at the receiving time;

[0032] -I is the identity matrix;

[0033] -K R (T N ) is the gain of the estimated filter at the receiving time; and

[0034] -H(T N ) is the observation matrix at the receiving time,

[0035] The influence matrix of the boundary error at the receiving time is equal to:

[0036] F(T N )K R (T N )

[0037] - the method further comprises, for each reception instant, the step of writing each transfer matrix in a transfer shift register and each received error boundary in a threshold shift register,

[0038] In the calculation step, the Nth transfer matrix is ​​equal to the influence matrix of the boundary error at the reception instant, and each other first transfer matrix is ​​calculated by multiplying the estimated error propagation matrix at the instant by each transfer matrix calculated at the previous reception instant.

[0039] If, in the receiving step, no measurement result from the sensor is received at the loss moment, the writing step of the loss moment comprises:

[0040] - a frozen threshold shift register, and

[0041] -Writing each transfer matrix in a transfer shift register without performing a shift in the transfer shift register.

[0042] - For the loss moment, in the first calculation step, the estimation error propagation matrix at the loss moment is equal to the propagation matrix of the state vector at the loss moment, and the influence matrix of the boundary error at the adjustment moment is equal to the zero matrix.

[0043] - for each reception instant, in the step of determining the protection radius, each unit contribution is determined by at least one sub-matrix extracted from the transfer matrix calculated at the reception instant preceding the reception instant,

[0044] The calculation of each unit contribution preferably comprises the calculation of an eigenvalue of one of the sub-matrices;

[0045] - in a receiving step, receiving the contribution of rare and normal errors of the protection radius for at least one receiving instant; and

[0046] The step of determining the protection radius includes the calculation of the sum between the contribution of rare and normal errors and the sum of the unit contribution.

[0047] Another aspect of the present application relates to an electronic device for determining at least one protection radius associated with a navigation parameter of a carrier, wherein the electronic device comprises technical means suitable for implementing the aforementioned determination method.

[0048] Another aspect of the present application relates to a computer program comprising software instructions which, when executed by a computer, tend to implement such a determination method.

[0049] The characteristics and advantages of the present application will emerge after reading the following description, given by way of example and not limitation, and with reference to the accompanying drawings, in which:

[0050] -[ Figure 1 ] Figure 1 is a schematic diagram of an electronic device on a carrier according to the present application;

[0051] -[ Figure 2 ] Figure 2 Is Figure 1 A flowchart of the determination method of the present application implemented by the determination device shown; and

[0052] -[ Figure 3 ] Figure 3 yes Figure 2 An illustration of the writing steps of the method shown is provided by way of example.

[0053] refer to Figure 2The carrier 5 is movable in the environment. The carrier 5 carries on board sensors suitable for providing measurement results, such as a GNSS receiver 10 suitable for receiving GNSS signals, an inertial positioning device 11 suitable for providing inertial measurement results, 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.

[0054] GNSS is the abbreviation of Global Navigation Satellite System.

[0055] Alternatively, the receiver 10 is a barometric pressure sensor, a Loch sensor, an odometer, a visual sensor, a LIDAR (Laser Imaging Detection And Ranging) sensor, a SONAR (Sound Navigation And Ranging) sensor, a RADAR (Radio Detection and Ranging) sensor, a Doppler Velocity Log (DVL) sensor, or a Pitot tube.

[0056] The carrier 5 is, for example, an aircraft moving in three-dimensional space, such as a drone, an airplane or a helicopter, or a land or sea vehicle moving in a two-dimensional plane, or a railway vehicle moving in one direction, such as a railway track.

[0057] The GNSS receiver 10 is configured to receive GNSS signals from satellites belonging to the same GNSS system (eg, GPS system). The GNSS receiver 10 comprises, for example, a receiving antenna 12 and a computing module 13, which are known per se.

[0058] The antenna 12 is configured to receive GNSS signals from a plurality of satellites and transmit the signals to the computing module 13 in the form of electrical signals.

[0059] Without loss of generality, in the following description, it will be considered that the measurement results from the sensor are GNSS positions. Obviously, the content to be described hereinafter can also be extended to other types of measurement results from other sensors.

[0060] The calculation module 13 is, for example, adapted to determine, using techniques known per se, the GNSS position of the receiver 10 from the GNSS signals received by the antenna 12. The GNSS position is, for example, in the form of a vector comprising three components: GNSS longitude, GNSS latitude and GNSS altitude. The GNSS position comprises rare and normal errors as well as marginal errors.

[0061] The boundary error falls within a finite range, but the probability of taking certain values ​​within the range is also uncertain. More specifically, the boundary error associated with the horizontal position of the carrier 5 is contained in the interval [-HIL; HIL], where HIL is a horizontal error threshold, which can vary over time. Similarly, the boundary error associated with the vertical position of the carrier 5 is contained in the interval [-VIL; VIL], where VIL is a vertical error threshold, which can vary over time.

[0062] These threshold values ​​are provided, for example, directly at the output of the receiver 10 and are calculated, for example, according to the RAIM algorithm (Receiver Autonomous Integrity Monitoring) defined in the RTCA DO-229 standard.

[0063] The calculation module 13 is configured to form an error boundary S based on the horizontal HIL and vertical VIL thresholds. For example, the error boundary S includes three components, wherein the first two components are equal to the horizontal error threshold HIL, and then the third component is equal to the vertical error threshold VIL.

[0064] The calculation module 13 is further configured to send the calculated GNSS position and the error margin S to the determination device 15 .

[0065] The inertial positioning device 11 includes, for example, an inertial measurement unit (IMU), which is configured to measure the linear acceleration and angular velocity of the carrier 5 in three mutually orthogonal directions. The inertial positioning device 11 is configured to determine the inertial position of the carrier 5 from these accelerations and these angular velocities according to a technique known per se, for example by applying a triple integral. Specifically, this technique includes, for example, first integrating the attitude of the carrier 5, then projecting the orientations of the different axes of the sensor, and doubly integrating the result. Therefore, this technique is used to continuously obtain information about speed and position. Therefore, the inertial position is in the form of a vector, consisting of three components: inertial longitude, inertial latitude and inertial altitude.

[0066] The inertial positioning device 11 is further configured to send the determined inertial position to the determination device 15 .

[0067] The determination device 15 includes an input module 17 , a processing module 20 and an output module 25 .

[0068] According to a preferred embodiment, the input module 17, the processing module 20 and the output module 25 are each implemented in the form of software stored in one or more storage devices (such as hard disks or flash drives), and implemented by one or more processors, memories (RAM) and other computer components known per se. Then, these components are included in the same computer or different computers / servers. In the latter case, the computers / servers are connected via a local or global network.

[0069] Additionally or alternatively, at least a portion of modules 17, 20 and 25 may be at least partially in the form of independent electronic components, such as programmable logic circuits, such as field programmable gate arrays (FPGAs) or others.

[0070] The input module 17 is configured to receive N Receive the GNSS position and error margin S(T) from the GNSS receiver 10 N ), and receiving the inertial position from the inertial positioning device 11.

[0071] The input module 17 is configured to send the received information to the processing module 20, namely: GNSS position, error margin S(T N ) and at the receiving time T N Received inertial position.

[0072] In the following description, for any number "W", the formula "W(T N )" refers to the receiving time T N The value of the quantity "W". In addition, the formula "(T i ) i＝1,...,N " refers to the time between the first receiving time "T1" and the current receiving time "T N " is the set of receiving times composed of i )) i＝1,...,N " refers to at each receiving moment "(T i ) i＝1,...,N ” is a set of number “W”.

[0073] The processing module 20 is configured to process the received information to determine a protection radius RP (T N ). "Navigation parameters" refer to parameters used to locate the carrier 5, such as horizontal position, vertical position, horizontal speed, vertical speed, horizontal acceleration or vertical acceleration, or roll, pitch or heading, the list being non-exhaustive. To this end, the processing module 20 is configured to process the received information, as described below in relation to the determination method of the present application. The processing module 20 comprises an estimation filter, which comprises a gain K R, the observation matrix H and the propagation matrix F of the estimated state vector X. The gain K R , the observation matrix H, the propagation matrix F and the estimated state vector X are prone to evolve over time. For the above reasons, we will use the labels K R (T N ), H(T N ), F(T N ) and X(T N The estimation filter is, for example, one of the forms of a Kalman filter, such as an extended Kalman filter.

[0074] Specifically, the processing module is configured to, for each receiving time T N , based on the estimation filter and according to the known techniques, the data between the GNSS position and the inertial position are merged. This data fusion is used to estimate the estimated state vector X(T N ).

[0075] The observation matrix H(T N ) is the state vector X(T N ) is a matrix of observable components of the estimated state vector. "Observable components" refer to the measured components of the estimated state vector. In the example shown, the observable components correspond to the position of the carrier 5.

[0076] The propagation matrix F(T N ) is the time at which the N The estimated state vector X(T N ) is connected to the next receiving time T N+1 The estimated state vector X(T N+1 ) matrix.

[0077] The traditional formulation of the Kalman filter is to use the measurement vector z(T N ) to convert each receiving time T N The estimated value of the state vector is adjusted to, for example, equal to the GNSS position and the reception time T N The difference between the received inertial positions.

[0078] It is known that the gain KR(T N ) and adjust the estimated state vector X(T N ), for example according to the following equation:

[0079] [Mathematical equation 1]

[0080] X(T N+1 )=X(T N )+KR (T N )*(z(T N )-H(T N )*X(T N ))

[0081] P(T N+1 )=(IK R (T N )*H(T N ))*P(T N )

[0082] Where P(T N ) is the same as the receiving time T N The estimated state vector X(T N ) is the covariance matrix associated with the estimated errors.

[0083] Those skilled in the art know that the covariance matrix is ​​symmetric and positive definite.

[0084] Equation 1 is recursive, that is, the state variable X(T N )、Gain KR(T N ), measurement vector z(T N ), the observation matrix H(T N ) and the covariance matrix P(T N ) for the receiving time T N Information about the estimated state vector X(T N+1 ) and the next receiving time T N+1 The covariance matrix P(T N+1 ) is required.

[0085] Furthermore, the processing module preferably includes in its memory, a transfer matrix shift register and a threshold shift register, the utility of which will be discussed in detail below.

[0086] The output module 25 is connected to the processing module 20. The output module 25 is configured to transmit the determined protection radius RP (T N ), and optionally the transmission and protection radius RP(T N ) associated with the navigation parameter.

[0087] If the output module 25 is configured to communicate with the user, the communication is performed, for example, via a screen (not shown).

[0088] Now refer to Figure 2 and Figure 3 Explain the determination method implemented by the electronic determination device 15 of the present application, Figure 2 A flowchart of the method is shown, Figure 3The steps of the method are shown.

[0089] Initially, the carrier 5 moves in the environment and the GNSS receiver 10 receives GNSS signals from a plurality of satellites via its antenna 12. The calculation module 13 calculates the above information and sends it to the determination device 15. Similarly, the inertial positioning device 11 calculates the inertial position and transmits it to the input module 17.

[0090] In the receiving step 110, at a plurality of consecutive receiving times (T i ) i＝1,...,N The input module 17 receives the GNSS position of the carrier 5, the inertial position of the carrier 5 and the error margin S(T N ). N is the receiving time T i The number of

[0091] Then, for each consecutive reception time T N , the method comprises the following steps.

[0092] In an optional evaluation step 120, the processing module 20 includes evaluating the gain K of the estimation filter R (T N The evaluation step 120 is advantageously based on a unity gain (K j (T N )) j＝1,…,M ) Calculate the gain K of the estimation filter R (T N ).

[0093] The unity gain corresponds to the receiving time T N The gains used in the component-by-component rescaling of the received measurement vector are continuous.

[0094] The processing module 20 is based on the unity gain (K j (T N )) j＝1,...,M To this end, the processing module applies, for example, the following equation, for example recursively over the number of measurements:

[0095] [Mathematical equation 2]

[0096] K R,1 (T N )=K1(T N )

[0097]

[0098] in:

[0099] -I is the identity matrix;

[0100] -* represents matrix product,

[0101] - It is at the receiving time T N For a measurement vector z(T N ) calculated, and

[0102] H j+1 (T N ) is the measurement vector z(T N )'s j+1th component is received at time T N Calculated with unity gain K j+1 (T N ) is the observation matrix associated with .

[0103] Equation 2 is based on the gain K R (T N ) must satisfy the following formula:

[0104] [Mathematical equation 3]

[0105]

[0106] in:

[0107] -For all j, is the gain K R (T N ), and

[0108] -For any j, H j (T N ) is the observation matrix H(T N )’s j-th row.

[0109] In the proposed example, where GNSS and inertial positions are received in the receiving step 110, the measurement vector z(TN) comprises three components, since the GNSS position and the inertial position each comprise three components. Thus, applying equation 2 to this case yields the gain K r (T N )equal:

[0110] [Mathematical equation 4]

[0111] K R (T N )

[0112] =[(I-K3(T N )H3(T N ))*(I-K2(T N )H2(T N ))*K1(T N )(I-K3(T N)H3(T N ))*K2(T N )K3(T N )]

[0113] Then, in a first determination step 130, the gain K estimated in the evaluation step 120 is determined according to a technique known per se. R (T N ), the observation matrix H(T N ) and the propagation matrix F(T N ), for example, by initializing the estimated state vector X(T1) to zero at the first reception time T1 and determining the estimated state vector (X(T N )).

[0114] Then, in a first calculation step 140, the processing module 20 calculates the state vector F(T N ) propagation matrix, estimate the filter gain K R (T N ) and the observation matrix H(T N ), calculate the estimated error propagation matrix A(T N ).

[0115] For example, the estimated error propagation matrix A(T N ) is calculated as follows:

[0116] [Mathematical equation 5]

[0117] A(T N )=F(T N )(IK R (T N )H(T N ))

[0118] Based on the estimated filter gain K R (T N ) Calculate the estimated error propagation matrix A(T N ).

[0119] Still in the first calculation step 130, the processing module 20 calculates the influence matrix B (T N ): For example, according to the following equation:

[0120] [Mathematical equation 6]

[0121] B(T N )=F(T N )K R (T N )

[0122] Estimated error propagation matrix A(T N) and the influence matrix of boundary error B(T N ) is determined by the estimated state vector X(T N ) is derived from the following evolution equation:

[0123] [Mathematical formula 7]

[0124] X(T N )=F(T N )(IK R (T N )H(T N ))X(T N-1 )+F(T N )K R (T N )Seq(T N )

[0125] Where Seq(T N ) is the boundary error vector, which includes the time T N The value of the boundary error at .

[0126] Obviously, the boundary error vector Seq(T N ) is unknown, because only the error limit S(T N ) is known. Therefore, the boundary error vector Seq(T N ) has an unknown value for each boundary error, including the HIL; in the error boundary S(T N ) in the associated component VIL, and the opposite value -HIL; in the error boundary S(T N ) in the associated component.

[0127] Those skilled in the art will note that using Equations 5 and 6, Equation 7 is written as follows:

[0128] [Mathematical equation 8]

[0129] X(T N )=A(T N )X(T N-1 )+B(T N )Seq(T N )

[0130] Then, in a second calculation step 150, the processing module 20 calculates N transfer matrices (V(N,i)) i＝1..,N Therefore, for the receiving time T N The estimated error propagation matrix A(T N ), and at the receiving time T N The boundary error B(T N ), the processing module 20 receives the influence matrix from the previous receiving time TN-1 The calculated N-1 transfer matrices (V(N-1,i)) i＝1,…,N-1 To calculate the transfer matrix (V(N,i)) i＝1,…,N .

[0131] For example, the processing module 20 calculates the transfer matrix (V(N,i)) according to the following equation: i＝1,…,N :

[0132] [Mathematical equation 9]

[0133]

[0134] V(N,N)=B(T N )

[0135] Obviously, for the first receiving time T1, that is, when N is equal to 1, the processing module 20 only calculates the influence matrix of the transfer matrix V(1,1) equal to the boundary error B(T1).

[0136] For example, at the second receiving time T2, the processing module calculates the following transfer matrices V(2,2) and V(2,1) according to the following equations:

[0137] [Mathematical formula 10]

[0138] V(2,2)=B(T2)

[0139] V(2,1)=A(T2)*V(1,1)=A(T2)*B(T1)

[0140] Similarly, at the third receiving 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:

[0141] [Mathematical equation 11]

[0142] V(3,3)=B(T3)

[0143] V(3,2)=A(T3)*V(2,2)=A(T3)*B(T2)

[0144] V(3,1)=A(T3)*V(2,1)=A(T3)*A(T2)*B(T1)

[0145] Then, in an optional writing step 160, the processing module writes each transfer matrix (V(N,i)) in the transfer shift register. i＝1,…,N ) and write each received error boundary (S(T i )) i＝1,…,N .

[0146] Therefore, according to the optional supplementary content, wherein the method includes a writing step 160, the second calculation step 150 and the writing step 160 are preferably performed simultaneously. Figure 3 In the left part, in steps 150 and 160, the transfer shift register is initially filled with the data at the previous receiving time T N-1 The calculated transfer matrix (V(N-1,i)) i＝1,…N-1 The value of the threshold shift register is filled with the value of the first receiving time T1 and the value of the previous receiving time T N-1 The threshold vector (S(T i )) i＝1,…,N-1 .

[0147] Then, the processing module 20 shifts each shift register to release a storage unit in each shift register.

[0148] Finally, from Figure 3 As can be seen from the right side, the processing module 20 multiplies each first N-1 value of the transfer shift register by the value at the receiving time T N The calculated error propagation matrix A(T N ) and writes the released (freed) unit of the register, at the receiving time T N The influence matrix B(T N ). According to equation 9, then, the transfer shift register contains at the receiving time T N Calculated transfer matrix (V(N,i)) i＝1,…,N The value of, and for each receiving time (T i ) i＝1,…,N are prior to or equal to the receiving time T N .

[0149] In parallel with the writing, the processing module 20 writes in the released cell of the threshold register the value of the value at the receiving time T N The received error margin S(T N ).

[0150] In one variant, each shift register includes a predetermined number of storage cells. The predetermined number of storage cells is also referred to as the "depth of the shift register". Therefore, when the processing module 20 performs the shift of each shift register, at the previous time T N-1 and for the oldest time T present in the transfer shift register L The calculated transfer matrix V(N-1,L) will be removed from the transfer shift register. Similarly, in this shift process, at the oldest time T L The received error margin S(T L) will be removed from the threshold shift register. The depth of the shift register is therefore equal to N-L+1.

[0151] For example, according to the aforementioned variants, the depth of each shift register is, for example, equal to 100, 50 or 10. If the depth is equal to 10, then for each reception instant T N , the transmission shift register only includes the receiving time T N-9 and T N The transfer matrix (V(N,i) calculated between i＝N-9,…,N Similarly, the threshold shift register includes the threshold vector (S(T i )) i＝N-9,…,N .

[0152] In a second determination step 170, the processing module 20 determines from the estimated state vector X(T N ) determines the navigation parameters of the carrier 5. For example, the navigation parameters are the horizontal position of the carrier 5, i.e. its longitude and latitude. According to another example, the navigation parameters are the vertical position of the carrier 5, i.e. its altitude.

[0153] The processing module 20 determines that the navigation parameter is equal to the estimated state vector X(T N ) or equal to the estimated state vector X(T N ) is a combination of one or more components of , such as a linear combination.

[0154] Also in the second determination step 170, according to the calculated transfer matrix (V(N,i)) i＝1,…,N The processing module 20 determines the protection radius RP (T N ).

[0155] To this end, if the navigation parameter is a horizontal position, the processing module 20 performs the following operations.

[0156] The processing module 20 is based on each transfer matrix (V(N,i)) i＝1,…,N Extract a horizontal-horizontal transfer submatrix V from h,h (N,i), which contains the coefficients of the transfer matrix V(N,i), where the rows of V(N,i) correspond to the estimated state vector X(T N ) are the rows of the components associated with the horizontal position, and the columns of V(N,i) correspond to the components within the error bound S(T N ) are associated with horizontal positions. Therefore, each horizontal-horizontal transfer submatrix V h,h (N,i) is a matrix of dimension 2-2.

[0157] Similarly, the processing module obtains from each transfer matrix (V(N,i)) i＝1,…,N Extract a horizontal-vertical transfer submatrix V from h,v (N,i), which contains the coefficients of the transfer matrix V(N,i), where the rows of V(N,i) correspond to the estimated state vector X(T N ) are the rows of the components associated with the horizontal position, and the columns of V(N,i) correspond to the components within the error bound S(T N ) are associated with vertical positions. Therefore, each horizontal-vertical transfer submatrix V h,v (N,i) is a matrix of dimension 2-1.

[0158] Then, the processing module 20, for the receiving time (T i ) i＝j,…,N At least part of the unit contribution PL(T i ), for example, for each receiving time (T i ) i＝j,…,N , or for the receiving time (T i ) i＝j,…,N The index variable j is equal to 1 if the depth of the shift register is greater than the number of values ​​stored in said register, or equal to L if the shift register is complete and the depth of the register is equal to N-L+1.

[0159] The processing module 20 calculates, for example, each unit contribution PL (T i ):

[0160] [Mathematical equation 12]

[0161]

[0162] in:

[0163] - is the square root function,

[0164] -eig(-) is the function for calculating eigenvalues.

[0165] -max(-) is the maximum function, and

[0166] -- T is the transpose of the matrix.

[0167] In one variant, if the navigation parameter is a vertical position, the processing module 20 performs the following operations.

[0168] The processing module 20 is based on each transfer matrix (V(N,i)) i＝j,…,NExtract a vertical-horizontal transfer submatrix V from v,h (N,i), which contains the coefficients of the transfer matrix V(N,i), where the rows of V(N,i) correspond to the estimated state vector X(T N ) are the rows of the components associated with the vertical position, and the columns of V(N,i) correspond to the components within the error bound S(T N ) is associated with a horizontal position. Therefore, each vertical-horizontal transfer submatrix V v,h (N,i) is a matrix of dimension 1-2.

[0169] Similarly, the processing module obtains from each transfer matrix (V(N,i)) i＝1,…,N Extract a vertical-vertical transfer submatrix V from v,v (N,i), which contains the coefficients of the transfer matrix V(N,i), where the rows of V(N,i) correspond to the state vector X(T N ) are the rows of the components associated with the vertical position, and the columns of V(N,i) correspond to the components within the error bound S(T N ) are associated with vertical positions. Therefore, each vertical-vertical transfer submatrix V v,v (N,i) is a matrix of dimension 1-1. In other words, each vertical-vertical transfer matrix V v,v (N,i) is a scalar value.

[0170] Then, the processing module 20, for the receiving time (T i ) i＝j,…,N At least part of the unit contribution PL(T i ), for example, for each receiving time (T i ) i＝j,…,N , or for the receiving time (T i ) i＝j,…,N .

[0171] For example, the process model calculates each unit contribution PL (T i ):

[0172] [Mathematical equation 13]

[0173]

[0174] Where |-| is the absolute value function.

[0175] Then, also in a second determination step 170, regardless of the way in which the unit contribution is calculated, the processing module 20 determines from each calculated unit contribution (PL(T i )) j＝1,…,N To determine the protection radius RP(TN )

[0176] To this end, the processing module 20 determines the protection radius RP (T N ):

[0177] [Mathematical equation 14]

[0178]

[0179] in:

[0180] -j is the calculation unit contribution PL(T i ),

[0181] - - is the sum of the index i varying between j and N, and

[0182] Then, in the transmission step 180, the output module 25 transmits the determined protection radius RP(TN) and, optionally, navigation parameters associated with the protection radius to a user or other electronic device (not shown).

[0183] According to a first variant of implementation, during the receiving step 110, the input module 17 also receives the protection radius PL from rare and normal errors. FF (T N )’s contribution.

[0184] According to a first variant of implementation, in a second determination step 170, the protection radius RP (T N ):

[0185] [Mathematical equation 15]

[0186]

[0187] A second variant of the embodiment is now proposed which can be combined with the first variant of the embodiment, for example. This variant can be used, for example, to determine the GNSS position and / or error bound S(T P ) is lost or fails every time T P For this moment, the method does not include the evaluation step 120. According to a second variant, in the first determination step 130, the estimated state vector X(T P ) is determined only by prediction, i.e., no adjustment is made. The above means that the gain KR(T N ) is set to zero.

[0188] According to a second variant, in said calculation step 140, the estimated error propagation matrix A(T N) and the influence matrix of boundary error B(T N ), for example according to the following equation:

[0189] [Mathematical equation 16]

[0190] A(T N )=F(T N )

[0191] B(T N )=0

[0192] Then, in the calculation step 150, each transfer matrix (V(P,i)) is calculated i＝j,…,P-1 , for example according to the following equation:

[0193] [Mathematical equation 17]

[0194]

[0195] Obviously, in the second calculation step 150, at most P-1 transfer matrices V(P,i) are calculated.

[0196] Then, in the writing step 160, the processing module 20 freezes the threshold shift register. In other words, the processing module does not shift the threshold shift register. In the writing step 160, the processing module 20 writes each transfer matrix (V(P,i)) calculated in the transfer shift register i＝j,…P-1 , without performing any prior shifting of the register.

[0197] Using the method described in this application, the protection radius RP (T N The protection radius RP (T) determined by the method according to the present application N ), the error in navigation parameters is greater than the protection radius RP(T N ) is, for example, less than 10 -7 / h.

[0198] Using the method described in this application, the protection radius RP (T N ) can be calculated simply and quickly. It is thus possible to implement the method described in this application on the electronic determination device 10 on the carrier 5.

[0199] The optional evaluation step 120 allows to estimate the gain KR(T N ) for real-time readjustment.

[0200] According to the method described in the first variant of the embodiment, the protection radius RP (T N) because it considers both boundary errors and rare and normal errors.

[0201] According to the method described in the third embodiment variant, the determination method is more robust since it allows to continue determining the protection radius even if the GNSS position is lost.

Claims

1. A method for limiting a sensed error on at least one navigation parameter of a carrier (5), in particular the position, velocity, attitude and / or heading of said carrier (5), said error being caused by a measurement error whose temporal evolution is unknown but whose one boundary is known and whose probability of not exceeding said boundary is also known; said boundary and said probability being known at a plurality of moments in the implementation of said method, said fact of limiting said sensed error being obtained by determining at least one protection radius associated with the navigation parameter of the carrier (5), said method being implemented by an electronic determination device (15) and comprising the following steps: - At the continuous receiving time (T N ) receiving (110) measurements from a sensor, such as a GNSS receiver, in particular a GNSS position, and at least one error bound (S(T) associated with the measurements from the sensor and with inertial measurements; N )): - For each consecutive reception time (T N ): - Determine (130) an estimated state vector (X(T)) of the vehicle by applying the measurements from the sensors and the inertial measurements to the estimation filter N ), for each receiving time ((T i ) i＝1，…，N ) The estimation filter includes a gain (K R (T i ))、Observation Matrix(H(T i )) and the propagation matrix of the state vector (F(T i )); -Based on the state vector (F(T N )) propagation matrix, estimate the filter gain (K R (T N )) and the observation matrix (H(T N )) calculates (140) the estimated error propagation matrix (A(TN)) of the state, and the propagation matrix (F(T N )) and gain (K R (T N )) Calculate the influence matrix of boundary error (B(T N )); -Based on the time of reception (T N )The previous moment (T N-1 ) calculates the N-1 transfer matrices (V(N-1,i) i＝1，…，N ), from the receiving time (T N ) and the estimated error propagation matrix (A(N)) from the receiving time (T N ) boundary error influence matrix (B(N)), to calculate (150)N transfer matrices (V(N,i) i＝1..，N ), N is the number of consecutive receiving moments ((T i ) i＝1，…，N ); as well as - by determining at least part of the reception time ((T i ) i＝j，…，N )Calculated unit contribution sum ((PL(T i )) i＝j，....，N ), from the estimated state vector (X(T N )) determines (170) a navigation parameter, and determines a protection radius (RP(T) associated with the navigation parameter N )), where each of the moments ((T i ) i＝j，…，N ) is associated with the unit contribution (PL(T i ) is based on the moment (T i ) calculated transfer matrix (V(N,i)) and at the receiving time (T i )Received error bound (S(T i )) is used to calculate.

2. The method according to claim 1, wherein for each reception time (T N ), the measurement result from the sensor includes M components, and where for each reception time (T N ), in the receiving step (110) and determining the estimated state vector (X(T N )) between step (130), the method further comprises an evaluation step (120), which comprises: - For each component of the measurement from the sensor, calculate the unity gain (K j (T N ));as well as -From M unity gain ((K j (T N )) j＝1,…,M )Evaluation gain(K R (T N )), In determining the estimated state vector (X(T N )) steps and calculate the error propagation matrix (A(T N )) and the influence matrix of boundary error (B(T N )) step, estimate the filter gain (K R (T N )) is the estimated gain.

3. The method according to claim 2, wherein for each receiving time (T N ), in the first calculation step (140), the receiving time (T N ) is equal to: F(T N )(IK R (T N )H(T N )) in: -F(T N ) is the receiving time (T N )’s state vector propagation matrix; -I is the identity matrix; -K R (T N ) is the gain of the estimated filter at the receiving time (T N );as well as -H(T N ) is the receiving time (T N ), At the receiving time (T N ) of the boundary error influence matrix (B(T N ))equal: F(T N )K R (T N )。 4. The method according to any one of the preceding claims, further comprising: For each receiving time (T N ), write each transfer matrix (V(N,i) in the transfer shift register i＝1,…,N ) and write each received error boundary (S(T N )) step (160), in the calculation step, the Nth transfer matrix (V(N,N)) is equal to the value at the receiving time (T N ) of the boundary error influence matrix (B(T N )), and by N )’s estimated error propagation matrix ((A(T N )) multiplied by the previous receiving time (T N-1 ) Each transfer matrix (V(N-1,j) calculated j＝1,…,N-1 ), to calculate each other first transfer matrix ((V(N,i) i＝j,…,N-1 ).

5. The method according to the preceding claim, wherein in the receiving step (110), if at the loss moment (T P ) does not receive the measurement result from the sensor, then the loss time (T P ) of the writing step (160) comprises: - a frozen 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. A method according to the preceding claim, wherein for the loss moment (T P ), in the first calculation step (140), at the loss time (T P ) of the estimated error propagation matrix (A(T P )) is equal to the loss moment (T P The propagation matrix (F(T P )), at the said loss moment (T P ) of the boundary error influence matrix (B(T P )) is equal to the zero matrix.

7. A method according to any one of the preceding claims, wherein for each reception time (T N ), in determining (170) the protection radius (RP(T N )) step, each unit contribution consists of at least one submatrix (V h,h (N,i),V h,v (N,i); V v,h (N,i),V v,v (N,i)) is determined from the submatrix at the receiving time (T N ) before the receiving time (T I ) is extracted from the transfer matrix (V(N,i)) calculated, Each unit contribution (PL i (T N )) preferably includes the submatrix (V h,h (N,i)) is the computation of the eigenvalue of one of the 8. The method according to any one of the preceding claims, wherein in the receiving step (110), for at least one receiving time (T N )Receive the protection radius (RP(T N ))'s contribution of rare and normal errors (PL FF (T N )), Determine (170) the protection radius (RP (T N )) step, including the contribution of rare and normal errors (PL FF (T N )) and unit contribution (PL i (T N ))Calculation of the sum between the sum.

9. A method for determining at least one protection radius (RP(T) associated with a navigation parameter of a carrier (5) N )) of the invention, wherein the electronic determination device (15) comprises technical means suitable for implementing the determination method according to any one of the preceding claims.

10. A computer program comprising software instructions which, when executed by a computer, are intended to implement the determination method of any one of claims 1 to 8.

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