Method and system for locating a carrier

Abstract

This location system (LOC) for an aircraft comprises an inertial navigation module (MNI) configured to provide an estimate of navigation quantities from inertial data (DI), a coarse extended Kalman filter (FKEG) and a fine extended Kalman filter (FKEF). It further comprises an effective covariance computation module (MCE) configured to estimate an effective covariance matrix of the coarse filter and to use it to initialize the estimated covariance matrix of the errors on the navigation quantities of the fine filter (FKEF).

Description

Description Title of the invention: Method and system for localizing a carrier Technical Field

[0001] The invention relates to the general field of hybridized inertial localization systems used by carriers, particularly in aircraft. Previous technique

[0002] The invention is more particularly relevant in the context of hybridized inertial navigation systems, the state of the art of which is described in document [1].

[0003] In a hybrid inertial localization system, the aircraft's navigation parameters (position, speed, and orientation) are obtained by temporally integrating the outputs provided by the inertial sensors (accelerometers, gyroscopes, etc.) of an inertial measurement unit (IMU).

[0004] These navigation systems generally use three main axes to define the aircraft's positions and speeds, namely: - an X axis (North South) and a Y axis (East West) which define a horizontal plane and; - a vertical Z axis, corresponding to the zenith, perpendicular to the horizontal X-Y plane.

[0005] We call: - horizontal track, maintenance of horizontal position and horizontal velocity (components along the X and Y axes) and aircraft attitude (roll, pitch and heading); and - vertical path, maintenance of vertical position and vertical velocity quantities (component along the Z axis).

[0006] As is known, the temporal evolution of inertial navigation errors of the horizontal and vertical paths are different.

[0007] Horizontal track navigation errors can exhibit oscillating behavior over time. The more inaccurate the aircraft's initial estimation, the more likely these oscillating errors are to amplify over time, creating periodic deviations from the intended trajectory.

[0008] Navigation errors in the vertical channel can diverge exponentially over time.

[0009] In order to accurately initialize attitudes, and thus minimize the drift of inertial errors, it is known to use, during the alignment phase, an extended Kalman filter, for example: - zero-speed hybridization; or - a center-on-center hybridization, for example to initialize the hybrid navigation of an aircraft's center from the hybrid navigation of an aircraft carrier's center; or - a hybrid system using an external position sensor, for example GPS.

[0010] At the start of alignment, the attitude error can be significant, for example, on the order of 180 degrees between the true heading and the estimated heading initialized to zero. Under these conditions, it is known to use, during this alignment phase, a coarse Kalman filter that does not use the assumption of small angles (sin(x)=x and cos(x)=l) for roll, heading, or pitch.

[0011] Once the coarse alignment is complete (on a timing criterion or convergence of covariances), it is known to implement an alignment phase which uses another Kalman filter, called the fine Kalman filter, which uses the small angle hypothesis.

[0012] But the transition from the coarse Kalman filter to the fine Kalman filter takes time: indeed, the convergence of errors and associated correlations achieved during the coarse alignment is lost, and the fine Kalman filter needs time to reconverge and re-estimate these correlations.

[0013] This disclosure proposes a localization system and method that does not present this drawback. Description of the invention

[0014] To this end, this disclosure proposes an aircraft location system comprising: - an inertial navigation module configured to provide an estimate of aircraft navigation quantities from inertial data provided by an inertial measurement unit; - two extended Kalman filters, each configured, when active, to: (i) fuse navigation quantities with data produced by at least one hybridization sensor; and (ii) calculate an estimated covariance matrix of the errors on these quantities; - one of the two filters, called the "coarse" filter, being configured to use a less complete error model than an error model used by the other filter, called the "fine" filter, and to take into account the non-linearities of the trigonometric functions, said localization system being characterized in that: - it includes an effective covariance calculation module configured to estimate an effective covariance matrix of the coarse filter; and in that: - it is configured to initialize said estimated covariance matrix of the fine filter from said effective covariance matrix.

[0015] Correspondingly, this disclosure proposes a method for localizing an aircraft implemented by a system comprising an extended Kalman filter, referred to as "coarse", and an extended Kalman filter referred to as "fine", the coarse Kalman filter being configured to use a less complete error model than an error model used by the "fine" filter, and to take into account the non-linearities of trigonometric functions, the method comprising: - an estimation of aircraft navigation quantities from inertial data provided by an inertial measurement unit; - steps implemented by the coarse Kalman filter for: (i) merge navigation parameters with data produced by at least one hybridization sensor; and (ii) calculate an estimated covariance matrix of the errors on these quantities; - an estimate of an effective covariance matrix of the coarse filter; - an initialization of an estimated covariance matrix of errors on the navigation quantities of the fine filter from said effective covariance matrix; - steps implemented by the fine Kalman filter for: (i) merge navigation quantities with data produced by said at least one hybridization sensor; and (ii) update its estimated covariance matrix of errors on these quantities.

[0016] In this document, the coarse filter is configured to account for the nonlinearities of trigonometric functions: This filter does not rely on the assumption of small angles. It is more robust to large angular errors than the fine filter. The coarse filter ensures optimal accuracy even when angles exceed 10 degrees.

[0017] The system and method of localizing this disclosure are remarkable in particular in that they propose to integrate a function for calculating the effective covariance into the real-time hybridized inertial localization software.

[0018] The system and method for localizing this disclosure are also noteworthy in that they use the effective covariance of the errors at the end of the coarse alignment to finely initialize the covariances estimated at the beginning of the fine alignment. Thus, initializing the estimated covariance matrix of the fine Kalman filter allows this filter to avoid wasting time re-estimating the correlations between the errors.

[0019] The system and method for locating this disclosure enable faster alignment, thus allowing the carrier to obtain an accurate navigation solution more quickly. This time saved can, for example, allow a commercial aircraft to take off sooner.

[0020] In one embodiment, the effective covariance module uses two different state models of the inertial localization system, namely: - a true-world model; and - said model of the coarse filter.

[0021] Equations for an effective covariance modulus that can be used in one embodiment of this disclosure are given in the Annex.

[0022] In one embodiment, the inertial navigation module is configured to activate at least one of the Kalman filters based on a hybridized inertial localization mode received from a sequencing module.

[0023] In one embodiment, the sequencing module determines the location modes according to a sequence defined in a sequencing diagram. For example, the sequence includes: - a standby phase; - an initialization phase for the speed and position of the aircraft; - a rough alignment phase; - a fine alignment phase; and - a navigation phase, - the coarse Kalman filter being activated during the coarse alignment phase; - the fine Kalman filter being activated during the fine alignment and navigation phases; - the estimated covariance matrix of the fine filter being initialized from said effective covariance matrix at the time of the transition between the coarse alignment phase and the fine alignment phase.

[0024] In one embodiment, the coarse Kalman filter is configured to send the effective covariance module an indicator representing the use, by said coarse Kalman filter, of the data produced by said at least one sensor for fusion with the navigation quantities. This indicator indicates, for example, whether the data from the hybridization sensors are used at each step of the coarse Kalman filter.

[0025] All or part of the localization process steps can be implemented by computer; preferably all steps of the process are implemented by computer.

[0026] Thus, the invention also relates to a computer program comprising code instructions which, when implemented, allow the execution of the steps of a localization process.

[0027] The aforementioned features and advantages, as well as others, will become apparent upon reading the detailed description that follows. This detailed description refers to the drawings and the Annex. Brief description of the drawings

[0028] The attached drawings are schematic and are primarily intended to illustrate the principles of the presentation.

[0029] In these drawings, from one figure to another, identical elements (or parts of elements) are identified by the same reference symbols.

[0030] [Fig. 1] Figure 1 represents an example of the implementation of the location system according to a particular embodiment of this disclosure,

[0031] [Fig. 2] Figure 2 illustrates an effective covariance modulus that can be used in the system of Figure 1,

[0032] [Fig. 3] Figure 3 illustrates in flowchart form the main steps of a localization process according to a particular embodiment of this disclosure,

[0033] [Fig. 4] Figure 4 represents an example of a sequencing diagram,

[0034] [Fig. 5] Figure 5 schematically illustrates an example of a computer enabling the implementation of the localization process.

[0035] The appendix provides equations for an effective covariance modulus that can be used in one embodiment of this disclosure. Description of the implementation methods

[0036] Figure 1 represents an example of an aircraft localization LOC system.

[0037] The LOC localization system receives inertial data DI from an inertial measurement unit UMI, namely in this example, an angular velocity Q and a specific force fs representative of the aircraft's acceleration.

[0038] In the embodiment described here, the inertial measurement unit UMI is of the gyrocompass class, which means that it autonomously determines the heading of the system, by measuring a projection error of its Earth's angular velocity, with a drift accuracy relatively small compared to the Earth's angular velocity (about 15 degrees per hour).

[0039] The inertial data (ID) is more precisely supplied as input to an inertial navigation module (IMM) of the localization system (LOC) configured to continuously provide an estimate of the X navigation quantities. nav of the aircraft.

[0040] In the embodiment described here, these navigation quantities X nav include: - a three-dimensional POS position; - a three-dimensional VIT speed; - a three-dimensional ATT attitude; - the specific force fs; and - the angular velocity Q.

[0041] Navigation quantities X nav These values ​​are supplied as input to at least one MNP module that consumes these quantities, for example a navigation and piloting module, a display module, a recording module, a black box...

[0042] Due to the inherent drifts of inertial sensors, the X estimates nav errors produced by the inertial navigation module require corrections.

[0043] To this end, the LOC localization system includes two Kalman filters, FKEF and FKEG, each configured to merge X navigation quantities when active. nav originating from the inertial measurement unit (IMU) with data produced by one or more CHi hybridization sensors.

[0044] This hybridization mechanism, known to those skilled in the art, allows the inertial system's drift on the horizontal track to be corrected by adjusting the X estimates. nav by merging the navigation quantities X nav and data from the CHi hybridization sensor(s).

[0045] In the example embodiment, these CHi hybrid sensors include a BA baro-altimeter, a DV motion detector configured to measure zero velocity and an external CP position sensor, for example a GPS, a high-resolution radar or an optical system.

[0046] More specifically, in the embodiment described here, the LOC localization system includes two alignment filters, namely a first extended Kalman filter FKEG called "coarse" and a second extended Kalman filter FKEF called "fine".

[0047] In this document, the terms "coarse" and "fine" are to be understood in a relative sense. In other words, the fine extended Kalman filter FKEF uses a more complete error model MODFKF than the error model MODFKG of the coarse extended Kalman filter FKEG.

[0048] The other fundamental difference between the coarse filter and the fine filter is that the coarse filter tolerates large attitude errors (typically up to 180 degrees), whereas the fine filter only tolerates small attitude errors (typically less than 10 degrees).

[0049] In the embodiment described here, after a general initialization phase, the inertial navigation module (IMM) activates one or the other of these filters depending on a hybridized inertial localization mode m (p received from an MSEQ sequencing module (or sequencer). [00δΦ] In the embodiment described here, the MESQ sequencing module is configured to manage the transition between different phases of the inertial navigation system.

[0051] In the embodiment described here, the MSEQ sequencing module determines the hybridized inertial localization modes according to a sequence defined in a DS sequencing diagram shown in Figure 4, each mode being associated with a specific phase of the inertial navigation system.

[0052] For example, the sequence includes: - a PH_V standby phase; - a PHJNIT phase for initializing the speed and position of the aircraft; - a PH_AG rough alignment phase; - a fine alignment phase PH_AF; - PH_NAV navigation phase.

[0053] More specifically, in the embodiment described here, the inertial navigation module (IMM): - does not activate either filter when it receives a mode representative of a standby or initialization phase of the aircraft's speed and position, for example from an external source, - activates the coarse extended Kalman filter FKEG when it receives an m mode (p representative of a rough alignment phase, - activates the extended Kalman filter fine FKEF when it receives an m mode (p representative of a fine alignment phase or a navigation phase.

[0054] As mentioned previously, each of the two Kalman filters is used to hybridize the DI inertial data provided by the UMI inertial measurement unit with the data provided by the CHL hybridization sensor(s).

[0055] More specifically, each of these FKEG and FKEF filters is configured to receive X navigation quantities as input navproduced by the MNI inertial navigation module and to send back, to this MNI module, 5X corrections nav on navigational quantities X nav .

[0056] In the embodiment described here, the 8X corrections nav include: - an 8POS correction of the three-dimensional POS position; - a three-dimensional 8VIT speed correction; - an 8ATT correction of the three-dimensional ATT attitude; - a correction of the specific force; and - a correction 5. of the angular velocity Q. [00δV] The Kalman filters FKEG and FKEF are extended filters. Recall that an extended Kalman filter is a statistical estimation algorithm that calculates, in addition to estimates of attitude, velocity, and horizontal track position, an estimated covariance matrix of the errors on these quantities. By calculating the square roots of the diagonal terms of this covariance matrix, we obtain the estimates of the standard deviations of the errors on these quantities.

[0058] Recall that, for a given quantity, the error s on that quantity theoretically corresponds to the difference between the true value of that quantity and its estimate by the system. Correction 5 is an estimate that the extended Kalman filter calculates to adjust the estimate of the quantity in order to minimize the error s.

[0059] Note: - an sPOS error of the three-dimensional POS position; - an error sVIT speed VIT in three dimensions; - an error£7irr of the three-dimensional ATT attitude; - an error efs of the specific force fs; - an error sQ of the angular velocity Q; and - snav = [sPOS sVlT sATT sfs efl] 7 the concatenated vector of navigation errors.

[0060] The 8X rating nav is used for simplification for both filters but a person skilled in the art understands that each filter produces its own corrections.

[0061] The following notation is used: £[X] is the mathematical expectation of the quantity X; and X is the estimate of the quantity X.

[0062] Each of the extended Kalman filters FKEF, FKEG calculates an estimate of the navigation error covariance matrix: filter pr ri Penav = E [ £nav - £nav ]

[0063] As is known to those skilled in the art, the square roots of the diagonal terms in the covariance matrix are the estimated standard deviations of navigation errors: filter > r filter filter filter filter filter °eNAV ~ L°fPOS °eVIT °eATT °efs °sl 1 and the non-diagonal terms of this matrix provide an estimate of the statistical correlations between the different errors.

[0064] In one embodiment of the invention, the navigation error covariance matrix o e f ^v estimated by the FKEF fine alignment filter selected according to the mode m (p is sent to the MNP module, which consumes the X navigation quantities na "Navigation data, for example to a navigation and piloting module.

[0065] This matrix can be used to initialize the hybridized inertial navigation of a missile or other type of payload: projectile, guided munition, aircraft on an aircraft carrier, helicopter on a frigate,...

[0066] To this end, in the embodiment described here, the coarse extended Kalman filters FKEG and fine extended Kalman filters FKEF send their matrix to the inertial navigation module, and this communicates it to the module consuming the X navigation quantities nav , in conjunction with these magnitudes.

[0067] According to this disclosure, the fine extended Kalman filter FKEF uses a more complete MODFKF error model than the MODFKG error model of the coarse extended Kalman filter FKEG.

[0068] In other words, the state vector of the fine filter FKEF includes all the terms of the state vector of the coarse filter FKEG and additional terms.

[0069] In other words, the state vector of the coarse filter FKEG is a truncated and large angular error adapted version of the state vector of the fine filter FKEF.

[0070] For example, in the embodiment described here, the fine filter FKEF includes the error terms of the inertial measurement unit (IMU) in its state vector, but the coarse filter FKEG does not. Only the fine filter FKEF is capable of accurately estimating navigation errors. In a particular embodiment, these error terms constitute the only difference between the fine and coarse filters.

[0071] Indeed, in the embodiment described here, the compatible "large angles" mathematical formulation of large initial angular errors used by the coarse Kalman filter FKEG does not allow the UMI error states to be included in the state vector of the coarse Kalman filter.

[0072] Because of this reduced state vector, the navigation error covariance matrix estimated by the coarse Kalman filter is not representative of the actual navigation error statistics at the end of coarse alignment.

[0073] Thus, even if the estimated navigation state at the end of coarse alignment is equal to the estimated navigation state at the beginning of fine alignment, the covariances estimated by the coarse Kalman filter FKEG at the end of coarse alignment cannot be used to initialize the covariance matrix of the fine Kalman FKEF at the beginning of fine alignment.

[0074] As mentioned earlier, in the current state of the art of inertial navigation systems using a coarse Kalman filter and a fine Kalman filter, the covariance matrix of the fine Kalman filter is initialized to a diagonal matrix, and does not model any correlation between the different error states.

[0075] On the contrary, the LOC localization system includes an effective covariance calculation MCE module configured to calculate an effective covariance matrix P^ v constituting a fine and complete estimate (diagonal terms and non-diagonal correlation terms) of the error covariances at the output of the coarse alignment filter FKEG, this effective covariance matrix P^ v en f in from the coarse alignment phase is used to finely initialize the estimated covariance matrix of the FKEF filter at the beginning of the fine alignment phase.

[0076] For further information on the methods for calculating effective covariance, those skilled in the art may refer to documents [2] and [3]. It should be noted that a principle of the effective covariance method is to use two different error state models of the inertial localization system.

[0077] In the embodiment described here, these two models include: (i) a real-world MODMV model; and (ii) the MODFKG model used by the extended Kalman filter FKEG.

[0078] In the embodiment of Figure 1, the MCE module, more precisely represented in Figure 2, includes its own instance of the MODFKG model. The MCE module for calculating effective correlation also includes a MODMV model of the real world whose state vector X vrai includes all the components of the FKEF filter vector, plus other components, the modeling of the true world being more detailed and more precise than that of the filter world.

[0079] For example, the MODMV true world model includes: - a real-world temporal propagation model: dX Vrai / dt = F vrai ·X vrai + w vrai r true* ^true " H w TRUE / - a model for observing the real world: Y vrai = H vrai ·X vrai + v vrai .

[0080] For example, the MODFKG model of the coarse extended Kalman filter FKEG includes: - a time propagation model of the coarse filter: dX filtre / dt = F filtre ·X filtre + w filtre - a model for observing the coarse filter: Y filtre = H filtre ·X filtre + v filtre where X filtre is the state vector used in the coarse Kalman filter FKEG for inertial hybridization with external sensors.

[0081] With the following notations: X state vector; Y is the observation vector; F: evolution matrix; H: observation matrix; w: noise of evolution; v. observation noise; K filtre: hybrid filter gain matrix P covariance matrix.

[0082] As is known, the evolution matrix F and observation matrix H of the MODMV model of the real world and the MODFKG model of the coarse Kalman filter depend on the trajectory and therefore on the navigation quantities X NAV provided by the MNI inertial navigation module.

[0083] The gain matrix of the hybridization filter, denoted K filtre varies over time: Kalman gains depend on the estimated covariance matrix, which itself varies over time.

[0084] In the embodiment described here, the MCE module for calculating effective covariance recursively calculates the effective covariance matrix P^, defined as the matrix of the effective error at the output of the coarse Kalman filter FKEG: Effective error s eff = X vrai - X filtre ; Effective covariance matrix Peff = E[s eff .s eff T ]

[0085] In the embodiment described here, the estimated covariance matrix of the FKEG fine filter P^^ l e is initialized from said effective covariance matrix P^ v au moment of transition between the coarse alignment phase and the fine alignment phase. In other words, the MNI module performs a simple copy of the covariance matrix P^ v en f in of coarse alignment, on the matrix P^^ l e at the beginning of the fine alignment.

[0086] In the embodiment described here, the REGFKG module designates the composition of the state vector of the coarse Kalman filter and the parameterization of the matrices: - initial covariance of navigation errors, denoted PO; - covariance of evolution noises, denoted Q - covariance of observation noises, denoted R.

[0087] The PMV module designates the statistical error parameters of the real-world sensors, namely, in this embodiment, the error statistics of the inertial measurement unit UMI and that of the hybridization sensors CHi (for example: motion detector DV, baro-altimeter BA, and position sensor CP).

[0088] In one embodiment, the coarse Kalman filter FKEG is configured to send an indicator IND to the effective covariance MCE module REC This indicator shows the recalibration of the hybridized inertial localization to what extent the data provided by the CHi hybridization sensors are used by the coarse Kalman filter FKEG for hybridizing the DI inertial data. For example, this indicator shows whether the hybridization sensor data is used at each step of the coarse Kalman filter FKEG.

[0089] An example of the use of the IND index RECis detailed in the Appendix to section 6.3 Registration by measurement of the covariance matrix of concatenated states.

[0090] Figure 3 describes the different steps of an aircraft location process in accordance with a particular embodiment of this disclosure.

[0091] This process includes a general step E10 of processing, by the inertial navigation module MNI, a hybridized inertial localization mode m (p received from the MSEQ sequencing module.

[0092] When the mode is representative of a standby phase or an initialization phase of the aircraft's speed and position, the inertial navigation module MNI deactivates the coarse filter FKEG and the fine filter FKEF (step E20).

[0093] During an E30 step, the inertial navigation module (IMM) begins to estimate the X navigation quantities navof the aircraft from the inertial DI data provided by the inertial measurement unit UMI.

[0094] When the mode m / p is representative of a rough alignment phase; the inertial navigation module (IMM) activates the coarse FKEG filter (step E40) so that it: (i) merges the navigation quantities X nav ) from the inertial measurement unit (IMU) with data produced by at least one hybridization sensor (HCi); and (ii) calculates an estimated covariance matrix (p^nav 6 errors on these quantities (X nav ).

[0095] The inertial navigation module MNI starts (step EδΦ) the MCE module to estimate the covariance matrix of the coarse filter FKEG from a MODFMV model of the real world and a MODFKG model of the coarse filter FKEG.

[0096] Navigation quantities X navcorrected by the coarse FKEG filter as well as the estimated covariance matrix of the errors on these quantities calculated by this filter are sent (step E60) to the MNP module which consumes these quantities.

[0097] When the mode m tf) is representative of a fine alignment phase; the inertial navigation module MNI initializes (step E70) the estimated covariance matrix of the fine filter FKEF from said effective covariance matrix P^ v calculated by the MCE module at the end of the rough alignment.

[0098] The MNI inertial navigation module then activates the FKEF fine filter (step E80) so that it: (i) merges navigation quantities (X na ) from the inertial measurement unit (IMU) with data produced by the hybridization sensor(s) (CHi); and (ii) calculates an estimated covariance matrix (p„ e ) errors on these quantities (X nav ).

[0099] Navigation quantities X nav corrected by the fine filter FKEF using the data from the CHi sensors as well as the estimated covariance matrix of the errors on these quantities calculated by this filter are sent (step E90) to the MNP module which consumes these quantities.

[0100] Figure 5 represents the hardware architecture of an ORD computer that can be used to implement a localization process in accordance with this disclosure.

[0101] This computer includes, in particular, a processor 10, a RAM 11, a ROM 12 and means of communication 13.

[0102] Read-only memory 12 constitutes a recording medium within the meaning of this disclosure. It contains a computer program PG that conforms to this disclosure.

[0103] This computer program PG includes instructions for performing the steps of a localization process when said program is run by the computer ORD.

[0104] The PG program defines functional modules of the ORD computer, which rely on or control the hardware elements 10, 11, 13 mentioned previously, and for example: - an inertial navigation module (IMM) configured to provide an estimate of X-ray navigation quantities nav of the aircraft from inertial DI data provided by an inertial measurement unit (IMU); -two extended Kalman filters FKEG, FKEF, each configured to, when active: (i) merge the navigation quantities X nav with data produced by at least one hybridization sensor (CHi); and (ii) calculate an estimated covariance matrix Pnav 6 errors in these quantities X nav one of the two FKEG filters, called "coarse", uses a MODFKG model that is less complete than the MODFKF model used by the other FKEF filter, called "fine" >>, -an MCE module for calculating effective covariance configured to estimate an effective covariance matrix of the coarse FKEG filter; and - an initialization module for an estimated covariance matrix of the fine filter FKEF from said effective covariance matrix P^ v -

[0105] References: [1]: Strapdown Inertial Navigation Technology, David Titterton, John L. Weston, John Weston, IET, 2004 - 558 pages [2]: Optimal Inertial Navigation and Statistical Filtering - Pierre Faurre, DUNOD 1971, Chapter 4, Supplement 3: Sensitivity of a Kalman-Bucy Filter. [3]: Strapdown Analytics Part 2, Paul G. Savage, Strapdown Associates 2000, Chapter: Covariance Simulation. APPENDIX Example equations for an example module for calculating effective covariance. 1. Notations: nF: dimension of the filter world state vector nV: dimension of the true world state vector nY: is the dimension of the measurement vector (the same for the real world and for the filter world) 5XF: filter world state vector, of dimension nF 5XV: true world state vector, of dimension nV SX: estimated value of an error SX: true value of an error ε: effective error F : vector of concatenated states, of dimension nF + nV SXV ξ is the concatenation of: • δX̂F: estimated values ​​of the filter world states • δXV: true value of the true world states 2. Example of a vector of error states in the filter world In a particular embodiment, the error state vector of the filter world is defined as: δDEPδV δΦ x ÔXF δΦ y ÔPROT X ÔPROTy δPG Z ÔDEP is the displacement error, of dimension 3 δV is the 3-dimensional velocity error oh x is the attitude error along the North axis, of dimension 1 ô(P y is the attitude error along the West axis, of dimension 1 ÔPROT X is the projection error of the Earth's rotation along the North axis, of dimension 1 ÔPROTy is the projection error of the Earth's rotation along the West axis, of dimension 1 ÔPG Z is the vertical acceleration error, of dimension 1 => The error state vector of the filter world ÔXF is therefore of dimension 3+3+1+1+1+1+1 = 11 = nF 3. Example of a vector of error states of the yrai world In a particular embodiment, the true-world error state vector is defined as: δr δV δΦ ÔDEP ÔXV = ÔPROT X ÔPROTy ÔPG Z ÔBa δDg δr is the position error in a local geographic coordinate system, of dimension 3; δV is the velocity error in a local geographic coordinate system, of dimension 3; 5 is the attitude error in a local geographic coordinate system, of dimension 3; ÔDEP is the displacement error in a local geographic coordinate system, of dimension 3 ÔPROT X is the projection error of the Earth's rotation along the North axis, of dimension 1 SPROTy is the projection error of the Earth's rotation along the West axis, of dimension 1 5PG Z is the vertical acceleration error, of dimension 1 ÔBa is the accelerometer bias error in the measurement frame, of dimension 3. ÔDg is the gyro drift error in the measurement frame, of dimension 3. => The true-world error state vector ÔXV is therefore of dimension 3+3+3+3+1 +1+3+3 = 20 = nV The dimension of the error state vector of the true world 5XV is therefore significantly larger than that of the error state vector of the filter world 5XF. 4. Example of a discrete noise vector In one embodiment, the concatenated true-world discrete noise vector oo is defined as the concatenation of the true-world state noise and measurement noise vectors: W v a> =: vector of concatenated discrete noises in the true world, of dimension V v nV + nY oo is the concatenation of: • Wv: discrete state noise vector of the true world, of dimension nV • Vv: discrete measurement noise vector of the true world, of dimension nY WUv: true user noise vector, of dimension nU <t>F: transition matrix of the filter world, of dimension nF x nF <t>v: true-world transition matrix, of dimension nV x nV HF: measurement matrix of the filter world, of dimension nY x nF; Hv: measurement matrix of the true world, of dimension nY x nV; KF: gain matrix of the filter world, of dimension nF x nY 5. Example of conversion matrix Since the dimension of the filter world state vector is not equal to the dimension of the true world state vector (nF + nV) in the embodiment described here, a conversion matrix is ​​used to link the two estimated state vectors: 8 KV = C VP .$Œ CVF is a rectangular matrix of dimension nV x nF The CVF matrix is ​​defined block by block using the following Matlab script (registered trademark): C VF=zeros(n V,nF); C VF(mv_dr,mf_dr)=ld3; C VF(mv_dv, mf_dv)=ld3; C VF(mv_phi, mf_phi)=ld3; C VF(mv_dep, mf_dep)=ld3; CVF(mv_protx,mf_protx)=1; CVF(mv_proty,mf_proty)=1; C VF(mv_pgz, mf_pgz)= 1; CVF(mv_ba,mf_ba)=ld3; C VF(mv_dgc, mf_dgc)=ld3; Id3 is the 3-dimensional identity matrix. Note: 11" = E\ / t ■ / t T , the covariance matrix of the concatenated states. n is a square matrix of dimension (nF + nV) 6. General equations for updating the effective covariance: 6.1 Initialization of the covariance matrix of concatenated states: In one embodiment, the initialization of matrix n is performed as follows: Within the framework of an extended Kalman filter operating on gaps, <5 F o can be taken to be equal to the zero vector. PVo is the initial covariance matrix of true-world errors. 6.2 Temporal prediction of the covariance matrix of concatenated states: In one embodiment, the covariance matrix of the concatenated states is propagated using the following formula: And so: EK.<] 0 With: Q v 0 A = E\CO- &>' ] = 0 Ek<] 0 R v A is the covariance matrix of concatenated state and measure noises of the true world. A is a square matrix of dimension (nV + nY) 0 0 0 Recall that: = and r = . o 4> v I 0 <t>F is the transition matrix of the filter world <t>v is the true world transition matrix Qv is the true-world evolution noise covariance matrix Rv is the true-world measurement noise covariance matrix The transition matrix $> F is the matrix exponential of the evolution matrix FF times the time step dt: $> F = expm(FF.dt) FF is the continuous evolution matrix of the filter world. The FF matrix can be defined block by block in the Matlab script below: FF=zeros(nF,nF); FF(mf_dv, mf_phi)=-A (fg); FF(mf_phix, mf_protx)=wt; FF(mf_phiy, mf_proty)=wt;FF(mf_dep, mf_dv)=ld3; FF(mf_dvz, mf_pgz)= 1; wt is the norm for Earth's angular velocity. fg is the specific force in the local geographic landmark The transition matrix <t>v is the matrix exponential of the evolution matrix FV times the time step dt: <t>v = expm(FV.dt) FV is the continuous evolution matrix of the filter world. The FV matrix is ​​defined in blocks in the Matlab script (registered trademark) below: FV=zeros(n V, n V); FV(mv_dr,mv_dr)=-[A(rho)+A(Vg)*Meta]; FV(mv_dr,mv_dv)=ld3; FV(mv_dv,mv_phi)=-A(fg); FV(mv_dv,mv_dv)=A(Vg)*Mrho-A(rho+2*Wtig); FV(mv_dv,mv_dr)=Mg+2*A(Vg) *A(Wtig) *Meta; FV(mv_phi,mv_phi)=-A (Wgig); FV(mv_phi,mv_dv)=-Mrho; FV(mv_phi,mv_dr)=-A(Wtig)*Meta; FV(mv_phix,mv_protx)=wt; FV(mv_phiy,mv_proty)=wt; FV(mv_dep,mv_dv)=ld3; FV(mv_dv,mv_ba)=Tgm; FV(mv_dvz,mv_pgz)=1; FV(mv_dv,mv_bam)=Tgm; FV(mv_phi,mv_dgc)=Tgm; FV(mv_phi,mv_dgm)=Tgm; rho is the angular velocity Wgtg of the local geographic frame relative to the Earth frame, projected onto the local geographic frame Vg is the velocity relative to the Earth's frame of reference, projected onto the frame of reference geographicMg is the matrix for converting positional errors to gravity errors Wtig is the angular velocity of the Earth's frame of reference relative to the inertial frame of reference, projected onto the local geographic frame of reference. Meta is the conversion matrix of linear position errors dr to angular errors on the matrix Tgt Mrho is the conversion matrix of velocity errors to errors in angular velocity rho 6.3 Registration by measuring the covariance matrix of concatenated states: In the embodiment described here, the concatenated covariance after the registration phase is given by: n t a +1 / t+1 = E[ +1 / k+1 • a +1 / t+1 Use If IND REC =1 H, a recalibration is indeed performed at this time step: Evolution equation of the covariance matrix of the concatenated states at the time of registration by measurement: And so: n" +1 / t+1 =.n;' +I / VA. V' K F H V As a reminder: Otherwise, if IND REC = 0 / / no recalibration at this time step: In the case of a time step without measurement recalibration, we simply have: r 1 A rfc+l / fc+l =IT L k+ k End Yes. HF is the observation matrix of the filter world, of dimension nY*nF The HF matrix can be defined in blocks using the following Matlab script (trademarked): HF=zeros(nY,nF); HF(:,mf_dep)=ld3;Hv is the observation matrix of the filter world, of dimension nY*nV The matrix Hv can be defined blockwise in the following Matlab script: HV=zeros(nY,nV); HV(:,mv_dep)=ld3; KF is the gain vector of the Kalman filter 6.4 Extraction of the effective covariance from the covariance matrix of the concatenated states: The true-world effective covariance can be defined as the covariance of the true-world effective error: PV eff = E[SV -£V T ] The effective covariance matrix on the true-world error states is calculated from the covariance matrix of the concatenated states using the following formula: PV eff =AV-n-AV T With: AV = −C VF / ] AV is a matrix of dimension nVx(nF+nV)< / t> < / t> < / t> < / t> < / t> < / t>

Claims

Tl Demands

1. Aircraft Localization System (LOC) comprising: - an inertial navigation module (MNI) configured to provide an estimate of navigation quantities (X na „) of the aircraft from inertial data (ID) provided by an inertial measurement unit (IMU); - two extended Kalman filters (FKEG, FKEF), each configured to, when active: (i) merge navigation quantities (X na ) with data produced by at least one hybridization sensor (CHi); and (ii) calculate an estimated covariance matrix (Pnav 6 ) errors on these quantities (X na „); - one of the two filters (FKEG), called "coarse", being configured to use an error model (MODFKG) less complete than an error model (MODFKF) used by the other filter (FKEF) called "fine", and to take into account the non-linearities of trigonometric functions, - said localization system (LOC) being characterized in that: - it includes an effective covariance calculation module (MCE) configured to estimate an effective covariance matrix (P^f) of the coarse filter (FKEG); and in that: - it is configured to initialize said fine filter covariance matrix (FKEF) from said effective covariance matrix (P^)-

2. Aircraft localization system (LOC) according to claim 1, wherein said effective covariance module (MCE) uses two different state models of the inertial localization system, namely: - a real-world model (MODMV); and - said model (MODFKG) of the coarse filter (FKEG).

3. Aircraft localization system (LOC) according to claim 1 or 2 wherein said inertial navigation module (MNI) is configured to activate at least one of said Kalman filters (FKEG, FKEF) according to a hybridized inertial localization mode (m^) received from a sequencing module (MSEQ).

4. Localization system (LOC) according to claim 3 wherein the sequencing module determines said hybridized inertial localization modes according to a sequence defined in a sequencing diagram.

5. Localization system (LOC) according to claim 4, wherein said sequence comprises: - a standby phase (PH_V); - a phase (PH_INIT) for initializing the speed and position of the aircraft; - a rough alignment phase (PH_AG); - a fine alignment phase (PH_AF); - a navigation phase (PH_NAV), - the coarse Kalman filter (FKEG) being activated during the coarse alignment phase (PH_AG); - the fine Kalman filter (FKEF) being activated during the fine alignment (PH_AF) and navigation (PH_NAV) phases; - the estimated covariance matrix of the fine filter (FKEG) being initialized from said effective covariance matrix (P^f V ) at the time of the transition between the coarse alignment phase (PH_AG) and the fine alignment phase (PH_AF).

6. Aircraft localization (LOC) system according to any one of claims 1 to 5, wherein the coarse Kalman filter (FKEG) is configured to send an indicator (JND) to the effective covariance module (MCE). REC) representative of the use, by said coarse Kalman filter (FKEG), of said data produced by said at least one sensor (CHi) for fusion with the navigation quantities (X nav ).

7. A method for localizing an aircraft implemented by a system (LOC) comprising an extended Kalman filter (FKEG), referred to as "coarse," and an extended Kalman filter (FKEF), referred to as "fine," the coarse Kalman filter (FKEG) being configured to use a less complete error model (MODFKG) than an error model (MODFKF) used by the "fine" filter (FKEF), and to take into account the nonlinearities of trigonometric functions, the method comprising: - an estimate (E30) of navigation quantities (X na „) of the aircraft from inertial data (ID) provided by an inertial measurement unit (IMU); - steps (E40) implemented by the coarse Kalman filter (FKEG) for: (i) merge navigation quantities (X na ) with data produced by at least one hybridization sensor (CHi); and (ii) calculate an estimated covariance matrix (Pnav 6 ) errors on these quantities (X na „); - an estimate (EδΦ) of an effective covariance matrix (P^ ) of the coarse filter (FKEG); - an initialization (E70) of an estimated covariance matrix of errors on the navigation quantities of the fine filter (FKEF) from said effective covariance matrix (P^); - steps (E80) implemented by the fine Kalman filter (FKEF) for: (i) merge navigation quantities (X na ) with data produced by said at least one hybridization sensor (CHi); and (ii) update its estimated covariance matrix (Pnav 6 ) errors on these quantities (X nav ).

8. Computer program (PG) comprising instructions which, when the program is executed by a computer (ORD), cause the computer to implement a localization method according to claim 7.

9. Computer-readable recording medium (12) on which a computer program (PG) according to claim 8 is recorded.

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