Inertial localization method implementing a gravimetric correlation and associated device

Abstract

One aspect of the invention relates to a method for achieving inertial localization of a carrier using a stochastic filter of recursive-Bayesian type implemented by an inertial localization device, the method comprising a plurality of cycles, each cycle comprising a propagation step and, when a measurement is available, an updating step, in which method, in the propagation step, the propagation is performed using a propagation model taking into account at least one component of a matrix of the spatial gradients of the gravity vector, which matrix is delivering using an enriched gravimetric model.

Description

DESCRIPTION TITLE: Inertial Localization Method Implementing Gravimetric Correlation and Associated Device TECHNICAL FIELD OF THE INVENTION The technical field of the invention is that of inertial localization. The present invention relates to an inertial localization method and, in particular, an inertial localization method using gravimetric correlation by error propagation. TECHNOLOGICAL BACKGROUND OF THE INVENTION Estimating the position of a moving object without GNSS assistance can be achieved using equipment consisting of a gravimeter and an inertial navigation system. A series of (position, gravity) pairs is sought in a gravimetric map representing the area traversed, based on measurements from the gravimeter and the position estimated by the navigation system to correct the position, where the gravimetric signal is a gravimetric functional such as gravity, gravitation, gravity anomaly, or gravity perturbation.Several methods exist for searching for position-gravimetric signal pairs on a map. The first method relies on a simplified model of position error. Over a given time interval, this error is modeled as an unknown constant. This constant is estimated by shifting the estimated trajectory within the search area and looking for a peak correlation between the values ​​read on the map along the shifted trajectory and the measurements taken over that time interval. This method is particularly useful when the position error is on the order of 10 km or more. A second method using the gravimetric map relies on a tight hybridization between the inertial navigation system and the gravimeter. The navigation state is then optimally estimated at each observation based on all previous inertial measurements and observations.These two methods share a common problem: the fact that the gravimeter is moving degrades the accuracy of the measurement and therefore limits the position correction. The higher the speed, the less the position is corrected. This is partly explained by the gravimeter's measurement time and variations in the field to which it is applied. The gravimeter was subjected to variations during measurement. A measurement time of 10 seconds at a speed of 900 km / h can lead to variations of 10 µg during the measurement in certain geographical areas, whereas the intrinsic accuracy of an absolute gravimeter is typically on the order of 10 ng. The cost of the equipment therefore becomes high relative to the quality of the measurement as the speed increases. GNSS and gravimeters are passive measurement methods offering the advantage of discretion, but GNSS is not always available, and gravimeters are less efficient at high speeds. Therefore, there is a need for an inertial localization method without availability constraints that can be implemented on vehicles moving at high speeds.SUMMARY OF THE INVENTION The invention offers a solution to the problems mentioned above, by proposing a method in which the external gravimeter can be replaced by a sensor whose measurement is a function of the position or speed of the carrier, and in which an enriched gravimetric model is applied in the propagation model of the navigation state (position, speed, attitude) at each position of the uncertainty zone modeled by the unit, the term "enriched" meaning that this model allows the gravity field to be described in a finer way than the normal model used by default in inertial positioning units, the normal gravity model being a term used in physical geodesy designating the gravity field generated by a rotating equipotential reference ellipsoid modeling the surface of a planet and which, in the state of the art concerning the planet Earth, is that described by the WGS84 or GRS80 reference system.To this end, a first aspect of the invention relates to an inertial localization method of a carrier using a recursive Bayesian stochastic filter implemented by an inertial localization device, the method comprising a plurality of cycles, each cycle comprising a propagation step and an update step, method in which, during the propagation step, the propagation is carried out using a propagation model taking into account at least one component of a matrix of spatial gradients of the gravity vector provided by an enriched gravimetric model. Thus, during propagation, the navigation state (position, velocity, attitude) is calculated based on the initial navigation state of each cycle, inertial measurements, and the enriched gravimetric model. The method according to the invention is particularly advantageous in that reading the enriched gravimetric model at the estimated position, which differs from the true position, creates, due to the non-uniform spatial distribution of the enriched gravimetric vector, a correlation between the velocity error and the position error in the vicinity of the estimated position, and in that the stochastic filter calculates the uncertainty by modeling this correlation during the propagation step by linearizing the enriched gravimetric vector as a function of position at each propagation instant in the form of a partially used spatial gradient matrix.Thus, a partial observation of the velocity allows for the correction of part of the position through this correlation during the update step. Similarly, a partial observation of the position allows for the correction of part of the velocity and another part of the position during this same step. Thanks to the invention, it is therefore possible to implement a localization method for carriers moving at high speeds by modeling the propagation of the error over time intervals shorter than the cycle associated with the stochastic filter (for example, the Kalman cycle when such a filter is used). Furthermore, this method can be implemented using a measurement that cannot be detected, such as a measurement of the carrier's altitude or its vertical velocity. In addition, its implementation requires minimal computing resources.In addition to the features mentioned in the preceding paragraph, the method according to a first aspect of the invention may have one or more complementary features from the following, considered individually or in all technically possible combinations. In one embodiment, the recursive Bayesian filter linearizes the propagation law. In one embodiment, the inertial localization device comprises a computing means, a block of inertial sensors, and at least one external sensor, and for each cycle, where is a non-zero positive integer: - during the propagation step, the navigation state at the end of the cycle. is calculated based on the navigation state at the beginning of the cycle inertial measurements, and of the gravity vector obtained from the enriched gravimetric model, the error state is calculated as a function of the state error and the covariance matrix is calculated based on the covariance matrix the calculation of the error state and its covariance is carried out using a transition matrix Φ k to the cycle ^ and a noise covariance matrix of model Q k to cycle k such that: the transition matrix Φ k being determined using at least one component of the spatial gradient matrix of the gravity vector obtained from the enriched gravimetric model, an observation matrix H k being then determined from the navigation state at the end of the cycle and an observation model; - During the update step, the error status after the update | and the covariance matrix of the estimation error after update are calculated, using the calculation method and the stochastic filter, from the error state before the update | of the covariance matrix of the estimation error before update , of the observation matrix of a covariance matrix of measurement noise and an observation relating to at least one function of the carrier's velocity and / or position performed by the external sensor during or at the end of the propagation step so as to at least partially reduce the error state after update. In one embodiment, each filtering cycle k is divided into ^ time intervals ∆T1 as well as into P time intervals ∆T2 such that are positive integers non-zero, where is the filter period, the propagation step of each cycle of filtering including, from a propagation matrix For each interval identified by the index i, with i between 1 and N, a substep of calculating the navigation state by propagation of the state based on measurements from the inertial sensor block, of the model gravimetric enriched at the state position For each interval identified by the index i, which is between (j - l)r + 1 and (j - l)r + r, where j is an integer between 1 and P, denoting the index of an interval, is the integer part of x, a substep calculation of an elementary transition matrix initialized to the identity matrix at the beginning of the time interval identified by the index i = (j - l)r + 1 and completed by integrating the propagation matrix F(t) with respect to time over the r time intervals comprising the interval AT2, the matrix obtained by integrating the propagation matrix over a time interval being added to the matrix obtained during integration over the time interval previous so as to progressively constitute this elementary transition matrix and a transition matrix on cycle k initialized to the identity matrix being calculated progressively at each new value of j by the matrix product At the end of the last interval of cycle k and therefore of the last interval A a sub-step of matrix determination observation H kbased on the propagated navigation state and a model observation, and a substep of propagation of the error state and the covariance matrix of that state:

[0018] with the transition matrix obtained at the end of the last interval at cycle k considered.

[0019] In one embodiment, the inertial localization device includes a laser rangefinder and / or lidar, and a measurement of the carrier's position and / or velocity is performed by telemetry during the update step. In one embodiment, the localization device includes a camera, and the position and / or velocity of the carrier is measured by the camera during the update step. In another embodiment, the localization device includes a means for measuring the vertical position, and the position and / or vertical velocity of the carrier is measured by said means during the update step. In one embodiment, the inertial localization device is strap-down and operates in the local geographic coordinate system (North, West, Up) or (North, East, Down). In another embodiment, the inertial localization device is strap-down and operates in a coordinate system whose axis coincides with the vertical axis of the local geographic coordinate system, known as a free azimuth coordinate system. This coordinate system allows, in particular, traversing the geographic poles without causing division by zero in the calculations.In one embodiment, the inertial positioning device is a mechanically linked component system in the geocentric frame of reference linked to the planet (generally denoted [t]). In another embodiment, the inertial positioning device is a mechanically linked component system in the geocentric inertial frame of reference (generally denoted [i]). In yet another embodiment, the inertial positioning device is a gimbal-type device. A second aspect of the invention relates to an inertial positioning device comprising an inertial sensor block, at least one external sensor, a memory for storing the enriched gravimetric model, and means configured to implement a method according to a first aspect of the invention.A third aspect of the invention relates to a computer program comprising instructions which lead the device, according to a second aspect of the invention, when these instructions are executed by the device, to implement the method according to a first aspect of the invention. A fourth aspect of the invention relates to a computer-readable medium on which the computer program is recorded according to a third aspect of the invention. The invention and its various applications will be better understood upon reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES The figures are presented by way of illustration and in no way limit the invention. [Fig. 1] shows a schematic representation of the principle of gravimetric correlation according to the invention. [Fig. 2] shows a schematic representation of the use of a Kalman filter for implementing gravimetric correlation. [Fig. 3A] shows a logic diagram of a localization method according to the invention. [Fig. 3B] illustrates the operation of the algorithm for calculating the solution (position, velocity, attitude) as a function of inertial measurements. [Fig.Figure 4 shows a schematic representation of a localization device according to the invention. Figure 5 compares the error behavior in horizontal position and heading for inertial sensors isolated from the vibratory and thermal environment between the prior art and the method according to the invention. Figure 6A illustrates the timing diagram of the calculations during the propagation step. Figure 6B illustrates the difference between closed-loop and open-loop states. Figure 7 illustrates the definition of the geocentric frame [t] linked to the planet and the local geographic frame (North, West, Up) [g], as well as the definition of latitude L, longitude G, and ellipsoidal altitude Z, also called 34. Figure 8 illustrates the definition of the geocentric frame [t] linked to the planet and the inertial geocentric frame [i]. DETAILED DESCRIPTION Unless otherwise specified, the same element appearing in different figures has a single reference. Introduction Inertial localization methods are generally implemented by an inertial navigation system (IMS) that includes an inertial sensor block (or ISB comprising accelerometers and gyroscopes or gyroscopes), a computing means, and, preferably, mechanical damping elements on which the ISB is usually mounted to minimize the impact of shocks and vibrations on localization accuracy. This ISB can operate in a first mode, called alignment mode, which corresponds to the initialization of the navigation state using measurements from the ISB and / or an external sensor. The present invention does not relate to this first mode.When alignment is complete, the positioning system can switch to navigation mode: this navigation mode is the subject of the invention. In this mode, navigation state estimates are calculated cyclically using a stochastic filter (also called a navigation filter), each cycle comprising at least two steps: a propagation step of the navigation state and the state of the stochastic filter; and an update step of the navigation state and the state of the stochastic filter. The most commonly used stochastic filter in navigation is the extended Kalman filter. The propagation calculation is shared between a non-linear propagation algorithm called the "navigator" and an error propagation algorithm with linearized distributions based on the navigator estimates at different times.This algorithm assumes that the errors are Gaussian and calculates the expected value and covariance matrix of the propagated errors. Observations are incorporated using an extended Kalman filter in an update step. This is the standard operation of an inertial navigation system. The method according to the invention differs from the standard operation described above in that the propagation model used during the propagation step to propagate the error state, denoted hereafter as ^^, takes into account at least one component, preferably a plurality of components, of the gradient matrix. The spatial components of the gravimetric vector of an enhanced gravimetric model are read from the model at the carrier's position estimated by the navigator. In one embodiment, an enhanced gravimetric model is defined as one whose model resolution is better than 15 arcminutes and whose RMS error is less than 15 mGal for most geographical areas (80% or more of the surface) likely to be traversed by the carrier. The resolution is generally defined as the average grid spacing of the measurements reduced to the reference ellipsoid used to construct the enhanced model. For a global model decomposed into spherical harmonics, this corresponds to a model whose highest degree of spherical harmonic is greater than approximately 700. In a preferred embodiment, the accelerometric errors provided by the inertial sensor array are less than approximately 10 mGal.Stochastic Filters Although the invention is illustrated hereafter using an extended Kalman filter, it is not limited to this single stochastic filter. All variants of the extended Kalman filter in which the propagation step is performed with a linearized propagation law can be used: for example, filters that improve the convergence rate, filters that improve numerical problems, or filters that improve robustness problems. Of course, other variants of stochastic filters exist, but the principle of the invention (i.e., gravimetric correlation by propagation) remains valid even though it may take different forms.Enhanced Gravimetric Models As mentioned previously, in the method according to the invention, the gravimetric model is an enhanced gravimetric model allowing the spatial gradient of the gravity vector to be defined at the estimated position of the carrier. By contrast, in prior art inertial navigation systems, the gravity model used is the normal model or an approximation thereof, the latter comprising 4 geodetic parameters which, in the case of the. The gravitational field of the planet Earth is defined in reference systems such as WGS84 or GRS80. The normal model describes the gravitational field generated by a smooth, ellipsoidal, equipotential, rotating surface with the mass of the planet. The effect of topographic relief on the gravitational field is not modeled. The difference between the true gravitational field and the normal gravitational field at a given position is called the gravitational perturbation field. This results in vertical deviations and errors in the gravitational modulus. Vertical deviations excite navigational errors and produce horizontal Schuler oscillations in position and velocity that can potentially diverge but can be partially damped by observations. Indeed, in the state of the art, vertical deviation models are used to reduce these oscillations in various navigation systems.These models are by definition richer than the normal model. Furthermore, spatial gradients of the normal model are modeled in the error propagation model of the extended Kalman filter. However, in the prior art, the spatial gradients of the enriched gravity vector are not modeled in the propagation matrix. As a result, in navigation systems using an enriched gravimetric model, an unmodeled correlation between velocity error and position error arises because, in the navigator, the enriched gravimetric model is read at the estimated position, not the true position. In addition to this inconsistency, it appears that the velocity error contains information about the position error, and that some existing sensors can capture this information to estimate the position error.The achievable performance depends on the richness of the gravimetric model and the quality of the accelerometers. Global models, including EGM2008, EIGEN-6C4, and XGM2019, built from terrestrial and space-based measurements of the gravitational field, can model the gravitational field with a resolution on the order of 10 km. Other state-of-the-art global models built from topographic models reduce this resolution to 6 km. Better resolutions are obtained with some local models. These models contain errors that are only partially modeled. Schematic illustration of the principle of the invention. Before illustrating the invention in detail, it may be useful to present, in a simplified manner, the principle on which it is based (i.e., gravimetric correlation by error propagation) in an embodiment where the filter used is an extended Kalman filter. This will show how, starting from at least one component of the spatial gradient of the enriched gravity vector, it is possible to improve the evaluation of position and / or velocity and / or attitude by reducing the error in these variables. This presentation will also demonstrate how the method according to the invention can be implemented even in the absence of a gravimeter, a position or velocity sensor being sufficient. In the simplified example described below, it is assumed that the gravity model is perfect or that the accelerometer measurements are perfect.Of course, this is not the case in reality, and the operations presented in the following paragraphs must be performed taking into account errors in the model and / or measurements. Figure 1 shows two positions of a carrier: the carrier's actual position PR, that is, the position where the carrier is actually located, and its estimated position PE, that is, the position of the carrier estimated by an inertial navigation system (IMS) located within the carrier. The IMS accelerometers measure a specific force FS at the actual position PR.To obtain the carrier's acceleration, the navigator supplements this measurement with the gravity vector (the gravity vector is the sum of the gravitational vector corresponding to universal attraction and the centrifugal acceleration due to the rotation of the planet on which the carrier is located), as well as accelerations dependent on the type of navigation system used by the navigator and known from the state of the art (the navigation system defines the frame of reference in which the navigation is expressed). This gravity vector is derived from an enhanced gravity model and is calculated at the estimated position PE. This acceleration then allows the calculation of the carrier's velocity at the next instant and therefore also its position. Thus, although the specific force FS is derived from a measurement, the value of the carrier's acceleration is a function of an estimated value of the gravity vector calculated using an enhanced model from the estimated position PE.Also, an error on the estimated position PE propagates, through the consideration of gravity, into an error on the acceleration of the carrier (and therefore on the speed and position of said carrier, these quantities being obtained by integration). In [Fig. 1], the position error on the positive axis is denoted δx. This position error on the positive axis results in a difference between the gravity along axis 3 at the actual position PR and the gravity determined using a model at the estimated position PE, denoted δg. z on [Fig.1]. These two errors can be linked to each other using the following relationship: [Math.1] Where is the error on the 3-component of gravity, is the The spatial gradient along the + axis of the 3-component of gravity at the estimated position PE is denoted by ^+, and ^+ is the error on the + component of the position. As already mentioned, this error on the value of gravity along the 3-axis directly translates into an error in the acceleration along this same axis according to the relation: [Math.2] It is possible to derive similar relations for the error on the 3-component of the velocity such that, during a time interval T during which the gradient can be considered constant, the contribution of the position error to the velocity error z, apart from all other contributors, is: [Math.3] In other words, it is possible to propagate the error ^+ onto the error ^<6 by establishing a (gravimetric) correlation between these two quantities. Furthermore, this propagation does not require an external measurement of the gravity vector or its spatial gradient (generally, states of the stochastic filter are reserved for estimating a correction to the gravity model, this estimation being considered an internal measurement of the gravity vector), the value of the vector and the Spatial gradients can, for example, be provided by an enhanced gravimetric model. An observation on the vertical track then allows the horizontal position to be corrected. The preceding relationship is obviously an approximation used to illustrate the invention, and other additional terms are present, such that the proportionality relationship [Math.3] is not verified. However, this approximation allows for a simplified presentation of the principle of the invention. Inertial Localization Method As illustrated in [Fig.2], [Fig.3A], [Fig.3B], and [Fig.4], a first aspect of the invention relates to a method 100 for the inertial localization of a carrier using a stochastic filter implemented by an inertial localization device (ID). The method 100 according to the invention comprises a plurality of cycles, each cycle comprising a propagation step 1E1 and an update step 1E2.Furthermore, in method 100 according to the invention, during propagation step 1E1, propagation is performed using a propagation model that takes into account at least one component of the spatial gradient matrix of the gravity vector provided using an enriched gravimetric model. In one embodiment, the stochastic filter is an extended Kalman filter. Of course, as detailed in the introduction, other filters can be used within the scope of the invention, but the extended Kalman filter was chosen to illustrate the invention because it is the most common filter in the field of localization. In an embodiment illustrated in [Fig.[4] The inertial localization device (DI) comprises a computing means (MC) (for example, a processor or an ASIC card), an inertial sensor block (ISB), at least one external sensor (CE), and a storage memory (MS) configured to store the instructions and data necessary for implementing a method 100 according to the invention, and in particular the enriched gravimetric model. In a preferred embodiment, a specific storage means is used to store the enriched gravimetric model, for example, a second storage memory separate from that storing the instructions for implementing the method 100 according to the invention. Figure 2 will be used to illustrate the different steps 1E1, 1E2 of the process 100 according to the invention. In this Figure 2, the invention is illustrated along two axes (the + axis and the = axis), and a measurement (or observation) of the velocity is shown along axis 3. Thus, in this simplified illustration, the error state, which in reality contains not only navigation errors but also complementary state errors that contribute to reducing navigation errors, is reduced to the error on the state vector denoted ^^ at time > and described by: [Math.4] Where ^+ is the uncertainty on the x-component, δy is the uncertainty on the =-component, and δv zis the uncertainty in the 3-component of the velocity. Furthermore, to further illustrate the principle of the invention in the case of a Gaussian model of the errors, in [Fig. 2], the uncertainty ellipsoids at 1σ are represented in projection onto three planes: - The (x, y) plane at the bottom left; - The (Xu1, v) plane z ) in the upper left where Xu1 represents the axis of the spatial gradient of the gravity vector in the direction - The plan (v z , Xu2) in the lower right where Xu2 represents the axis orthogonal to the gradient. As mentioned in the introduction, the method 100 according to the invention comprises two steps: a propagation step 1E1 and an update step 1E2, these two steps being repeated according to a period each repetition corresponding to a cycle ^ where ^ is a non-zero natural number. The period is the associated period to the stochastic filter, here the extended Kalman filter. These two steps will be detailed later. In one embodiment, the enriched gravimetric model includes a set of data and functions (for example, interpolations or spherical or ellipsoidal harmonic functions) providing a gravimetric vector and a function of the spatial gradient matrix of this vector providing at least one spatial gradient that allows for approximations such as local average gradient values, depending on the carrier's position. For example, in the case of a grid, the rate of spatial change between two grid points is also an approximation of the gradient in that direction This rate of change is therefore the average value of the spatial gradient of g zin the + direction. In an alternative embodiment, the enriched gravimetric model provides a gravimetric vector and a spatial gradient matrix of this vector corresponding to the gravity vector 54 and a function of its Jacobian in a coordinate system [g] (or geographic coordinate system) at positions expressed in geographic coordinates relative to the reference ellipsoid where L is the geographic latitude, G the longitude and z g the ellipsoidal altitude, where is a Jacobian approximation function allowing, for example, forcing certain terms to zero or performing a local average based on parameters, as well as an associated error model, the gravimetric vector and its spatial gradient matrix being the mechanization frame corresponding to the reference frame to which the inertial tracking system is linked. For example, the reference frame [g] makes the platform reference frame of the inertial tracking system horizontal and oriented towards North. If the inertial tracking system is gimbal-based, the BSI (Body Systems Interface) is fixed relative to a mechanical platform made horizontal and oriented towards North. If the tracking system is strapdown-based, the BSI is fixed relative to the carrier, and a virtual platform is calculated, equivalent to the mechanical platform of the gimbal-based system. Currently, all systems are strapdown-based. In some cases, the strapdown system can itself be mounted on a gimbal platform, making the virtual platform fixed relative to the physical platform.For the record, the platform frame in free azimuth known to a person skilled in the art allows passage through the geographic poles and corresponds to a frame deduced from [g] by an angle V around the axis 34 where V is maintained by the West velocity of the carrier, or for example the geocentric terrestrial frame [t]. Furthermore: [Math.5] Where are the coordinates of the gravity vector in the reference frame [g] at the position defined by the latitude L, the longitude G and the ellipsoidal altitude 34, and where a component such that represents the variation when the linear position (in meters as opposed to angular position such as L and G) evolves along the y-axis of [g] by the value H=4, the enriched gravity vector and its spatial gradient matrix being calculated by: [Math.6] In an alternative embodiment, the enriched gravimetric model provides a gravimetric vector and a spatial gradient matrix of this vector corresponding to the gravity perturbation vector and a function of its Jacobian in the frame [g] at positions expressed in coordinates geographical relative to the reference ellipsoid where L is the latitude geographical, G the longitude and 34 the ellipsoidal altitude, where is a function an approximation of the Jacobian allowing, for example, forcing certain terms to zero or performing a local average based on parameters, as well as an associated error model, the gravimetric vector and its spatial gradient matrix being [Math.7] Where are the coordinates of the perturbing vector of gravity in the frame [g] at the position defined by the latitude L, the longitude G and the ellipsoidal altitude 34, and where a component such as represents the variation of when the linear position (as opposed to the angular position) evolves along of the y-axis of [g] with the value H=4. , the enriched gravity vector and its spatial gradient matrix being calculated by: [Math.8] where are defined at the same altitude 34 and at the same In the horizontal position, the calculation of the enriched gravity vector can be performed equivalently in the navigation state calculation algorithm by integrating the velocity with the vector and supplementing the accelerometer measurements. with R's help S, a possible approximation, valid up to 100 km altitude for the planet Earth, being in the coordinate system (North, West, Up – such a coordinate system is illustrated in [Fig.7]): [Math.9] With: [Math.10] Where are the geodetic parameters of the gravity model? normals represent respectively the equatorial radius, the flattening, the angular velocity of rotation in inertial space, and the product of the universal gravitational constant and the mass of the planet. In an alternative embodiment, the enriched gravimetric model provides a gravimetric vector and a spatial gradient matrix of this vector corresponding to the gravity anomaly vector Δg g and a function of its Jacobian in the frame [g] at positions expressed in coordinates geographical relative to the reference ellipsoid where L is the latitude geographical, G the longitude and z g the ellipsoidal altitude, where is a Jacobian approximation function allowing, for example, forcing certain terms to zero or performing a local average based on parameters, as well as an associated error model, the gravimetric vector and its spatial gradient matrix being with : [Math.11] Where are the coordinates of the anomaly vector of gravity in the frame of reference [g] at the position defined by the latitude L, the longitude G and the ellipsoidal altitude and where a component such that 8XM represents the variation of lorsque la position linéaire (par opposition à la position angulaire) évolue le long of the y axis of [g] of the value the enriched gravity vector and its spatial gradient matrix being calculated by: [Math.12] Or are defined at the ellipsoidal altitude 0 at the horizontal position are defined on the water's surface at the same horizontal position (L,G). This scenario is reserved for maritime navigation. In this case, can be calculated more simply than [Math.9] and [Math.10] with the following expressions: [Math.13] The calculation of the enriched gravity vector can be performed equivalently in the navigation state calculation algorithm by integrating the velocity with the vector and supplementing the accelerometer measurements using Y q . In one embodiment, the enriched gravimetric model provides a gravimetric vector and a spatial gradient matrix of this vector corresponding to the gravitational vector G g, the latter being the attraction exerted by the mass of the planet, and a function of its Jacobian in the frame [g] at positions expressed in geographic coordinates relative to the reference ellipsoid where L is the geographic latitude, G the longitude and z g the ellipsoidal altitude, where is an approximation function of the Jacobian allowing by An example of forcing certain terms to zero or performing a local average based on parameters, along with an associated error model, where the gravimetric vector and its spatial gradient matrix are: [Math.14] [Math.15] Where are the coordinates of the gravitational vector in the reference frame [g] at the position defined by the latitude L, longitude G and ellipsoidal altitude, and where a component such that represents the variation when the linear position (as opposed to angular position) evolves along the y-axis of [g] by the value of the enriched gravity vector and its spatial gradient matrix being calculated by: [Math.16] Or is the centrifugal acceleration due to the planet's rotation in space, and where are calculated at the same position with: [Math.17] Of course, some terms can be approximated during the calculation. In an alternative embodiment, the enriched gravimetric model provides a gravimetric vector and a spatial gradient matrix of this vector corresponding to the gravitational vector and a function of its Jacobian in the geocentric frame [t] (such a frame is illustrated in [Fig. 8] linked to the planet at positions expressed in Cartesian coordinates is a a Jacobian approximation function allowing, for example, forcing certain terms to zero or performing a local average based on parameters, as well as an associated error model, the gravimetric vector and its spatial gradient matrix being a vec : [Math.18] Where are the coordinates of the gravitational vector in the reference frame [t] at the position defined by the latitude L, the longitude G and the ellipsoidal altitude e t où une composante telle que représente la variation lorsque la linear position (as opposed to angular position) evolves along the y-axis of [t] by the value of the enriched gravity vector and its spatial gradient matrix being calculated by: [Math.19] Where are calculated at the same corresponding position to Cartesian coordinates in [t] with: [Math.20] Other enhanced models can also be used within the scope of the invention. The propagation step 1E1 of the method 100 according to the invention includes a propagation step 1E1 in which the navigation state at the end of the cycle is calculated as a function of the state navigation of the start of the inertial measurement cycle, of the gravity vector obtained from the enhanced gravity model (and Newton's laws of dynamics: this propagation is carried out according to equations known in the field and detailed in part below, the equations in question depending on the chosen frame of reference). Similarly, during this step, the error state at the end of propagation | , is calculated based on the error state at the beginning of the cycle of a transition matrix and the covariance matrix at the end of spread is calculated based on the covariance matrix at the beginning of the cycle of the transition matrix of a noise covariance matrix of model, so that: [Math.21] Furthermore, the transition matrix is ​​determined using at least one component, preferably a plurality of components, of the spatial gradient matrix of the gravity vector given by the enriched gravity model. In other words, during this step 1E1, in cycle k, the error state and its matrix of covariance errors at the beginning of the cycle are propagated, leading to the error state and its covariance matrix at the end of the cycle k. Furthermore, during this In step 1E1, an observation matrix Hk is determined from the propagated navigation state and an observation model. This propagation step 1E1 is illustrated in [Fig.2] where the initial cycle error corresponding to the uncertainty ellipsoid E1 is propagated in such a way to obtain the error after propagation step 1E1 corresponding to the uncertainty ellipsoid E2. The position errors are assumed to be independent here to simplify the illustration, and the projection at the bottom left of [Fig.2] shows the absence of correlation between (the ellipses with a thick solid line E2 and with a thin solid line E1 are superimposed in projection onto the plane It is clear from [Fig. 2] that the uncertainties in the position errors after propagation are unchanged. On the other hand, propagation between or between is present thanks to the correlation between these quantities created by the presence of a gradient of the gravity vector. In other words: [Math.23] Furthermore, in this example, est choisi égale au vecteur that is to say, along the axis The axes defined by are therefore special. Indeed, the propagation of a given position error along a given azimuth is zero along the axis defined by and maximum along the axis defined by The present invention is distinguished from the prior art in particular by the elements taken into account during this propagation step 1E1, and especially by the consideration of at least one component of the spatial gradient matrix of the gravity vector, preferably several components of the spatial gradient matrix of the gravity vector, or even all nine components of the spatial gradient matrix of the gravity vector. In other words, the propagation matrix, and therefore the transition matrix, includes at least one term, preferably a plurality of terms, each depending on a component of the gravity vector gradient matrix. As illustrated in the introduction, using one or more components of the gravity vector gradient matrix improves the error propagation model. As a reminder, the components of the spatial gradient of the gravity vector can be represented in the form of a matrix (here, in the case of a so-called local geographic frame – other frames can of course be used): [Math.24] With is the component of the vector of gravity along the considered axis i, the x-coordinate being relative to the component of the position on the south-north axis, the y-coordinate being relative to the component of the position with respect to the east-west axis, and 3 being relative to the component of the position with respect to the axis pointing at the zenith (called the local geographic reference point). From this component or these components, the propagation matrix (and therefore of the transition matrix and the matrix observation is the index of the Kalman cycle considered can be determined. More specifically, at least one component of the spatial gradient of the gravity vector is inserted into the error propagation function, which allows the propagation matrix F to be calculated and, from the latter, the transition matrix. In other words, the filter propagation model takes into account at minus one component of the spatial gradient of the gravity vector, preferably from an enriched model. As a reminder, the transition matrix can be determined to order 1 at using the propagation matrix using the following relationship: [Math.25] where I is the identity matrix and is the propagation matrix. In one embodiment, the vertical component of the gravity vector is measured using a gravimeter. However, such a measurement device is bulky and difficult to integrate into a small DI localization device. Also, in an alternative embodiment already mentioned, the component(s) of the gravity gradient are determined by the calculation method MC using an enriched gravimetric model, from the estimated position PE of the carrier.More specifically, in this embodiment, the determination of at least one component of the spatial gravity gradient comprises: - the determination, using the MC calculation method, with measurements from the BSI inertial sensor block and from a gravity vector calculated using the enriched gravimetric model, of the carrier's navigation state, including its position (speed and attitude), referred to as the estimated position PE; and - the determination, using the MC calculation method, of the spatial gradient of the gravity vector with the enriched gravimetric model and the aforementioned estimated position PE of the carrier, for example, using a function that converts the enriched gravimetric model into a gravity vector and an approximation of its Jacobian matrix, for example, based on the gravity vector grid or on the spherical harmonic coefficients. The enriched gravimetric model could, for example, be the EGM2008 model (see NK Pavlis, SA).Holmes, SC Kenyon and JK Factor. “An Earth Gravitational Model to Degree 2160: EGM2008”. EGU General Assembly 2008, Vienna, Austria, April 13-18, 2008. More generally, as illustrated previously, the enhanced gravimetric model used can take different forms. The simplest form consists of geographical maps of the gravity vector (three components) and horizontal gradients of the gravity vector (the six components of the matrix introduced previously). However, it is not necessary to map all nine components, as there are only five independent components of the spatial gravity gradient. Alternatively, the gravity model can take a compressed form, that is, be presented as a list of coefficients, for example, spherical harmonic coefficients of the gravitational potential. Other basis sets, such as ellipsoidal harmonics or spherical wavelets, can be used. To utilize these, it is possible to calculate the basis set functions at the estimated position using state-of-the-art mathematical methods, and Perform the appropriate linear combination to obtain the gravity vector and the spatial gradient matrix of the gravity vector. Numerous global models of the gravitational potential decomposed into spherical harmonics exist. For example, the EIGEN-6C4 model or the XGM2019 model. Explanations of the spherical harmonic decomposition of the gravitational potential can be found in the book "Physical Geodesy, Second Edition" – Bernhard Hofman-Wellenhof, Helmut Moritz, Springer Wien Network, 2006. This book does not deal with the spatial gradients of the gravity vector. However, this aspect is addressed, for example, in the article "On the computation of the gravitational potential and its first and second order derivatives," R. Koop and D. Stelpstra – Manuscripta geodaetica – Volume 14 – pages 373-382.In one embodiment, the inertial localization device (DI) comprises a computing means MC, an inertial sensor block (BSI), and at least one external sensor CE. The method preferably includes, prior to the propagation step, an alignment phase during which the computing means MC initializes the navigation state and its uncertainty. In one embodiment, each cycle k is divided into N time intervals, as well as P time intervals. so that are non-zero positive integers and where is the period of the filter. In this embodiment, as illustrated in [Fig. 6A], during propagation step 1E1, each cycle k comprises, for each interval ∆^ ^ identified by the index i, between 1 and N, a sub-step 1E11 of the navigation state calculation (including the position, velocity, and attitude of the carrier) by propagating the state from the measurements of the BSI inertial sensor block, of the model gravimetric analysis enriched with the position of the state and the laws of dynamics Newton. Furthermore, during this step, a time integration of the propagation matrix is ​​implemented, this integral then being used to calculate an elementary transition matrix at regular intervals (denoted interval j). Indeed, as mentioned later, calculating a matrix of elementary transition is carried out at intervals j, with is the integer part of x, initialized to the identity matrix when being an integer between 1 and P, and completed by the integration with respect to time of the propagation matrix over the r time intervals component of the interval of index j, where F is the propagation matrix corresponding to the linearized propagation function which can be simplified or considered constant on the interval

[0143] More specifically, the integration of the propagation matrix is ​​performed using a discretized version of the relation [Math. 25] introduced earlier, for example using a counter initialized at each interval i between 1 and N such that i - 1 is a multiple of r, positive or zero. In other words, for considered constant on The value is accumulated in the identity matrix as the iterations progress. so as to progressively build the transition matrix over an interval

[0144] To achieve this, in an example implementation, the enriched gravimetric vector at iteration i is read from the enriched gravimetric model as a column matrix expressed in a frame [q]. Then, the enriched gravimetric vector is converted into an enriched gravity vector in the frame [q], the enriched gravimetric vector being a functional of the enriched gravity vector. Finally, using a transformation matrix T pq , the enriched gravity vector is expressed in the frame [p].

[0145] To this end, in an example implementation, the navigation mechanization frame is a frame [p] and the gravimetric model is expressed in a frame [q]. As already mentioned, for this propagation, the transition matrix is ​​obtained from the propagation matrix calculated according to the state of the art, and comprising the 3x3 propagation submatrix which propagates the position error vector expressed in the frame [p] onto the velocity error vector expressed in the frame [p], with:

[0146] [Math. 26]

[0147] where T pq is the transformation matrix from the frame [q] in which the gravity vector is expressed to the mechanization frame [p], where T q is the transposed matrix de is the spatial gradient matrix approximated by the column matrix coordinates in the frame [q] of the enriched gravity vector calculated from the enriched gravimetric model, including at least one spatial gradient of this gravity vector, and where M q is a 3x3 matrix modeling the effect of the curvature of the reference ellipsoid on the velocity error and dependent on the coordinate system in which the gravimetric model is expressed. The calculation of Mq depends on how the enhanced gravimetric model is used. If the gravimetric model is used by locating the position of points using their Cartesian coordinates in the geocentric frame [t] attached to the planet (see figure at the end), then the frame [q] is equal to the frame [t] and 0 3 x3 If the gravimetric model is used by identifying the position of points using their geographic coordinates relative to the reference ellipsoid where L is the geographic latitude, G the longitude and z g the ellipsoidal altitude, then the frame [q] is equal to the local geographic frame [g] (North, West, High), and: [Math.27] where R N and R E are the North and East radii of the reference ellipsoid with respect to which the geographic coordinates are defined, and where z g is the ellipsoidal altitude, with: [Math.28]

[0153] Where a is the equatorial radius of the reference ellipsoid, and e is its eccentricity.

[0154] In one embodiment, can be forced to zero in the matrix M q which is then given by:

[0155] [Math. 29]

[0156] In another embodiment, the local geographic reference point can be defined by the axes (North, East, Down) where g xg and g yg may or may not be forced to zero, the new formula becoming:

[0157] [Math. 30]

[0158] In one embodiment, during propagation step 1 E1, for each interval of index i that is a non-zero multiple of r, at the end of substep 1 E11, a transition matrix being available with between 1 and P, index of an interval A substep 1 E12 includes the calculation of the transition matrix initialized to the identity matrix at the beginning of cycle k, obtained progressively at each new value of j by matrix multiplication. As a reminder, the The transition matrix for cycle k is obtained by multiplying the elementary transition matrices of all intervals of cycle k. Therefore, by realizing the product of the elementary matrices at each new value of j, the transition matrix associated with cycle k is given by the value of obtained at the last interval of the considered cycle k. In one embodiment, during this substep 1 E12, the navigation error and its covariance matrix are also calculated from the navigation error state of the previous interval using of the following relationship: Where is an elementary propagation matrix, given by being given by + These time intervals maintain the correlation between position error and velocity error during the considered cycle, up to the point of observation during the update step 1E2 (described later). The propagation step 1E1 also includes, at the end of the last interval, a substep 1E13 for calculating the matrix. observation H k based on the propagated navigation state and a model observation, and the calculation of the propagation of the error state and the covariance matrix of that state: In one embodiment, the inertial localization DI device includes a gravimeter measuring the gravitational modulus and (in addition to calculating the transition matrix based on the spatial gradient matrix approximated by the enriched gravitational vector) calculating the observation matrix at the end of step 1E1 of Propagation is performed using the horizontal gradients of the vertical component of gravity in the [g] frame extracted from the enriched gravimetric model. In one embodiment, the transition matrix also includes terms relating to the gravity vector (in addition to the gradient), and the value of this gravity vector is determined using the enriched gravimetric model. In one embodiment, to improve the robustness of the estimation, an error model of the gravity model can be used during the propagation step E1. The update step 1E2 of the method 100 according to the invention then includes an update step 1E2. The update step 1E2 first includes a substep 1E21 for measuring, using the external sensor, an observable related to at least one function of the vehicle's velocity and / or position. It is understood that a velocity or position observable is considered to be related to at least one function of velocity or position – generally, an observable is considered a function of velocity or position when its value is a function of the velocity or position. For this purpose, in one embodiment, the inertial navigation system includes an altitude sensor, that is, a sensor that determines the vehicle's position along axis 3 (in the local coordinate system). This embodiment is particularly advantageous since an inertial navigation system generally includes such a sensor.In an alternative or complementary embodiment, the inertial navigation system includes a gravimeter, a velocity sensor (for example, based on the Doppler effect), a camera, a laser rangefinder, a lidar, a radar, and / or any other registration means. In one embodiment, the error model of the stochastic filter includes states that complement the gravity vector calculated from the enriched gravimetric model. These states participate in the propagation of velocity errors and are registered by observations, thus constituting a gravimetric measurement integrated into the inertial navigation system. In one embodiment, the platform is a boat, and the external sensor is a virtual sensor. Indeed, since the altitude is given by the water level, it is not necessary to perform a measurement.In particular, for a carrier at sea, the altitude measurement can be considered to be zero or read from an ellipsoidal altitude chart of the geoid. It should be noted that the device according to the invention can include a plurality of external sensors, with one observable per external sensor being measured during measurement substep 1E21. Finally, update step 1E2 includes a substep 1E22 for updating, by means of the calculation method (MC), the state of the stochastic filter based on the measurement performed during the preceding measurement substep 1E21, so as to at least partially reduce the error state. This step is implemented in a manner... identical to prior art methods. As a reminder, in the extended Kalman filter, for example, an innovation is calculated corresponding to the difference between the measured value and the predicted value using the observation matrix and the propagated state. A gain matrix is ​​then calculated, and the state is corrected by the product of the gain and the innovation. The covariance matrix of the state is corrected based on this gain and the observation matrix H. k There exists an optimal gain that minimizes the trace of the covariance matrix. depending on the propagated covariance matrix and the observation matrix For each cycle k, at the end of the update step, a correction at time called recalibration, illustrated in [Fig. 6B], determines, according to state-of-the-art techniques, the initial value of the navigation state of the next cycle based on the state at that same instant combined with the error state portion containing the navigation error estimates, and determines the initial value at cycle k+1 of complementary states contributing to the quality of the navigation state estimates based on their value at the end of cycle k combined with the error state portion | containing the estimated errors on these additional states, then is reset, the state recalibrations and the resetting of error states being applied to all or part of these states at that moment The components of the recalibrated states are called "closed-loop states" and the others "open-loop states"; Navigation states combined with the navigation section of the error state (whose closed-loop components are zero) forms the navigation solution at the end of cycle k at time , associated with confidence intervals extracted from the covariance submatrix containing the covariance of navigation error states. The update step 1E2 is illustrated in [Fig. 2] where the error after update corresponds to the uncertainty ellipsoid E3. In this example, the observation is done only according to the 3 component of the velocity. When this observation occurs, it is taken into account in the update step of the Kalman filter and, if the optimal Kalman gain is used, the uncertainty ellipsoid is reduced along the axis ^<6 while remaining inscribed in the ellipsoid E2 and being tangent to the latter at the intersection of the ellipsoid E2 and the unobserved state space points so as to obtain the ellipsoid E3. Furthermore, the points of the ellipsoid E2 belonging to the plane Points passing through the origin remain statistically unchanged by observation because they correspond to state vectors belonging to the plane orthogonal to the observation axis. These points therefore also belong to the ellipsoid E3. These points form an ellipse in the plane. not shown except in the figure at the top left where they are represented by two small circles. The fact that ellipsoid E3 is inscribed in ellipsoid E2 results in a correlation between positional errors in the plane The position uncertainty ellipse has therefore shrunk in the direction corresponding to the direction of the horizontal gravity gradient. Examples of external sensors As already mentioned, the method according to the invention uses one or more external sensors to measure one or more observables. In the introduction to the description, examples were illustrated using a measurement of altitude or velocity along axis 3. However, as already mentioned, other external sensors can be used within the framework of the method 100 according to the invention. In one embodiment, the external sensor is a laser rangefinder. The observation then consists of a measurement of the distance of the carrier from a point (known or unknown). The position error produces, in particular, an observable acceleration error corresponding to that of the gravity vector projected onto the line of sight. In the method according to the invention, when the uncertainty zone If the position is within the linearity zone of the gravity vector, the spatial gradient matrix of the gravity vector, calculated from the enriched gravimetric model, allows for the linear modeling of this acceleration error as a function of the three-dimensional position error vector. This acceleration error creates a velocity error along this projection axis, as well as a discrepancy between the predicted and actual measured distances. The filter gains are applied to this discrepancy (or innovation) to correct the state vector (which, as a reminder, includes position, velocity, and attitude errors, as well as the error model of inertial and external sensors) during filter updates. Thus, in the method according to the invention, the position error along the line of sight is corrected directly by The rangefinder measurement is used, while the error on the two other components, those located in a plane orthogonal to the line of sight, is corrected according to the spatial gradient matrix of the gravity vector calculated from the enriched gravimetric model in said plane. The gradients providing the most information are those describing the variations in the projection of the gravity vector onto the line of sight as a function of the position errors in said plane, thus establishing correlations between the velocity error on the line of sight and the position errors in this plane. When the line of sight is vertical, the observation is an altitude observation, and these gradients correspond to the horizontal gradients of the z-component of gravity. This is the case mentioned in the introduction. More generally, when the line of sight is constant, as in the case of the vertical axis, two gradients of the gravity vector may suffice.Conversely, when the line of sight is variable, it is necessary to have the nine spatial gradients of the gravity vector calculated from the enriched gravimetric model in order to observe position errors in the plane orthogonal to the line of sight, regardless of its orientation. The position error is naturally observable as a linear combination of spatial gradients dependent on the line of sight. It should be noted that the same principle can be adopted with a Lidar. Similarly, some inertial navigation systems have a camera. The displacement of fixed points relative to the Earth in the image provides information on the movement of the carrier parallel to the image plane. The position error produces, in particular, an observable acceleration error corresponding to that of the gravity vector projected onto the image plane. According to the invention, when the positional uncertainty zone falls within the linearity zone of the gravity vector, the spatial gradient matrix of the gravity vector, calculated from the enriched gravimetric model, allows for the linear modeling of this acceleration as a function of the three-dimensional positional error vector. This acceleration creates a velocity error when projected onto the image plane. This results in a discrepancy between the predicted position of fixed points in the image and the actually observed position. The filter gains are applied to this discrepancy to correct the state vector during filter updates. The positional component in the image plane is corrected directly by this type of observation. The other positional component, that located on the line of sight, is corrected according to the spatial gradient of the The gravity vector is calculated from the enhanced gravimetric model, with the gradients providing the most information being those describing the variations of the gravity vector's projection onto the image plane as a function of the position error. on the line of sight, thus establishing correlations between velocity errors in the image plane and the position error on the line of sight. Measuring errors in the image plane therefore allows for the correction of errors on the line of sight, the acquired information depending on the amplitude of the spatial gradients. When the line of sight is constant, as in the case of the vertical axis, two gradients of the gravity vector may suffice. Conversely, when the line of sight is variable, it is necessary to have all nine spatial gradients. Alternatively, when the line of sight is servo-controlled to a fixed point, this velocity error is present in the line of sight control. This information can be treated as a measurement to correct the position error on the line of sight through the matrix of spatial gradients along the line of sight of the projection onto the image plane of the gravity vector calculated from the An enhanced gravimetric model. This method can be more precise than the first, which depends on the number of pixels in the image. If the camera is targeting nearby points, the sequence of images also provides information about the line of sight without the aid of spatial gradients of the gravity vector. The correlation between velocity error and position error then provides additional information and further improves the estimation. If the camera is targeting distant points such as stars (stellar targeting), very little information along the line of sight is acquired by the sequence of images because the stars are too distant, and only the gravimetric correlation between velocity error and position error allows for its acquisition. Of course, several cameras can be used based on the same principle.In all cases, a gravimeter can be added to the external sensors to improve the performance of the vertical chain and to estimate, for example, the accelerometric bias of the vertical inertial chain. This bias constitutes a performance limitation when exploiting the gravimetric correlation between velocity error and position error when only the altitude sensor is available. By using an external gravimeter, it is thus possible to lower this limitation and improve performance. Advantages associated with the method according to the invention. The method according to the invention allows fast carriers to benefit from the multiple advantages of the correlation between velocity error and position error without necessarily using a gravimeter. It allows not only the correction of position errors, but also the correction of gyroscopic drift errors, velocity errors, attitude errors, and heading errors. [Fig.5] illustrates this by comparing the behavior trends of the position and heading error of a hybridized inertial navigation system at altitude, this behavior also depending on the quality of the BSI, the mechanical damping elements and the thermal environment as well as the quality of the altitude sensor, using three types of gravimetric model on a timescale of a few hours: - The default mode corresponding to the normal model applied to the gravity vectors and the spatial gravity gradients which corresponds to a first process according to the state of the art (the two leftmost graphs on the [Fig.5]); - The mode sometimes called "compensation" corresponds to an enriched gravimetric model to describe vertical deviations or the complete gravity vector, but where spatial gradients are described by the normal model, which corresponds to a second method according to the prior art (the two graphs in the center of [Fig. 5]); - The gravimetric correlation mode, which corresponds to the implementation of a method according to the invention (the two graphs furthest to the right of [Fig. 5]). Horizontal position error of a hybridized altitude-based system. In the default mode, the horizontal position error includes Schuler oscillations, as well as errors related to gyroscopic errors and heading error. As a reminder, part of the Schuler oscillations is due to the profile of vertical deviations along the trajectory, the other part being related to accelerometric and gyrometric errors, as well as alignment errors.Observing the position or velocity sensor or the gravimeter allows us to observe part of the horizontal position through the correlation between velocity error and position error. The evolution of said horizontal position... The trajectory contains information on gyroscopic drift and heading, and its partial observation nevertheless makes it possible to reduce errors in these quantities in geographical areas with terrain, which can advantageously replace the GNSS signal when the latter is unavailable. In the method according to the invention, the originality lies in reducing errors in this quantity based on an altitude measurement (and not a measurement from GNSS) by using horizontal gradients of the gravity vector calculated from a gravimetric model enriched in the propagation matrix. To be more precise, the other components of the gradient also contribute, to a lesser extent, to reducing errors: horizontal position errors propagate not only along the vertical axis, but also horizontal velocity errors through the other gradients and then propagate along the vertical axis.Thus, they contribute to the observation of gyroscopic and heading errors. By measuring an observable other than altitude (for example, with a laser rangefinder used repeatedly over time), other gradients can contribute more significantly to the observation of gyroscopic and heading errors. In the compensated mode, some of the Schuler oscillations are attenuated because the high-resolution gravity model reduces the excitation of these oscillations due to the profile of vertical deviations along the trajectory. However, this does not reduce the slope of the position error. In the gravimetric correlation mode between velocity and position errors, the Kalman filter algorithm allows the position error to be estimated based on knowledge of the spatial gradients of the gravity vector and measurements of the recalibration methods, regardless of the source of the position errors.Heading error of a hybridized power plant at altitude. In the default mode, the heading error is poorly estimated. The explanation for its low observability can be found in the literature. As shown in [Fig. 5], the compensation mode does not improve the heading estimation. On the other hand, in the gravimetric correlation mode between velocity error and position error, when the platform performs a maneuver, the specific horizontal force measured by the accelerometers is projected onto the platform frame with a heading error, producing a horizontal velocity error and therefore... A horizontal position error, and since a portion of the position error (the projection of the error in the direction of the spatial gravity gradient) is observed, it is possible to improve the heading estimate within a few hours. For a submarine or surface vessel not using GNSS, measurements can be taken regularly over several days. The heading error is one of the contributors to a 24-hour period horizontal position oscillation. Observing it on this long timescale allows for better decoupling from other errors. Other errors: In the gravimetric correlation mode between velocity error and position error, gyroscopic drift errors can be partially estimated. Indeed, gyroscopic drifts strongly impact the horizontal position error.Their signature depends on the carrier's trajectory but includes, at least on the timescale of a few hours, a position error slope, as well as Schuler oscillations. Over longer periods, they also produce a longitude error slope and oscillations with a period on the order of 24 hours. Furthermore, observing the Schuler oscillations of the position also provides observability to the accelerometer errors. Solving Observability Problems: The method according to the invention increases the dimension of the observable space to a greater or lesser extent depending on the amplitude of the spatial gradients of the gravity vector at the estimated position. Therefore, the method according to the invention makes it possible to solve classic false observability problems.In these problems, where the normal gravity model is used and the ellipsoidal altitude is small, the gravity vector is considered to have a nearly constant magnitude and to be oriented along the geometric vertical at every point on Earth. A change of orientation or a translation does not alter the projections of the gravity vector in the local geographic coordinate system. In stationary observation situations where the unobservable axes depend on the current state, a Kalman-type navigation filter can create false observability and become inconsistent: its estimated covariances decrease unjustifiably and no longer cover the possible errors. In the prior art, these problems are solved in some cases by the invariant filter or the OCEKF filter (Observability-Constrained Extended Kalman Filter – in this type of filter, a model of the unobservable axes is used, and the filter is forced not to make observations along these axes). However, the OCEKF filter has a narrower range of application than an extended Kalman filter. The method according to the invention also makes it possible to solve some of these problems while retaining the Kalman filter, which has the advantage of operating in a broader range of application than the invariant filter or the OCEKF.An example of an observability problem can be found in the context of simultaneous localization and mapping (SLAM), related to the classic problem of tracking characteristic points in an image to determine an estimate of velocity and position. Appropriate processing allows these points to be selected and their velocity to be set to zero. From the movement of these points in the image, it is possible to deduce the motion of the camera and therefore that of the wearer. This can be done with an inertial measurement unit coupled to the camera (in other words, the observable is measured using a camera). It is known that when the motion is small, false observability problems can occur if the stochastic filter is an extended Kalman filter.This is explained by the fact that the observation is relative: the same scene can be created by rotating both the camera and the characteristic points without changing the observations. This is true if the gravity vector is orthogonal to the reference ellipsoid and has a nearly constant magnitude at all points. With a method according to the invention, the spatial gradient matrix of the gravity vector makes it possible to distinguish the different possible orientations of the scene, and the axis that is unobservable or weakly observable with the gradients of the normal model can become observable with the gradients of the gravity vector calculated from the enriched gravimetric model as used in the present invention. Another inconsistency problem of the Kalman filter in the prior art exists when the carrier is moving: the apparent motion of the image points along the line of sight is zero. In scenarios where the trajectory is... In uniform rectilinear motion, inconsistencies can arise due to a lack of observability along the line of sight. The method according to the invention provides a solution by modeling the spatial gradients of the gravity vector of an enriched gravimetric model. This model improves observability along the line of sight, thereby reducing the risk of inconsistency in the extended Kalman filter. Inertial Localization Device: A second aspect of the invention relates to an inertial localization device (or inertial navigation system) comprising means configured to implement a method according to the invention.More specifically, the device according to the invention comprises an inertial sensor block (or ISB comprising accelerometers and gyroscopes or gyroscopes), a computing means (for example, an ASIC card or a processor with associated memory), and preferably, mechanical damping elements on which the inertial sensor block is typically mounted to minimize the impact of shocks and vibrations on localization accuracy. In one embodiment, the device according to the invention is configured to operate in: - a first mode, called alignment mode, which corresponds to the initialization of the navigation state using measurements from the inertial sensor block and / or an external sensor; - a second mode, called navigation mode, in which the method according to the invention is implemented by the device according to the invention.The device according to the invention also includes at least one external sensor CE, for example, an altimeter, a laser rangefinder, or a camera. In one embodiment, the computing means MC is associated with a memory, the memory comprising the instructions and data necessary for implementing the reduction method according to a first aspect of the invention. The memory may, in particular, include one or more gravity models and one or more gravity error models. In one embodiment, the inertial localization device DI according to the invention is used in an inertial navigation device.

Claims

CLAIMS

1. A method (100) for the inertial localization of a carrier using a recursive Bayesian stochastic filter implemented by an inertial localization device (ID), the method comprising a plurality of cycles, each cycle including a propagation step (1E1) and an update step (1E2), the method being characterized in that, during the propagation step (1E1), the propagation is performed using a propagation model that takes into account at least one component of a spatial gradient matrix of the gravity vector provided by an enriched gravimetric model.

2. A method (100) for inertial localization according to the preceding claim, wherein the recursive Bayesian filter linearizes a propagation law.

3. Method (100) of inertial localization according to any one of the preceding claims wherein the inertial localization device (ID) comprises a computing means (CM), an inertial sensor block (ISB) and at least one external sensor (ES), and for each cycle ^ with ^ a non-zero positive integer: - during the propagation step (1E1), the navigation state at the end of the cycle. is calculated based on the navigation state at the beginning of the cycle From inertial measurements and the gravity vector obtained from the enriched gravimetric model, the error state is calculated depending on the error state and the covariance matrix the error state is calculated based on the matrix of covariance: calculating the error state and its covariance being carried out using a cycle transition matrix ^ and a cycle model noise covariance matrix ^ such that: the transition matrix being determined using at least one component of the matrix of spatial gradients of the gravity vector obtained from the enriched gravimetric model, an observation matrix then being determined from the navigation state at the end of the cycle and an observation model; - during the update step (1E2), the error status after the update and the covariance matrix of the estimation error after update are calculated, using the calculation method (MC) and the stochastic filter, from the error state before the update of the covariance matrix of the estimation error before update of a measurement noise covariance matrix, of the matrix observation and measurement of an observable relative to at least a function of the carrier's velocity and / or position as determined by the external sensor during or at the end of the propagation step (1E1) so as to at least partially reduce the error state after update.

4. A method (100) of inertial localization according to the preceding claim, wherein each cycle k is divided into N time intervals , as well as in P time intervals so that are non-zero positive integers and where is the filter period, the propagation step (1E1) of each cycle k comprising, from a propagation matrix - For each interval identified by the index i, a substep (1E11) of the navigation state calculation by propagation of the state based on measurements from the inertial sensor block, the enriched gravimetric model at the state position - For each interval identified by the $ index between being an integer between 1 and P denoting the index of an interval is the integer part of x, a substep of calculating an elementary transition matrix initialized to the identity matrix at the beginning of the time interval identified by the index and completed by integrating the propagation matrix with respect to time over the time intervals composing the interval, the matrix obtained by integration of the propagation matrix over a time interval being added to the matrix obtained during integration over the time interval previous so as to gradually build this matrix elementary transition and a transition matrix on the k-cycle initialized to the identity matrix, which is calculated progressively at each new % value by matrix multiplication. - At the end of the last interval i, a sub-step (1E13) of determining the observation matrix from the propagated navigation state and an observation model, and propagation of the error state and the covariance matrix using the matrix of transition associated with the cycle k considered and given by the elementary matrix calculated at the interval and the noise matrix of model using relationships:

5. A method according to any one of the preceding claims, wherein the inertial tracking device (ID) comprises a laser rangefinder and / or a lidar, and a measurement of the carrier's position and / or velocity is performed by telemetry during the update step (1E2).

6. A method according to any one of the preceding claims, wherein the tracking device (ID) comprises a camera, and a measurement of the carrier's position and / or velocity is performed by the camera during the update step (1E2).

7. A method according to any one of the preceding claims, wherein the tracking device (ID) comprises a means for measuring the vertical position, and a measurement of the carrier's vertical position and / or velocity is performed by said measuring means during the update step (1E2).

8. An inertial localization device (ID) comprising an inertial sensor block (ISB), at least one external sensor (ES), and means configured to implement a method according to any one of the preceding claims.

9. A computer program comprising instructions that cause the device (ID) according to the preceding claim, when such instructions are executed by the device (ID), to implement the method (100) according to any one of claims 1 to 7 when said program is executed by a computer.

10. Computer-readable medium on which the computer program according to the preceding claim is recorded.

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