EP1157284A1

EP1157284A1 - Device for hybridizing a satellite positioning receiver with an inertial unit

Info

Publication number: EP1157284A1
Application number: EP00990065A
Authority: EP
Inventors: Nicolas Thomson-CSF Propriété Intell. Martin
Original assignee: Thales Avionics SAS
Current assignee: Thales Avionics SAS
Priority date: 1999-12-21
Filing date: 2000-12-19
Publication date: 2001-11-28
Also published as: IL144914A; FR2802732B1; IL144914A0; ZA200106724B; WO2001046712A1; FR2802732A1

Abstract

The invention concerns the hybridization of an inertial unit and a satellite positioning receiver in order to correct the long-term drift of the inertial unit. There are two known types of hybridization, one called loose and the other one called tight . Loose hybridization has the disadvantage of requiring complete measurements from the positioning receiver but it does not involve the use of sensitive data from the positioning receiver. Tight hybridization operates even with a positioning receiver supplying incomplete data but requires the use of sensitive data from the positioning receiver. The invention provides a hybridization halfway between loose hybridization and tight hybridization having the advantages of both but without their drawbacks.

Description

DEVICE FOR HYBRIDIZING A SATELLITE POSITIONING RECEIVER WITH AN INERTIAL POWER PLANT

The present invention relates to hybridization using a

Kalman, information delivered by a satellite positioning receiver with information coming from an inertial unit.

Kalman filtering, which appeared in 1960, is a signal processing technique making it possible to optimally reduce the noises of various origins accompanying, inevitably, the signals generated by an equipment, from a modeling of the evolution of the state of the equipment considered within its environment and of a modeling of the dependence relationship existing between the measurable signals coming from the equipment and its state. It implements a recursive filter whose realization is greatly facilitated by the generalization of digital signal processing. Its field of application is very wide since it applies to any system whose evolution of the state and the relation of dependence between its state and signals accessible to the measurement can be modeled. It is widely used in aeronautics, for the treatment of noises affecting measurements renewed periodically and for the fusion of information of the same type coming from measurements coming from several pieces of equipment implementing different physical principles.

An important field of use of Kalman filters is that of navigation computers which must develop information for piloting assistance such as position, attitudes (roll, pitch and heading) and speed vector with the best possible precision, despite noises measurement and faults specific to each sensor. In the context of navigation computers, the Kalman filter makes it possible to make short-term predictions on the errors affecting the expected inertial data (position, attitudes, and speed vector) from the estimates of the values taken by these same errors in a recent past and their known laws of evolution according to the environment of the flight computer, and to deduce from these short-term forecasts, corrections to be made to the information drawn from the measurements coming from the sensors to make them optimal, it that is, as precise as possible. -.

The Kalman filtering technique will not be detailed here since it is within the competence of a person skilled in the art and has already been the subject of an abundant literature.

Briefly, the Kalman filtering technique is based on the possibility of modeling the evolution of the state of a physical system considered in its environment, by means of an equation called "evolution", and on the possibility of modeling the dependence relation existing between the state of the physical system considered and the signals or "measure" by which it is perceived from the outside, by means of an equation called "observation" to make a forecast a priori of the state of the system and of the measurement, taking into account the history

It consists in subjecting the effective measurement designated by the term of "measurement vector" because it often relates to several quantities, to a filtering making it possible to extract from it an estimate a posteriori of the state of the system also designated by "vector of state "because the state of a system is often defined from several pieces of information not necessarily equal to that of the measured variables, which is optimal, in the sense that it minimizes the covaπance of the error made on this a posteriori estimation of the state of the system The filter used to do this is an adaptive recursive filter which generates a priori estimates of the system state vector and the measurement vector from the evolution and observation equations , and which uses the difference observed between the measurement vector actually observed and its estimated a priori to generate a corrective term which, applied to the a priori estimate of the state vector of the system, leads to obtaining the optimal estimate a posteriori

The adaptive adjustment of the Kalman filter is obtained using a servo loop tending to minimize the covaπance of the error made on the posterior estimation of the state vector of the system. Kalman which are well known, will be recalled later

One of the oldest applications of the Kalman technique, in aeronautics, concerns the correction of errors affecting position, attitude and speed vector information obtained by a navigation computer on the basis of the only information delivered by the sensors of an inertial measurement unit, an operation known as "hybridization of an inertial unit"

In this application, the Kalman filter is used to provide an optimal estimate of the errors affecting the information extracted from the measurements delivered by the inertial unit by the navigation computer. The system, whose dynamic behavior is modeled, has as state vector, a vector having as components the errors on the information made by the computer from the measurements of the inertial unit and for vector of measurement a vector having as components the errors measured on information accessible to the measurement The modeling of its dynamic behavior is defined by means of an evolution equation translating, as faithfully as possible, the deterministic laws known to be followed by the errors considered in the environment in which the system is immersed, a function for example of the kinematics of the movement of the carrier of the inertial unit, and by an observation equation translating the r dependency relationships existing between the errors on the information accessible to the measurement and the errors taken into account in the state vector In the case where the deterministic evolution of an error on an information is not known, it is considered as static in the definition of the evolution equation In practice, the measurement vector, which does not necessarily have the same dimension as the state vector, is made up of the differences observed between two versions of the same information deduced one of the signals from the inertial unit and the other from the signals from one or more other equipment not subject to the same drift This information can be, for example, the heading deduced on one side, from the measurements of the the inertial unit and on the other, the measurement of a compass or a radio compass, the altitude deduced on one side, measurements of the sensors of the inertial unit and on the other, measurements of a radio altimeter or barometric, the speed or the relative position of the mobile with respect to a reference to the ground on one side delivered by a radar and on the other reconstructed from the measurements of the inertial unit, or again, the position and the speed vector on the one hand delivered by a satellite positioning receiver or GNSS receiver (Global Navigation Satellite System in Anglo-Saxon language) and on the other extracts from the measurements of the inertial unit In a first step, the navigation computer performs the conventional calculations by integrations, making it possible to obtain information on the position, the attitudes and the speed vector of its carrier from the raw data provided by the sensors of the measurement unit. inertial, while in a second step, a Kalman filter performs optimal estimates of the errors made, used to correct or readjust, in a third step, the information delivered by the navigation computer

The fact of applying the Kalman filtering to the estimation of the errors affecting the physical quantities measured and not to the estimation of the physical quantities themselves allows the Kalman filter to operate on a signal of lesser amplitude and less scalable whose dynamic behavior modeling lends itself better to a linear approximation

Another known application of the Kalman filter concerns the filtering of measurement noise in the processing part of a GNSS receiver.

A GNSS receiver is made up of a reception part which provides, for each satellite in the constellation of the positioning system from which the transmission signals are received, the data transmitted by this satellite and two kinds of measurements which are pseudodistance and pseudo- speed of the receiver with respect to the satellite considered, and of a calculation part which provides from this data and measurements, the position and the speed vector of the receiver carrier as well as the time The calculation part operates on the basis of the data transmitted by the visible satellites and measurements of the reception part

The system which the calculation part must solve to obtain the position (or the speed) has four unknowns (position x, y, z, and time t or speed Vx, Vy, Vz and clock drift) and has as many equations as of visible satellites A GNSS receiver is therefore capable of delivering a position and speed vector measurement of its carrier, as well as of time, as soon as it receives four satellites from the positioning system In practice, it often receives more than four The number of equations then being greater than the number of unknowns, the resolution can be carried out by the method of least squares, which makes it possible to minimize the vanance of errors on the position and the resolved speed, due to measurement noises In this case the precision on the position and the resolved speed depends only on the geometry of the constellation of the visible satellites, characterized by the parameter DOP (Dilution Of Precision in English language) -saxon) This technique is a special case of the Kalman filter, without memory effect, because we often lack, at the GNSS receiver, to make a real Kalman filter, a reliable model of the dynamics of the carrier

In the presence of a GNSS receiver and an inertial unit, we have quite naturally sought to use the Kalman filtering technique to achieve the fusion of their navigation information at the level of the navigation computer of the inertial unit Such an operation is known in the art as "hybridization between a GNSS receiver and an inertial reference"

Two types of hybridization are known between a GNSS receiver and an inertial reference, a so-called "loose" hybridization and a so-called "tight" hybridization.

Loose hybridization consists in using, with a navigation computer equipped with an inertial measurement unit, a complete GNSS receiver, with its specialized computer often provided at the output with a first Kalman filter usually degenerated into a least squares filter , without memory effect, and to provide the navigation computer with an error estimator, in the form of a second Kalman filter based on the modeling of the dynamic behavior of a physical system made up of the inertial measurement unit , the navigation computer and the part of the GNSS receiver delivering the clock signal

The modeled system used for the design of this second Kalman filter has, among the components of its state vector, the expected errors on the position coordinates of the mobile carrying the navigation computer and the GNSS receiver and the expected errors on the components of the mobile speed vector, taken from the acceleration and angular velocity components delivered by the navigation computer The measurement vector adopted to operate this second Kalman filter has, among the components of its measurement vector, the differences between two versions of the position coordinates and of the components of the speed vector, one delivered by the GNSS receiver, the other delivered by the mertiel navigation computer

The modeling of the dynamic behavior of the adopted system is defined, in the usual way, by an evolution equation translating the deterministic laws of evolution known for the components of its state vector and by an observation equation translating the relations of dependence between the measurement vector and the state vector

This loose hybridization has various disadvantages

First of all, it requires the GNSS receiver to deliver a complete position and speed vector measurement and cannot operate if the GNSS receiver only receives an insufficient number of satellites in the positioning system (less of four)

It does not allow to take into account the quality of the information delivered by the GNSS receiver, linked to the geometry of the constellation of visible satellites (Dilution Of Precision) On the other hand, it can be used in all circumstances, without particular precautions, since it does not call on the GNSS receiver any confidential data such as pseudorange measurements corrected for intentional interference intended to reduce positioning accuracy for users not approved by the manager of the satellite positioning system. Securing the GNSS system, however, arises within the GNSS receiver itself, but it can be resolved by special provisions ensuring the confinement of confidential data in a restricted protected volume.

The tight hybridization between a GNSS receiver and an inertial reference consists in operating at the level of the basic information available in a GNSS receiver that are the pseudo-distances or relative distances separating the GNSS receiver from the received satellites and the pseudo-speeds or speeds of the relative displacements of the satellites received by report to the GNSS receiver and therefore to short-circuit, for the resetting of the navigation computer the calculation part of the receiver

The Kalman filter used in the navigation computer is then based on the modeling of the dynamic behavior of a system defined by

a state vector with, among its components, the expected errors on the position coordinates and on the components of the speed vector, extracted from the acceleration and angular velocity components delivered by the navigation computer, and the bias and the derived from the receiver clock, an evolution equation translating the known evolution laws of the components of its state vector,

- a measurement vector with, among its components, differences between two versions of pseudo-distances and pseudo-speeds originating from one the satellite positioning receiver and the other the navigation computer, an equation of observation translating the dependence relationships existing between the measurement vector and the state vector,

The navigation computer performs the processing necessary to extract measurements from the inertial measurement unit, the position, speed vector and attitude information of the wearer II then uses this position and speed vector information of the wearer as well that information on the positions and speed vectors of the satellites of the positioning system supplied to it by the GNSS receiver from the data transmitted by these satellites themselves to calculate the values of the pseudo-distances and pseudo-speeds between the carrier and these satellites

We are then in possession of two versions of pseudo-distances and pseudo-speeds, one drawn from the measurements of the inertial measurement unit and data transmitted by the satellites, the other drawn from the measurements of the GNSS receiver concerning the durations of transmission and Doppler shifts affecting the signals emitted by the satellites visible from the positioning system The differences between these two versions, constituting the measurement vector, are then subjected to Kalman filtering to filter the measurement noise and obtain an optimal posterior estimate of the state vector used to readjust the navigation computer L ' most apparent advantage of this form of tight hybridization is to avoid involving the computing part of the GNSS receiver and using a single Kalman filter and not two nested, one processing the output signals of the computing part the GNSS receiver and the other the drift of the navigation computer The other advantage, important from the point of view of accuracy, is the taking into account of the geometry of the satellites (number and arrangement in space) because of the possibility of resetting the a priori estimate of the position and of the speed vector deduced from the measurements of the inertial unit according to the different directions of the satellites received, whatever their number. The tight hybridization, te lle that it is currently made, on the other hand the disadvantage of requiring the extraction, within the GNSS receiver, of the measurements of pseudo-distances, pseudo-speeds of the satellites of the positioning system which are sensitive information as soon as they are corrected for the effects of intentional interference. This forces the GNSS receiver and the navigation computer to be placed within the same security perimeter, which can cause arduous problems in the arrangement of equipment on a carrier and increase the cost of their installations.

The object of the present invention is to avoid the abovementioned drawbacks

It relates to a hybridization device, within a navigation computer, of a satellite positioning receiver with an inertial unit equipping a mobile, comprising a filter

Kalman, with an input and an output, based on the modeling of the dynamic behavior of a system and defined by a state vector with, among its components, the expected errors on the position coordinates and on the components of the speed vector, extracted from the acceleration and angular velocity components delivered by the navigation computer, an evolution equation translating the known evolution laws of the components of its state vector,

a measurement vector with, among its components, differences between two versions of pseudo-distances and pseudo-speeds originating from one of the satellite positioning receiver and the other from the navigation computer,

- an observation equation translating the dependence relationships existing between the measurement vector and the state vector, characterized in that it comprises, inserted before the input of the Kalman filter, a circuit for synthesizing the differences between pseudo -distances and pseudo-speeds operating from the two versions of position information and speed vector of the mobile delivered one, by the satellite positioning receiver and the other, by the navigation computer, and using, for do the direction cosines of the axes connecting the mobile to the visible satellites of the positioning system, deduced from the positions of said visible satellites extracted from the data transmitted by the latter and captured by the satellite positioning receiver and from one of the available versions of the position information of the mobile

Advantageously, the Kalman filter has, among the components of its state vector, the bias and the drift of the receiver clock.

Advantageously, the synthesis circuit deduces the directing cosines of the axes connecting the mobile to the visible satellites of the positioning system, from the positions of said visible satellites extracted from the data transmitted by the latter and picked up by the satellite positioning receiver, and from the version d position information of the mobile delivered by the navigation computer

As a variant, the synthesis circuit deduces the director cosines of the axes connecting the mobile to the visible satellites of the positioning system, from the positions of said visible satellites extracted from the data transmitted by the latter and picked up by the receiver of satellite positioning, and the mobile position information version from the satellite positioning receiver

As a variant, the synthesis circuit receives the values of the directing cosines of the axes connecting the mobile to the visible satellites of the positioning system directly from the satellite positioning receiver which itself deduces them from the positions of said visible satellites extracted from the data transmitted by the latter and its own version of information on the position of the mobile delivered by the navigation computer

A hybridization is thus obtained, having the same advantages from the point of view of a criterion of least squares (optimality) as tight hybridization while not using sensitive or not necessarily accessible data from the reception part of the GNSS receiver.

Other characteristics and advantages of the invention will emerge from the description below, of an embodiment of the invention given by way of example. This description will be made with reference to the drawing in which a figure 1 represents the diagram. in principle of a Kalman filter,

FIG. 2 represents the block diagram of a “loose” hybridization between an inertial unit and a GNSS receiver according to the state of the prior art,

- Figure 3 shows the block diagram of a "tight" hybridization between an inertial unit and a receiver

GNSS according to the state of the prior art, and

- Figure 4 shows the block diagram of a hybridization according to the invention

In FIG. 1, a distinction is made between the quantities relating to the measurement or to the state of a system, as a function of the fact that it is a measurement or an effective state or that it is of a measurement or state estimation by assigning or not the terms which represent them with a circumflex accent and a double index Thus, the effective measurement applied to the input of the Kalman filter shown in FIG. 1 is denoted by z while the optimal estimate of the state of the system available at the output of this Kalman filter is designated by x _lh or _,, „, The index i / i means that we are dealing with an a posteriori estimate on step ia starting from information available in step i while a double index ι / ι-1 means that we are dealing with an a priori forecast on step i from information coming from step ι-1

A Kalman filter makes it possible to obtain an estimate of the posterior state of an optimal system in the sense that the probability of the error made on this posterior estimate is minimal II is based on a modeling of the evolution of the system and on a modeling of the relation existing between the measurement and the state of the system

In its greatest generality, the modeling of the evolution of the state of the system is defined by a first order vector differential equation which is expressed after discretization of the continuous model by an evolution equation of the form Y, = x +, ιι _k T 11 _; x being a state vector of dimension n, u a control vector, F, a matrix defining the relationship between the state vector in step 1 and the state vector in step ι + 1 in l absence of control vector and operating noise, L, a matrix defining the relationship between the control vector and the state vector during the same step and w an operating noise during a step, assumed white and gaussian with zero mean value

The modeling of the relation existing between the measurement and the state of the system is defined by another first order differential equation which is expressed, after discretization of the continuous model, by an equation of observation of the form

-, = ^H ι ^X , + ^V ι z being a measurement vector of dimension m, H, a matrix defining the relation between the measurement vector and the state vector during the same step and v a noise of measurement during a step assumed to be white and Gaussian with zero mean value

As shown in Figure 1, the Kalman filter is recursive. It is based on the determination of an a priori estimate, „_, of the state vector of the system in step i from a posteriori knowledge of the vector d state of the system *, _,, _, in the previous step ι-1 and of the application to this estimated a priori À-,,, of a corrective term depending on the difference found between the vector measure r, observed during this step i and its estimated a priori f,, _, deduced from the a priori estimate v ,,, of the state vector

The a priori estimate z,, _, of the measurement vector in step i is determined by applying the evolution and observation equations to the posterior estimate Ϋ,,,, of the state vector and at control vector II. corresponding to step ι-1 above This operation is illustrated in your figure 1 by the presence of a feedback loop consisting of a delay circuit 1, three filters 2, 3 4 and a summator 5 The circuit delay 1 connected at the output of the Kalman filter makes it possible to store the posterior estimate v,,, _, of the state vector available at the output of the Kalman filter during the previous step ι-1

The two filters 2 and 3 and the summator 5 make it possible, by implementing the observation equation, to obtain the a priori estimate v, - of the state vector in step i, from of the posterior estimate î,,,, of the state vector of the system in the previous step ι-1

Filter 2 provides the component of the a priori estimate J _{1 / (} _, of the state vector in step i depending on the a posteriori estimate £, _ ,,, _, of the state vector at l step ι-1 Its transfer function is defined by the matrix E, _, of the observation equation

The filter 3 provides the component of the a priori estimate x _ι _ _] of the state vector in step i depending on the control vector w, _, corresponding to step ι-1 Its transfer function is defined by the matrix

Z _; _, from the observation equation The summator 5 adds the two components delivered by filters 2 and 3 and provides the a priori estimate x _; _, from the state vector in step i as it results from the application of the evolution equation

This a priori estimate ,,,, of the state vector in step i is then used to obtain, by means of a third filter 4, the a priori estimate i _{; / ι} _, of the measurement vector at l step i by application of the evolution equation This third filter 4 has, to do this a transfer function defined by the matrix H, of the observation equation

The a priori estimate z _lh of the measurement vector in step i obtained in the feedback loop is applied, at the input of the Kalman filter, to a subtractor circuit 8 which also receives the measurement vector actually measured during step i, z _t and which delivers an error vector /; attesting to the error made during the a priori estimation This error vector r, is transformed by a fourth filter 6 into a correction vector This correction vector is added by a second summator 7 to the a priori estimate v ,, of the state vector for step i from the first summator 5, to obtain the posterior estimate x,, of the state vector which constitutes the output of the Kalman filter

The fourth filter 6, which provides the corrective term, is known as the registration gain filter II has a transfer function defined by a matrix K _t determined so as to minimize the covaπance of the error made on the estimate. a posteriori

Kalman showed that the optimal gain matrix K, could be determined by a recursive method from the equations of the covaπance matrix of the a priori estimate of the state vector.

F = h PF ^τ + 0

- defining the gain matrix itself

- updating the covaπance matrix of the a posteriori estimate of the state vector

P,, = {l - K, H,) P _ι ^

P being the covaπance matrix of the state vector, either estimated a priori for step i from step ι-1 if P is affected by the index ι / ι-1, or estimated a posteriori if P is assigned the index ι-1, R being the covaπance matrix of observation noises w _t , Q being the covaπance matrix of state noises v,

On initialization, the covanance matrix of the state vector and the state vector are taken equal to their most likely estimates. At worst, the covanance matrix is a diagonal matrix with infinite or very large terms (so to have very large standard deviations in front of the domain in which the state vector is likely to evolve) and the estimated state vector the null vector, when we have no idea about the initial values

In practice, the correction gain of a Kalman filter is "proportional" to the uncertainty on the a priori estimate of the state of the system and "inversely proportional" to the uncertainty in the measurement If the measurement is very uncertain and the estimate of the state of the system relatively precise, the difference observed is mainly due to the measurement noise and the resulting correction must be low On the contrary, if the uncertainty on the measurement is low and that on the estimation of the state of the system large, the difference observed is very representative of the estimation error and must lead to a strong correction. the behavior towards which we tend with the Kalman filter

In summary, the construction of a Kalman filter requires the definition of two matrices F and L corresponding to the evolution equation defining the evolution of the state vector of the modeled physical system, of a matrix H corresponding to the observation equation defining the relations allowing to pass from the measurement vector to the state vector, and from the gain matrix K updated using an iterative process bringing into play the covanance matrix of the vector of state P itself updated during the iterative process and Q and R covanance matrices of state and observation noise

We note, this will have its utility thereafter, that if we want to no longer take into account the state vector of the system in the previous step and therefore delete the memory effect of a Kalman filter, it suffices for that of replacing at each step E _,,, = E _{,, E,,,,} E ^r , + 0 _,, by a diagonal matrix P _ιh _ _} with infinite or very large terms (so as to have standard deviations very large in front of the domain in which the state vector is likely to evolve) _{/ / /} _ ₁ r, In this case the matrices F and Q become useless and the estimate a posteriori Y, ,, of the state vector becomes independent of the a priori estimate, _, of the state vector, which can be taken equal to zero

The Kalman filtering technique is often used when it is a question of seeking an optimal estimate of the same physical quantity, several estimates of which are available from several pieces of equipment operating according to different physical principles and not presenting the same defects. In the case of a hybridization between an inertial unit and a GNSS satellite positioning receiver, the Kalman filtering is carried out at the level of the discrepancies noted between two versions of information of the same type coming from one of the inertial unit and, the other of the GNSS receiver, because it allows to work on variables with more restricted areas of variation on which the linear approximation can be used to simplify the modeling and evolution equations

In this use of Kalman filtering, the evolution equation modeling the foreseeable evolution of the errors made by the navigation computer on the information that it deduces from the measurements provided by the inertial measurement unit is rather translated by a single matrix. F which depends on the parameters of the carrier's movement, that is to say the flight parameters in the case where the carrier equipped with the navigation computer and the inertial measurement unit is an aircraft. The definition of the different versions of this matrix F as a function of the parameters of the movement of the wearer leaves the field of the present invention It will not be detailed hereinafter because it is well known to those skilled in the art specializing in the field of inertia

FIG. 2 represents the diagram of the principle of a loose hybridization between an inertial unit and a GNSS receiver. A distinction is made therein the inertial measurement unit UMI 10 which delivers increments of angles Δφ ^ Aφ ^ toφ. and speed increments AV _x , V _y , AV _l according to an orientation tπedre x, y, z linked to its sensors, - the navigation computer 1 1 which receives the increments of angles and speeds coming from the UMI 10 and extract from it the position P, the speed vector V and the attitudes Att of the wearer and, - the GNSS receiver 13 which provides another version of the position P and the speed vector V To facilitate comparison with the following assemblies, the GNSS receiver 13 is shown in a representation detailing its reception part 13a delivering the pseudo-distances pd and pseudo-speeds pv of the carrier relative to the visible satellites and its computer part 13b extracting from 1 D

pseudo-distance pd and pseudo-speed pv information, the position P and the speed vector V of the carrier

In this loose hybridization, position and speed vector from the navigation computer 11 and the GNSS receiver 13 are subjected to a subtractor 14 determining their deviations The deviations observed in position ΔP and speed vector ΔV feed a Kalman filter 15 which extracts them an optimal posterior estimate of the measurement bias of the sensors of the inertial measurement unit UMI 10 and of the errors made on the position P, the speed vector V and the attitudes of the wearer by the navigation computer, and which applies this optimal estimate a posteriori to the navigation computer in order to readjust it

The Kalman filter 15 used here is based on an evolution equation corresponding to a modeling of the drifts of the system consisting of the navigation computer 1 1 supplied with information by the inertial measurement unit 10 and on an observation equation modeling the relationships between the measurement vector and the state vector

The computer 13b of the GNSS receiver 13 generally uses a Kalman filter often reduced to a least squares filter without memory which performs spatial filtering in order to extract, from the information of pseudo-distance pd and pseudo-speed pv, a single information of position and vector speed of the carrier and time which is as precise as possible by reducing the measurement noise of the GNSS receiver We are then in the presence of a complex structure with two nested Kalman filters Independently of this, the loose hybridization also has the disadvantage of requiring, to be operational, a complete measurement on the part of the GNSS receiver 13 which must therefore have been able to receive at least the signals of four satellites of the positioning system

FIG. 3 represents the block diagram of a close hybridization between an inertial unit and a GNSS receiver

As before, the UMI 10 delivers increments of angles Δ (- ^* ^, Δ < ^* 0 _v , Δ! - / ^* > _ and increments of speed AV, Al, V. according to an orientation tπèdre x , y, z linked to its sensors to a navigation computer 1 1 responsible for extracting from these increments of angles and speed, the position P, the speed vector V and Attitudes of the wearer, while the GNSS receiver 13 provides another version of the position P and of the speed vector V of the wearer

Here, the GNSS receiver 13 is used to readjust the navigation computer 1 1 in a manner different from the loose hybridization. The final information on the position P and the speed vector V of the carrier delivered by its computer 13b, are not used for registration They are replaced by the intermediate measurements of pseudo-distances pd and pseudo-speeds pv with respect to the different visible satellites of the constellation of the positioning system which are available at the output of its reception part 13a

To do this, a synthesizer circuit S 20 is added at the output of the navigation computer 1 1 II receives from the GNSS receiver, by a particular link, additional information on the positions and speeds of the satellites extracted from the data transmitted by the satellites themselves and calculates, from this additional information and information of position P and speed V of the carrier delivered by the navigation computer 1 1, estimates pd ei pv of the pseudo-distances and pseudo-speeds The two versions of pseudo-distances pd and pseudo-pv speeds available, one calculated by the synthesizer S 20 and the other measured by the reception part 13a of the GNSS receiver 13 are subjected to a deviation detector 21 The observed deviations Δpd and Δpv between the two versions of each pseudo-distance and each pseudo-speed are applied at the input of a Kalman filter 22 which delivers, at the output, an optimal estimate a posteriori of s measurement bias of the sensors of the inertial measurement unit UMI 10 and of the errors made on the position P, the speed vector V and the attitudes of the wearer by the navigation computer This optimal estimate a posteriori is then submitted to the navigation computer in order to readjust it The Kalman filter 22 used HERE can be based on the same evolution equation as the Kalman filter 15 used previously for the loose harmonization illustrated in FIG. 2 However, its observation equation must be adapted to the new measurement vector In general, the estimated state vector X of the Kalman filters used in the loose or tight harmonization devices of FIGS. 2 and 3 is of dimension n and contains different components including

= [~, δ „, δ„, δ ,. , d „δ, δ,, δ _; , T, -]

5 _^ , 0 ^, t) _% . being the errors on the components v _χ) v _v , v of the speed of the carrier, t being the bias of the clock of the GNSS receiver, d being the drift of the clock of the GNSS receiver, δ _x , δ _y , δ . being the errors on the coordinates χ, y, z of the position of the carrier, and it is associated, with the state vector estimates X, a square matrix of covanance P of dimension nxn The Kalman filtering consists, to readjust optimally , the state vector estimated from the measurement vector Z by providing it with a correction δX = KZ

K being the gain matrix, the determination method of which, described in relation to FIG. 1, uses the covanance matrix P of the state vector updated according to an iterative process, the covaπance matrix R of the observation noises , to the observation matrix H and to the measurement or observation vector Z

As the covanance matrix P of the state vector is updated iteratively starting from the worst of an initial covanance matrix having an infinite standard deviation, the Kalman filter is perfectly defined by means of its estimated state vector X , of the matrix F defining by modeling, the evolution of its state vector, of its observation vector

Z, of the matrix H defining the relationships between observation vector and state vector, and of the covanance matrix R of the observation noises

Within the framework of the loose hybridization of figure 2, the elements to be taken into consideration for the definition of the Kalman filter, outside the matrix F translating the evolution equation of the model are - for the part relating to the registration position x -b δ δ _t δ _: t

^XX C \ 'SS b 0 0 z = y - y _GN s R 0' o

_. '~ ^Z GVSS 0 0 r.

> position estimated by the navigation computer in terrestrial reference

^X GNSS

} 'G \ SS position estimated by the GPS receiver in terrestrial reference

^Z GNSS)

bb vanance associated with measures x _cvss , y _aNSS , z _GNSS r.

and for the speed adjustment part:

x - [δ _n δ _ι: ï

v - v OvSS ^ 0 0

V - v „., _- R o ^ 0 v. - V. „„ _< .- 0 0 r v speed vector in terrestrial coordinate system delivered by the navigation computer

speed vector in landmark issued by the GPS receiver

variances associated with the speed vector measured by the GPS receiver

In the calculator part of the GNSS receiver, we use another Kalman filter often reduced to a least square filter, that is to say without memory effect, to resolve the position, the speed vector of the carrier and the time while minimizing measurement noise The elements to be taken into consideration for its definition are '

- for the part relating to position registration.

δX _z = [δ, δ. ï

x - X a. =

A y -y, β,

P, r,

P P = V (* - ² + o -j, y + (----,) ^:

p, = i ( ^χ - ^χ , y + {y -y, y + (= - -, δ _x .δ _y .δ _∑ being the differences between the actual position of the carrier and an a priori estimate of this position, t being the error made over time by the clock of the GNSS receiver, made homogeneous at a distance by multiplication by the speed of light, α „β„ γ, being the direction cosines of the axis connecting the carrier to the same satellite in the coordinate system used by the navigation computer, x, y, z being the a priori estimate of the position of the carrier, given by the GNSS receiver before correction, deduced for example from the position estimated at the previous resolution, x ,, y ,, z, being the position of the lth satellite of the positioning system extracted from the data of the lth satellite, expressed in the same frame as the position of the carrier, p, being the a priori pseudo-distance separating the carrier from the lth satellite, calculated from the a priori position of the carrier and the data transmitted by the lip e satellite pd, being the pseudo-distance between the carrier and the same satellite measured by the GNSS receiver, and r _pd , the vanance of the pseudo-distance measured pd,

for the speed part

^d P, - ^V v,) β, + { ^V. ^{~ V} .n) r,

δv _x , δVy, δv _z being the components of the difference between the real speed vector of the carrier and an a priori estimate of this speed vector, d being the drift of the clock of the GNSS receiver, made homogeneous at a speed by multiplication by the speed of light, v _x , v _y , v _z being the a priori estimate of the components of the speed vector of the carrier, given by the GNSS receiver before correction, deduced for example from the speed vector estimated at the previous resolution, v _xι , v _yι , v _z , being the components of the speed vector of the satellite system of the positioning system extracted from the data of the satellite itself, expressed in the coordinate system used for the speed vector of the carrier, dp, being the pseudo-speed between the carrier and the satellite lemme calculated from the a priori speed vector of the carrier and the satellite data, pv, being the pseudo-speed between the carrier and the satellite lemme measured by the GNSS receiver, and r _pvι l a vanance of the pseudo-speed measured pv. Within the framework of the tight hybridization of figure 3 the elements to be taken into consideration for the definition of the Kalman filter, apart from the matrix F translating the evolution equation of the model are

- for the part relating to position registration

δX = [δ _Υ δ _t δ. ï

X - Y, a.

A y - y, β,

AT

Y,

AT

A = V ( ^v - ^γ *) ^{2 +} C ^y -,) ^{: +} (- - ^: δ _x , δ _y , δ _z being the differences between the coordinates of the actual position of the carrier and the coordinates of the position of the carrier given by the navigation computer, t being the error made over time by the clock of the GNSS receiver, made homogeneous at a distance by multiplication by the speed of light, αi.βi.γ, being the direction cosines of the axis connecting the carrier to the lemma satellite in the coordinate system used by the navigation computer, x, y, z being the coordinates of the position of the carrier given by the navigation computer, x „y„ z, being the coordinates of the position of the same satellite of the positioning system extracted from the data of the lth satellite itself and expressed in the reference frame used for the position of the carrier, p, being the pseudo-distance calculated between the carrier and the i-th satellite, pd, being the pseudo-distance between the carrier and the lem satellite measured by the GNSS receiver, and r _pd , the variaπce of the pseudo-distance measured pd,

for the speed adjustment part

δX = [δ, „. δ, δ _v: d

p, - pv

Z, = R = pvi

pvm

- ^V y,) β, + ( ^V _- ^{~ V} _a ) Y, δvx, δyy, δ _vz being the differences between the components of the carrier's real speed vector and those given by the navigation computer, d being the drift of the clock of the GNSS receiver, made homogeneous at a speed by multiplication by the speed of the light, x, v _y , v _z being the components of the speed vector of the carrier given by the navigation computer, v _X ι, v _y ι, v _zl being the components of the speed vector of the same satellite of the positioning system extracted from the data from the same satellite itself, expressed in the coordinate system used by the navigation computer, dp, being the pseudo-speed calculated between the carrier and the satellite, pv, being the pseudo-speed between the carrier and the measured satellite by the GNSS receiver, and r _pvι the vanance of the pseudo-speed measured pv,

X - X

A y - y, β,

A _ z - z, y,

AT

To improve the hybridization between an inertial unit and a GNSS receiver, a new arrangement is proposed, shown schematically in FIG. 4.

As before, the inertial measurement unit UMI 10 delivers increments of angles Δ J _X , ΔÇ9 _V , ΔÇ9. and speed increments ΔF ^ ΔJ- ^ ΔF. according to an orientation tπèdre x, y, z linked to its sensors, to a navigation computer 1 1 responsible for extracting from these increments of angles and speed, the position P, the speed vector V and the attitudes Att of the carrier, while the GNSS receiver 1 3 provides another version of the position P and the speed vector V of the carrier

Here, the GNSS receiver 13 is again considered in its integrity, as in the case of loose hybridization, without direct access to the intermediate information delivered by its reception part, which are its pseudo-distance and pseudo-speed measurements, this which avoids the problems linked to the output of its sensitive information unit Only the final information, that is to say position, speed vector, clock information and the data transmitted by the satellites of the positioning system which are delivered by its calculation part 13b As in the context of the loose hybridization described with reference to FIG. 2, the deviations noted between the two versions of the position information and of speed of the carrier coming on the one hand from the navigation computer 1 1 itself and on the other hand from the GNSS receiver However, instead of being used as such in the measurement vector of a Kalman filter delivering the instructions for recalibration of the navigation computer, as in the case of a loose hybridization, the differences in position ΔP and in speed vector ΔV are transformed beforehand by a synthesizer circuit S _Λ 30 into ec arts of pseudo-distances Δpd and pseudo-speeds Δpv These deviations of pseudo-distances Δpd and of pseudo-speeds Δpv are then used, as in the context of the tight hybridization described with reference to FIG. 3, as components of the vector of the Kalman filter 32 delivering the readjustment instructions for the navigation computer 1 1

The synthesizer circuit S ^ receives the two versions of the position P and speed vector information V delivered one by the navigation computer 1 1 and the other by the satellite positioning receiver 13 with in addition the positions P, and speed V vectors, satellites visible from the positioning system extracted from the data transmitted by these satellites captured and decoded in the satellite positioning receiver 13

To operate the synthesis of the pseudo-distance deviations Δpd and the pseudo-speed deviations Δpv from this basic information, it needs, at an intermediate stage, the cosine directors α ,, β ,, γ, of the satellite axes in the coordinate system used by the navigation computer and the GNSS receiver

For the determination of the direction cosines α ,, β ,, γ, of the satellite axes, it uses the coordinates x ,, y ,, z, the positions of the satellites visible from the positioning system and the coordinates x, y, z of the position of the carrier The coordinates of the positions x „y,, z, of the visible satellites are supplied to it by the GNSS receiver For the coordinates x, y, z of the position of the carrier, he has the choice between two sources either, the GNSS receiver 13 or, the navigation computer 1 1

From these different coordinates, it implements the classical relationships

^p = V ( ^v - ^{2 +;} -.>',) ^: + (- - ² and

Y - X

A =

A β y - y,

P

P z - z y, =

P

It is advantageous for the synthesizer circuit S _Δ 30 to use, when determining the director cosines of the satellite axes, the information relating to the x, y, z coordinates of the position of the carrier coming from the navigation computer 11, rather than that from the GNSS receiver 13 because they are always available, which allows the synthesizer circuit S _Δ 30 to calculate the direction cosines of the directions of all the visible satellites and therefore to arrive at the pseudo-distances and pseudo-speeds of these satellites, even s '' they are insufficient in number to allow the GNSS receiver to provide an estimate of the position of the carrier.However, it is possible for the latter to use, when determining the cosines of the satellite axes, the information relating to the x coordinates. , y, z of the position of the carrier from the satellite positioning receiver II is even possible that the directing cosines of the directio ns visible satellites are directly supplied to it by the satellite positioning receiver because they are not part of the sensitive information

The Kalman filter 32 is analogous to that (22 FIG. 3) described in the context of "tight" hybridization, with the exception of the observation vector which has, as components for the pseudo-distances the quantities

a (* ^" - * CΛ S + A y -) GS-) ^T Yx (" - "C * S)

Z =

ai ^{x ~} * G ^ ss) + β, (-) G "S) + Y, (- - -GVS) J

with

position estimated by the navigation computer in terrestrial reference

^ GNSS yGtsSS position estimated by the GPS receiver in terrestrial reference

(the diagonal term of the state noise matrix Q corresponding to the estimated clock bias is increased, for example to a value greater than 10 ⁶ , so as to not take into account the time t estimated at the previous registration because there is no seeks more to model the clock of the GNSS receiver in this kind of hybridization) and, as regards pseudo-speeds, the quantities

/. ( ^V r - ^V .GV-.

) ~ Y ^(v - ^v.-Σvss)

with speed vector in landmark issued by the navigation computer

speed vector in landmark issued by the GPS receiver

(in the same way, the diagonal term of the state noise matrix Q corresponding to the estimated clock drift is also increased, for example to a value greater than 10 ^6. so as to not take account of the drift d estimated at the previous registration since we no longer seek to model the clock of the GNSS receiver in this kind of hybridization)

If the error t and the drift d of the clock of the GNSS receiver estimated by its calculation part are available as output, it is possible to take them into account in the measurement vector

for position adjustment

≈ι ( ^x - ^x cr, ss) ⁺ β (-> ^• GNSS) + / "-, (-:) + <^"

Z

a, ^(.Y - Cuss ^X) + β (y} GNSS) + ï Σ- -GNSS) ^{+ _t.} for speed registration

at - ^l '.G *) + β \ (", - ^V , CV≈ ( ^V : - ^V * sss) + ^'

Z

AT ) + d

In this case it is advantageous to model the behavior of the clock of the GNSS receiver in the evolution equation The new hybridization arrangement between an inertial unit and a GNSS receiver illustrated in FIG. 4 presents the cumulative advantages of tight hybridization and loose hybridization when the information on the position and the speed vector of the carrier used by the synthesizing circuit for calculating the directing cosines of the directions of visible satellites originate from the navigation computer

Indeed, as in tight hybridization, it allows to take into account, for the correction of the drift of the navigation computer, the precision of the information delivered by the GNSS receiver which is very dependent on the geometry of the constellation of satellites that '' it uses at the time of its triangulation (Dilution Of Precision) It also allows a certain registration of the navigation computer as soon as at least one of the satellites of the positioning system is visible from the GNSS receiver, this registration improving with the increase the number of satellites received (when the number of available satellites is less than four, the receiver's computer provides a partially readjusted position from an a priori position, deduced for example from the previous resolution)

As in loose hybridization, it does not use any confidential information from the GNSS receiver, the precision on the direction cosines of the satellite axes used by the synthesizer circuit of the pseudo-distance and pseudo-speed differences not being critical

To make it easier to understand, the navigation computer, the synthesizer circuit and the Kalman filter used to correct the errors of the inertial unit have been represented in the form of an assembly of separate boxes. It should not be concluded that this is necessarily the case in practice Indeed, as we are dealing with signals which are very often digitized, all the processing and functions performed in these different boxes can be done by means of one or more processors controlled by software and grouped in the navigation calculator

Claims

1. Hybridization device, within a navigation computer (1 1), of a satellite positioning receiver (13) with an inertial unit (10) fitted to a mobile, comprising a Kalman filter (32), with an input and an output, based on the modeling of the dynamic behavior of a system and defined by a state vector with, among its components, the expected errors on the position coordinates, the components of the speed vector, extracted from the components of acceleration and angular speeds delivered by the navigation computer,

- an evolution equation translating the known evolution laws of the components of its state vector, - a measurement vector with, among its components, differences between two versions of pseudo-distances and pseudovitesses originating from the one the satellite positioning receiver and the other the navigation computer,

- an observation equation translating the dependence relationships existing between the measurement vector and the state vector, characterized in that it comprises, inserted before the input of the Kalman filter, a synthesis circuit (30) of the deviations between pseudo-distances and pseudo-speeds operating from the two versions of position information and speed vector of the mobile, one delivered by the satellite positioning receiver (13) and the other by the navigation (1 1) and using, for this purpose, the directing cosines of the axes connecting the mobile to the visible satellites of the positioning system deduced from the positions of said visible satellites drawn from the data transmitted by the latter and picked up by the satellite positioning receiver ( 13), and one of the available versions of the mobile position information.

2. Device according to claim 1, characterized in that the synthesis circuit (30) deduces the directing cosines of the axes connecting the mobile to the visible satellites of the positioning system, positions said visible satellites extracted from the data transmitted by the latter and captured by the satellite positioning receiver (13), and from the version of position information of the mobile delivered by the navigation computer (1 1)

3 Device according to claim 1, characterized in that the synthesis circuit (30) deduces the directing cosines of the axes connecting the mobile to the visible satellites of the positioning system, from the positions of said visible satellites extracted from the data transmitted by the latter and captured by the satellite positioning receiver (13), and the mobile position information version delivered by the satellite positioning receiver (13)

4 Device according to claim 1, characterized in that the synthesis circuit (30) receives the values of the direction cosines of the axes connecting the mobile to the visible satellites of the positioning system directly from the satellite positioning receiver (13) which deduces them therefrom -Even of the positions of said visible satellites extracted from the data transmitted by them and from its own version of information on the position of the mobile

5 Device according to claim 1, characterized in that the Kalman filter has, among the components of its state vector, the bias and the drift of the clock of the receiver