EP2686640A1

EP2686640A1 - Method and device for fusing partitioned correlated signals

Info

Publication number: EP2686640A1
Application number: EP12713901.2A
Authority: EP
Inventors: Marc-André BEYER; Arne Petersen
Original assignee: Raytheon Anschuetz GmbH
Current assignee: Raytheon Anschuetz GmbH
Priority date: 2011-03-15
Filing date: 2012-03-15
Publication date: 2014-01-22
Also published as: WO2012123545A1; DE102011005584A1

Abstract

The present invention relates to a method, a device, a computer program product, and a navigation system for determining a piece of navigation information for an object, preferably a moving object, in particular a vehicle or aircraft, on the basis of source signals (1...K) of at least two sensors, which provide information about a navigation state of the object. Source signals are received in the form of average and covariance pairs, of which at least two can be partitioned into a potentially correlated part and an uncorrelated part. The target signal is transmitted, for example in the form of an average and covariance pair, and so a reaction of a physical system that receives the target signal is enabled.

Description

Method and apparatus for fusing partitioned correlated signals

The present invention relates to a method, a device, a computer program product and a navigation system for determining navigation information for a, preferably moving, object, in particular vehicle or aircraft, based on source signals of at least two sensors that provide information about a navigation state of the object.

The problem of data fusion of multiple source signals is a long-standing research area of signal processing. In the simplest case, simple mean values are determined from the sources and passed on as the target signal. An extension to this is represented by the weighted fusion algorithms. In this case, weights are specified for all components of the source signals, which are taken into account in the estimation of the target signal. Such algorithms include, for example, the Weighted Least Squares Estimator (WLSE). A more detailed description of the WLSE can be found in J. Chris McGIone, "Manual of Photogrammetry," 5th Ed., 2004, American Society for Photogrammetry and Remote Sensing , A commonly used data fusion method uses a Kalman filter (see also Greg Welch and Gary Bishop, "An Introduction to the Kalman Filter," UNC-Chapel Hill, 2006) In addition to measurements made via the object system, the filter uses a process model which adapts the internal state of the Kalman filter to the dynamics of the sequence of states to be estimated.This step is called prediction, and then measurements (also called observations) are used. to minimize the error introduced by the process model, this step is called correction or update.

In the correction step - the actual step of data fusion - the internal, predicted state and the measurements are fused. It is therefore possible to interpret the predicted state and the measurements as source signals to be fused which contain information about the object system.

To ensure optimum fusion of these source signals, they are provided with generalized, inverse weight matrices. These covariance matrices determine a Gaussian distribution density (see also J. Chris McGIone, "Manual of Photogrammetry", 5th edition, American Society for Photogrammetry and Remote Sensing, 2004), which describes the stochastic distribution of the errors in the Thanks to the covariances, the source signals can not only be weighted in a weighted manner, but also their internal stochastic correlations (correlations) of the source signals are considered.

In order to merge a set of source signals, given in the form of mean and covariance pairs {^ pwj, the source signals must be transformed into a common coordinate system. Such transformations are well known and are used by default in Kalman filters. For the following explanations, we assume that the source signals have been transformed into a common coordinate system and are in the form of fe P * «}. The extended form of the Kalman filter (see J. Wendel: "Integrated Navigation Systems", Oldenbourg Verlag, 2007), in which correlations {j ^ P * '* «} may exist between the different source signals, for the fusion of K signals {x _tl ^x i ^x i} in a uniform coordinate space

covariance:

Mean: z

where H = [i ... i] ^T. The fusion result is present as the mean and kovarance pair {z, P ^ZZ }.

Usually, the correlations to P ^XIX > = 0 are assumed, which simplifies the fusion equation to the well-known inverse form of the Kalman filter:

The numerator variables and in the above and for all subsequent equations are defined as follows:

Counter variable: i = 1 ... AT

Counter variable: j = 1 ... K

A fundamental problem is that often the cross-correlations P ^XIX > 0 are. If you take them in the Kalman filter to P ^XI J = 0 - which is a common practice - so the fusion result can be inconsistent, ie which means that the estimated error covariance matrix P ^{zz is} smaller than the covariance of the true error P ^zz . This inconsistency can lead to useless results of the estimation process.

In the case of unknown cross correlations of source signals, various methods have been developed in the past to ensure the consistency of the estimate of the target signal and its covariance.

The simplest method is to scale the obtained covariance matrix P ^z by a factor greater than one.

However, since this factor can only be determined empirically, such a procedure is very error-prone. If the scaling chosen is too small, the covariance is underestimated, which leads to the problems mentioned above. If the factor is too large, the estimate loses information because it is considered to be too inaccurate.

An improved method is the "Covariance Intersection" (Cl) SJ Julier and JK Uhlmann, "A Non-divergent Estimation Algorithm in the Presence of Unknown Correlations"; Proceedings of the American Control Conference, Albuquerque New Mexico, 1997. It determines the inverse of the error covariance matrix of the target signal from a convex combination of the inverse of the error covariance matrices of the source signals With

In this case, all components of the different source signals are assumed to be potentially correlated. Under this assumption, the method provides an improved estimate of the target signal and its covariance. However, no known information about the structure of the correlations of the source Signals are exploited, which would further improve the estimation of the target signal.

A generalization of CI is provided by the so-called "split covariance intersection" (SCI, see also SJ Julier and JJ LaViola Jr.: "An Empirical Study into the Robustness of Split Covariance Addition (SCA) for Human Motion Tracking"). It allows an additive distribution of the source signals into uncorrelated and correlated parts: p ^x l ^x ip ^x i ^x i

' ^r u' ^r c> where the first term with index u represents uncorrelated parts and the second term with index c represents potentially correlated parts.

To merge the data, the incoming covariances are divided into blocks according to the division. Subsequently, scalings for the potentially correlated blocks P ^x _c ^{m of} the source signals are determined and applied to them. The correlations between the blocks within the individual covariances are discarded. In this way, the correlations between the source signals can be further limited. However, since the correlations of the blocks within the covariances of the source signals are discarded, information about the structure of the covariances contained in them is lost.

Because of this, no optimal result is obtained for the estimation using the source signals.

The invention has for its object to provide a method and apparatus for determining a navigation information, which are characterized by high accuracies.

This object is achieved with the features specified in claim 1 and 7 respectively.

Furthermore, the invention provides a corresponding navigation system. Some embodiments of the method and apparatus are adapted to receive source signals, here in the form of mean and covariance pairs, of which at least two may be partitioned into a potentially correlated part and an uncorrelated part, and to transmit the target signal, in the form a mean and covariance pair so as to enable a response of a physical system receiving the target signal.

Advantages of embodiments of the invention are that the knowledge about the partitioning can be introduced optimally into the estimation process, whereby the accuracy of the fusion result is increased while at the same time guaranteed consistency.

The invention will be described below.

The invention has several alternative or additive embodiments, e.g. a method for data fusion, a device (device) for data fusion, as well as an implementation of the method in the device.

These three parts are explained in detail below.

The invention is explained in more detail below with reference to exemplary embodiments with reference to the drawings.

Fig. 1 shows a basic flow diagram of an inventive

Data fusion,

2 shows a schematic block diagram of a data fusion system according to the invention,

Fig. 3 shows a practical embodiment of an inventive

Data fusion procedure, and

Fig. 4 shows a practical embodiment of an inventive

Data fusion device in the form of a navigation system. FIG. 1 shows a basic flow chart of a data fusion according to the invention with several stages or steps.

The fusion used here is done by subdividing the source signals into their correlated and uncorrelated components. The structure of the correlations or partitioning is known or recognizable by analysis or estimation. Each source signal of a uniform coordinate space, present in the form of a mean and covariance pair {x P ^x ^}, is transformed into an unknown, potentially correlated partition and a known correlated partition according to FIG

rP ^x i, cu ^x i, cu p ^x i, cu ^x i, ck ~ \

p ^x i ^x i-

ip ^x i, ck i, cu p ^x i, ck ^x i, ckl

disassembled. These decompositions according to stage or step 04 take place in stage or step 02 for all source signals. The composite mean vector and the encryption bundkovarianzmatrix (mean values and covariance matrices of the composite system) are given by p ^x i, cu ^x i, cu p ^x l, cu ^x i, c k p ^x i, cu ^x K, cu p ^x K, cu i , cu p ^x K, cu ^x i, ck p ^x K, cu ^x K, cu

p ^x K, ck i, cu p K, ck ^x i, ck p ^x K, ck ^x K, cu where the cross covariances ρ * <^' . ™ * \ ™ are unknown. Here, cu stands for "correction unknown" and ck for "correlation known" (known correlation). A conservative estimate of this composite is given by p ^x i, cu ^x i, cu p ^x i, cu ^x i, ck

% lp ^x i, ck ^x l, cu p ^x l, ck ^x l, ck 1

^Χκ 0 ... p ^x KK p ^x K, ck ^x i, cu p ^x K, ck ^x ck

p K, ck ^x K, cu p ^x K, ck ^x K, ck with

The conservative estimation of the composite is passed on to step or step 06, in which the associated optimum weights λ, are determined. The choice of weights is fundamentally not decisive for the consistency of the fusion result, but rather for its quality in the form of a measure for the fused covariance matrix. The task of determining the weights corresponds to a nonlinear optimization problem of the form min / (P ^zz )

and can be treated with standard methods e.g. according to S. Boyd and L. Vandenberghe, "Convex Optimization", Cambridge University Press, 2008. The quality function can be any measure of the covariance matrix, such as trace, determinant, Lp norm, etc.

The resulting weights λ, are passed on after the determination in step or step 06 at step or step 08. There, the outputs of the stages or steps 04 and 06 are used to separate the partitioning and corresponding scaling of the different covariance matrices in the partitions according to step 10.

The conservatively estimated composite system is now in step 12 or over

z = p ^zz

fused, where H = [i ... i] ^T. This fusion form with the conservatively estimated composite system guarantees the consistency of the fusion result while at least equal accuracy compared to the existing approaches and is an aspect of the invention.

Finally, the fused target signal (mean and covariance pair) is transferred to stage or step 14, where it is made available for further processing.

In the following, a basic data fusion system according to the invention will be described with reference to FIG.

Fig. 2 shows a block diagram of the data fusion system according to the present invention. This includes a measuring system 16 for measuring properties of an object system 44.

A detector 18 detects signals of the object system 44 which contain information about the states of the object system 44. A connection 20 connects the detector 18 to the measuring system 16 in order to realize a signal transmission from the detector 18 to the measuring system 16. It should be noted that the connection 20 and all of the following connections may represent wired, wireless or other connection types or a combination thereof.

A connection 22 connects the measuring system 16 to a signal processing unit 24 for transmitting the information about the object system 44 obtained via the measuring system 16.

The signal processing unit 24 includes a central processing unit or CPU (Central Processing Unit) 26 for processing signals supplied from the measurement system 16 via the connection 22. The CPU 26 may be a computation unit such as a microprocessor, a multiprocessor, or an analog computer, but is not limited to these examples. The signal processing unit 24 further includes a machine-readable memory 28 for storing signals received from the measuring system 16, for storing intermediate signals. and final results of the CPU 26 and for storing program instructions for the CPU 26. The machine-readable memory 28 consists for example of a combination of optical and electronic storage media and may be, for example, a combination of writable (read-write) and write-protected (read-only) storage media ,

A connection 32 connects the signal processing unit 24 to an optional display unit 30 for transmitting signals for display on the display unit 30.

A connection 36 connects the signal processing unit 24 to an optional input unit 34 for transmitting signals to the signal processing unit 24 that are input by the user to the input unit 34. The input unit may e.g. a combination of input units such as e.g. Mouse, keyboard, or any other device for manually entering information to the signal processing unit 24.

A link 40 connects the signal processing unit 24 to a response system 38 for communicating signals from the signal processing unit 24 to the response system 38. The response system 38 is responsive to signals received from the signal processing unit 24 over the link 40 by performing a function depends on the state of the object system 44. This condition is determined by the signal processing unit 24. The reaction of the reaction system 38 may be e.g. affect the state of the object system 44.

If, for example, the system according to FIG. 2 is a navigation system for vehicles, in particular for watercraft, the measuring system 16 corresponds to a collection of vehicle-specific sensors, such as inertial navigation systems, GNSS receivers (Global Navigation Satellite System), Compasses, logs, rotation sensors, depth sensors, or other sensors that provide information about the condition of a vehicle. The signal processing unit 24 receives this information in the form of mean value pairs and covance pairs and calculates therefrom a navigation state for the vehicle in FIG Form of a mean and covariance pair and a set of derived navigation information. The results of the signal processing unit 24 are then transmitted to the reaction system 38. The response system 38 may respond to this navigation information.

For example, if the system of FIG. around a navigation system for vehicles, in particular for watercraft, the reaction system 38 may e.g. a system for dynamic positioning of vehicles or a system for the management of weapons for vehicles or a system for course or train or speed or depth or position control for vehicles.

Fig. 3 shows a flow chart of a practical embodiment of a data fusion method according to the present invention.

Processing instructions according to steps 46 and 48 form a set of source signals consisting of received measurements and stored estimates calculated from previous measurements.

In step 50, the measurements and estimates are transformed into a uniform coordinate space, so that source signals in the form {χ ₀ Ρ ^χ ι ^χ ί} are present.

In the following step 52, the partitions of the source signals are determined. Following this, in step 54, the optimal weights for scaling the partitions of the source signals are determined.

Scaling and partitioning are done in step 56. The optimal fusion is done in step 58.

An output of the estimate is made in step 60.

Step 62 generates a physical response based on the signal transmitted in step 60.

Step 64 determines whether the calculated target signal should be stored (step 66) for eventual further processing. At step 68, the calculated target signal is optionally propagated forward in time. The presented implementation describes a system for estimating a state sequence using a Kalman filter. An optimal combination of the multiple measurements and their covariances with previous estimates is made. The method shown in FIG. 3 may be implemented as a software program for controlling a computerized system, wherein code means of the program are configured to generate at least some of the steps shown in FIG. 3 when executed on a processor device of the computerized system. The software program can be stored on a removable and computer-readable medium.

FIG. 4 shows a practical exemplary embodiment of a device according to the invention, which is designed here as navigation system 70 for determining navigation information for a preferably moving object, in particular a vehicle or aircraft, based on source signals Qi of at least two sensors. At least two sensors provide information about a navigation state of the object as source signals to a receiving device 71. A detection device 72 connected to the receiving device 71 serves to detect the source signals in the form of mean value and covariance pairs. A first setting device 73 effects a determination of partitions for at least two source signals. A second setting device 74 connected to the first setting device 73 is provided for determining optimum weights for scaling the obtained partitions of the at least two source signals in a defined coordinate space.

A signal processing device 75 is provided for partitioning and scaling the at least two source signals into potentially correlated components and uncorrelated components using the partitions and weights determined by the first and second setting devices 73, 74. An evaluation device 76 is designed for fusing the partitioned and scaled source signals taking into account the potentially correlated components in order to obtain a fused target signal, and for deriving navigation information Nl from the fused target signal. An example of deriving navigation information is the conversion of a speed of Cartesian coordinates in polar coordinates. In the merged target signal, velocities are typically in Cartesian coordinates (eg, velocity to the north and east), from which polar coordinates (eg, velocity and heading over ground) are derived. Alternatively or additionally, data such as, in particular, navigation information data may be present in the fused target signal, which need no further conversion, but can be used directly for the desired purposes, so that in this case the derivation is ultimately limited to removal from the target signal.

An embodiment of the invention provides a method for determining a fused target signal from a set of K> 2 source signals, wherein each source signal / ^' , 1 <i <K carries information about a physical object system in the form of a mean and covariance pair.

Each source signal / is decomposable into a potentially correlated and known correlated partition, according to

A conservative estimate of the source signal / ^' at unknown correlation pHcuH uj _s t then given by causing the new composite system

With results.

The fused target signal is defined by a mean and covariance pair {z, P ^zz } which passes through

z

calculated, where H = [i ... i] ^T. The parameters λ, are calculated as a function of the covariance matrix P ^zz .

In this method, the parameters λ, can be determined so that the covariance matrix P ^zz or a sub-block of P ^{zz is} of minimum size, based on the arithmetic measures determinant, track, weighted Lp norm and largest eigenvalue.

Alternatively or additionally, in this method, the parameters λ, can be determined so that the covariance matrix P ^zz or a sub-block of P ^{zz is} of maximum size, based on the arithmetic measures determinant, track, weighted Lp norm and largest eigenvalue.

The merged target signal may correspond to the navigation state of a vehicle, in particular a watercraft. One or more source signals may correspond to position and / or velocity measurements from inertial navigation systems and / or GNSS receivers.

According to one embodiment, a programmed signal process unit may be provided for determining a fused target signal from the set of K> 2 source signals. The parameters λ, are calculated as a function of the covariance matrix P ^zz , whereby the programmed signal process unit can be designed by means of mathematical algorithms for determining the parameters λ, such that the covariance matrix P ^zz or a sub-block of P ^{zz is} of minimum size, relative to the arithmetic measures determinant, lane, weighted Lp norm and largest eigenvalue.

Alternatively, the programmed signal processing unit, including mathematical algorithms for determining the parameters λ, can be designed so that the covariance matrix P ^zz or a sub-block of P ^{zz is} of maximum size, based on the arithmetic measures determinant, track, weighted Lp norm and largest eigenvalue ,

In the signal processing unit, the merged target signal may correspond to the navigation state of a vehicle, in particular a watercraft, and one or more source signals may correspond to position and / or speed measurements from inertial navigation systems and / or GNSS receivers.

The following proves a theorem that can serve as a basis for embodiments of the invention:

For this it is assumed that vectors

Xi, l <i <K, are constructed as follows from partitions:

, cu ^x l, ck]

2 = [ ^X 2, cu 2, cfc]

^X K- [ ^x K, cu ^x K, ck and that P can be represented as a positive definite error covance matrix, ie a ^T Pa> 0 for all column vectors with a 0, as follows:

It should now be proved that for the matrix

- p ^x i, cu ^x i, cu p ^x i, cu ^x i, ck 0

P ^x X i, cck ^x K, cu

, p ^x i, ck ^x i, cu p ^x i, ck ^x i, ck

P ^x K, cu ^x i, ck p K, cu ^x K, cu p ^x K, cu ^x K, ck p ^x K, ck Xck

p ^x K, ck K, cu p K, ck ^x K, ckl for all A _t with 0 <X _t <1 and = 1 holds that P _x > PI

The requirement Ρ _λ > P corresponds to Ρ _λ - P> 0, ie Ρ _λ - Ρ must be positive semidefinite. You can calculate:

This matrix can be rotated with a rotation matrix R (similarity transformation) without changing the eigenvalues, so that

This matrix is positive semidefinite if the upper left block matrix is positively semidefinite, ie it must be shown that - -pXiXK

> 0

, (7- - ϊ) Ρ * κ * κ holds.

By transformation, one obtains the requirement:

_L pxixi

, ρ κ ^χ κ ρ ^χ κ ^χ κ

The validity of this requirement can be found in JK Uhlmann, "Covariance consistency methods for fault-tolerant distributed data fusion", Information Fusion, 2003. The theorem is thus proved, since Ρ _λ > P, it follows directly that Ρχ> 0, ie P _x positive definite because of P> 0.

In summary, a method, a device, a computer program product and a navigation system have been described for determining navigation information for a preferably moving object, in particular a vehicle or aircraft, based on source signals of at least two sensors which provide information about a navigation state of the object. Source signals are received in the form of mean and covariance pairs, of which at least two can be partitioned into a potentially correlated part and an uncorrelated part. The target signal is transmitted, for example in the form of a mean and covariance pair, so as to enable a response of a physical system receiving the target signal.

Claims

claims

1. A method for determining navigation information for a, preferably moving, object, in particular vehicle or aircraft, based on source signals of at least two sensors, which provide information about a navigation state of the object, with the steps of

• detecting (46) the source signals in the form of mean and covariance pairs;

• determining (52) partitions for at least two source signals;

• determining optimal weights (54) for scaling the fixed partitions of the at least two source signals in a defined coordinate space;

Partitioning and scaling (56) the at least two source signals into potentially correlated components and uncorrelated components using the determined partitions and weights;

Fusing (58) the partitioned and scaled source signals, taking into account the potentially correlated components, to obtain a fused target signal; and

Deriving the navigation information from the merged target signal.

The method of claim 1, wherein the partitioning and scaling (56) is performed separately using different covariance matrices in the determined partitions.

The method of claim 1 or 2, wherein the source signals include first source signals containing received measurements and second source signals indicating stored estimates calculated from previous samples.

The method of at least one of the preceding claims, _{wherein said} partitioning comprises decomposing the mean value x _t of each source signal / ^' into an unknown correlated partition x _liCU and a known correlated partition x _ck and forming a covariance matrix *' according to:

~ p ^x i, cu ^x i, cu p ^x i, cu ^x i, ck

.p ^x i, ck ^x l, cu p ^x l, ck ^x l, ck.

and a conservative estimate of the source signal / given unknown correlation p ^x ucu ^x u is given by: resulting in the new composite system of mean and covariance pairs with:

with 0 < _t <1 and = 1, where K denotes the number of source signals. The mean value f and the covariance matrix P ^{ZZ of} the fused target signal are calculated as:

-1

Η

, ρ ^χ κ ^χ ί. , ρ ^χ κ κ. z

■ ^χ κ- where Η = [/ ... ι] ^τ and the parameters are calculated as a function of the covariance matrix P ^ZZ .

5. The method of claim 4, wherein the parameters are determined such that the covariance matrix or a sub-block of the covariance matrix of minimum size is at least one of the arithmetic measures determinant, track, weighted Lp norm, and largest eigenvalue.

6. The method according to at least one of claims 1 to 5, wherein the merged target signal indicates a navigation state of a vehicle, in particular a watercraft, and one or more of the source signals based on measurements of the position and / or speed of the object.

7. Device for determining navigation information for a, preferably moving, object, in particular vehicle or aircraft, based on source signals of at least two sensors that provide information about a navigation state of the object with

A receiving device (71) for receiving the source signals (Qi) of the at least two sensors;

• detection means (72) for detecting the source signals in the form of mean and covariance pairs; A first fixing device (73) for defining partitions for at least two source signals;

Second determining means (74) for determining optimal weights for scaling the obtained partitions of the at least two source signals in a defined coordinate space;

• signal processing means (75) for partitioning and scaling the at least two source signals into potentially correlated components and uncorrelated components using the partitions and weights determined by the determining means; and

An evaluation means (76) for fusing the partitioned and scaled source signals, taking into account the potentially correlated components, to obtain a fused target signal and for deriving navigation information from the fused target signal.

The apparatus of claim 7, wherein the source signals (Qi) include first source signals that include received measurements and second source signals that indicate stored estimates calculated from previous samples.

9. Navigation system with a device according to claim 7 or 8.

10. Navigation system according to claim 9, wherein the obtained fused target signal is supplied to a physical system and a reaction of the physical system takes place on the obtained target signal.

11. The navigation system of claim 10, wherein the physical system is a system for dynamically positioning a vehicle, to Weapons line for vehicles or a system for course or train or speed or depth or position control has.

12. Navigation system according to at least one of claims 9 to 10, wherein the merged target signal indicates a navigation state of a vehicle, in particular a watercraft, and one or more of the source signals (Qi) based on measurements of the position and / or speed of the object.

13. Navigation system according to at least one of claims 9 to 12, which at least one satellite-based navigation system and another navigation system, in particular an inertial navigation system, comprises.

14. Computer program product with code means for generating the steps according to at least one of claims 1 to 6 in its execution on a processor device.