CN115615456A - Sensor error registration method and device based on iteration nearest integer point set - Google Patents

Sensor error registration method and device based on iteration nearest integer point set Download PDF

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CN115615456A
CN115615456A CN202210929959.8A CN202210929959A CN115615456A CN 115615456 A CN115615456 A CN 115615456A CN 202210929959 A CN202210929959 A CN 202210929959A CN 115615456 A CN115615456 A CN 115615456A
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刘海宁
詹光
段恒宇
耿欢
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Shenyang Aircraft Design and Research Institute Aviation Industry of China AVIC
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Abstract

The application provides a sensor error registration method and device based on an iteration nearest integer point set, which comprises the following steps: constructing an equation for describing the track state of the maneuvering target; constructing an equation for describing the measurement of the sensor on the target; calculating to obtain system error estimation based on the measurement point set of the operation target; substituting the target track state estimation and the error covariance thereof at the previous moment into a maneuvering target track state equation to calculate so as to realize real-time track prediction of the target; adopting a Kalman filtering algorithm, and carrying out track filtering updating after obtaining the measurement of the target by the sensor, thereby obtaining the target track state estimation and the error covariance thereof at the current moment; and subtracting the system error estimation from the sensor target measurement to realize system error compensation, substituting the compensated target measurement into the track filtering residual error again to obtain a target track state estimation value at the current moment, and finally obtaining an unbiased tracking result of the target track.

Description

Sensor error registration method and device based on iteration nearest integer point set
Technical Field
The application belongs to the technical field of aircraft airborne multi-source information fusion, and particularly relates to an iterative nearest integer point set sensor error registration method and device.
Background
The airplane airborne multi-source information fusion is that target measurement information is obtained through various sensors such as radar, infrared and electronic countermeasure, and the multi-source information is subjected to layered processing and integration, so that the space-time coverage is expanded, the target precision is improved, and the use strategy of the sensors is optimized. The error registration of the sensor is the primary link of multi-source information fusion, and means that the influence on the target track tracking precision is reduced by carrying out real-time estimation and compensation on the regular system errors in the measurement information of the sensor under a unified space-time system.
The existing sensor error registration method mainly comprises two types of off-line estimation and on-line estimation. Off-line estimation is usually only applicable to the case of constant system error of the sensor, and is not effective for a Non-cooperative target (Non-cooperative target); on-line estimation needs decoupling processing of system error estimation and track filtering, and meanwhile, a system model is required to be accurate enough and harsh for algorithm application.
Disclosure of Invention
It is an object of the present application to provide a sensor error registration method based on an iterative nearest integer point set to solve or mitigate at least one of the problems of the background art.
The technical scheme of the application is as follows: a method of sensor error registration based on a set of iterative nearest-neighbor integer points, the method comprising:
constructing an equation for describing a maneuvering target track state, wherein the equation of the maneuvering target track state is expressed by a linear recursion equation, and the linear recursion equation contains zero-mean random process noise;
constructing an equation for describing the measurement of the sensor to the target, wherein the equation for the measurement of the sensor to the target contains volume average random measurement noise and stable system error;
calculating by adopting a minimum mean square error estimation method based on the measurement point set of the synthetic target to obtain system error estimation;
substituting the target track state estimation and the error covariance thereof at the previous moment into a maneuvering target track state equation to calculate so as to realize real-time track prediction of the target;
adopting a Kalman filtering algorithm, and carrying out track filtering updating after obtaining the measurement of the target by the sensor, thereby obtaining the target track state estimation and the error covariance thereof at the current moment;
and subtracting the system error estimation from the sensor target measurement to realize system error compensation, substituting the compensated target measurement into the track filtering residual error again to obtain a target track state estimation value at the current moment, and finally obtaining an unbiased tracking result of the target track.
Further, the linear recurrence equation is: x (k) = A (k) x (k-1) + w (k)
In the formula, k is a sampling time, x (k) and x (k-1) are target motion states of the current time k and the last time k-1 respectively, A (k) is a state matrix, and w (k) is random process noise with zero mean and covariance of Q.
Further, the equation of the sensor for the target measurement is as follows:
z i (k)＝H i (k)x(k)+e i +v i (k)
wherein i is a sensor number, z i (k) For the target measurement, H i (k) To measure the matrix, v i (k) Random measurement noise with zero mean and covariance R, e i Is the systematic error.
Furthermore, in a two-dimensional plane, aiming at the characteristics of distance measurement and angle measurement, the measurement matrix is
Figure BDA0003779164800000021
The system error is
Figure BDA0003779164800000022
Wherein x is s 、y s Respectively for sensor to targetMeasuring point in X-axis coordinate and Y-axis coordinate of plane rectangular coordinate system, e r 、e θ The system errors of the sensor in the distance dimension and the azimuth angle dimension are measured on the target respectively.
Further, the process of obtaining the systematic error estimate includes:
based on the set of metrology points for the same cooperative target, the m-time repeated metrology set Z is Z = { Z = { (Z) } i,1 ,z i,2 ,...,z i,m }；
Obtaining the estimated value of the system error by solving by adopting a minimum mean square error estimation algorithm
Figure BDA0003779164800000031
Optimal estimation of established system errors
Figure BDA0003779164800000032
E is the mathematical expectation symbol, and the right end of the equation indicates that the deviation between the estimated systematic error value and the actual systematic error value under the condition of the known measurement set is minimal.
Further, in the real-time track prediction of the target, the target track state estimation at the previous time k-1 meets the time updating equation:
Figure BDA0003779164800000033
the error covariance at the last time instant k-1 satisfies the time update equation: p (k | k-1) = A (k) P (k-1) A T (k)+Q；
Wherein the content of the first and second substances,
Figure BDA0003779164800000034
p (k-1) is the covariance of the track state estimation error at the previous time,
Figure BDA0003779164800000035
and P (k | k-1) is the covariance of the prediction error of the track state at the current moment.
Further, in the kalman filtering algorithm, the kalman filtering state update equation is as follows:
Figure BDA0003779164800000036
Figure BDA0003779164800000037
the target track state estimation and the error covariance at the current moment are respectively as follows:
Figure BDA0003779164800000038
P(k)＝[I-G(k)*H i (k)]P(k|k-1)
wherein res i (k) G (k) is the filter gain;
Figure BDA00037791648000000310
and P (k) is the target track state estimation value at the current moment, P (k) is the target track state estimation error covariance at the current moment, and I is an identity matrix of a corresponding order.
Further, compensated target metrology
Figure BDA00037791648000000311
Compensated filtered residual
Figure BDA00037791648000000312
After the flight path filtering residual equation is substituted into the flight path filtering residual equation again, the target flight path state estimated value at the current moment is as follows:
Figure BDA0003779164800000041
and finally obtaining an unbiased tracking result of the target track.
In addition, the present application also provides an apparatus, comprising:
a memory for storing a computer software program;
a processor for reading and executing the computer software program, thereby implementing the sensor error registration method based on the iterative nearest integer point set as described in any one of the above.
Finally, the present application also provides a non-transitory computer readable storage medium having stored therein a computer software program for implementing the iterative nearest-neighbor integer point set-based sensor error registration method as defined in any of the above.
Compared with the prior art, the method provided by the application realizes effective identification and estimation of the inherent regularity system error of the sensor, guarantees the unbiased characteristic of target track tracking, improves the precision and guarantees the global consistency of target track tracking.
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In order to more clearly illustrate the technical solutions provided by the present application, the following briefly introduces the accompanying drawings. It is to be expressly understood that the drawings described below are only illustrative of some embodiments of the invention.
FIG. 1 is a schematic diagram of an overall point set of sensor to target measurements in the present application.
Fig. 2 is a flowchart of a sensor error registration method based on an iterative nearest neighbor global point set in the present application.
Fig. 3 is a schematic diagram of an electronic device in the present application.
Fig. 4 is a schematic diagram of the composition of a computer-readable storage medium in the present application.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application.
According to the iterative nearest neighbor-based error registration method for the integral point set sensor, the optimal system error estimation value with the minimum mean square error significance is obtained through integral utilization of a target actual measurement point set, and the method is continued to a target track iterative updating process taking Kalman filtering as a frame. The method can improve the accuracy and stability of the maneuvering target track tracking, and effectively inhibit the influence of system errors.
As shown in fig. 1, the iterative nearest neighbor based error registration method for an overall point set sensor provided by the present invention includes:
s1, constructing a mathematical model or equation for describing the maneuvering target track state, wherein the maneuvering target track state can be expressed by a linear recursion equation and contains zero-mean random process noise.
In the application, the following equation is adopted to describe the maneuvering target track state:
x(k)＝A(k)x(k-1)+w(k)
wherein k is a sampling time, x (k) and x (k-1) are respectively a target motion state at the sampling time k and a last sampling time k-1, A (k) is a state matrix, and w (k) is random process noise with zero mean and covariance of Q.
And S2, constructing an equation for describing the measurement of the sensor on the target.
The following equation is used in this application to describe the measurement of the target by the sensor:
z i (k)＝H i (k)x(k)+e i +v i (k)
wherein i is a sensor number, z i (k) For the target measurement, H i (k) To measure the matrix, v i (k) Random measurement noise with zero mean and covariance R, e i Is the systematic error.
Wherein, in the two-dimensional plane, aiming at the distance measurement and angle measurement characteristics, the measurement matrix and the system error are respectively defined as:
Figure BDA0003779164800000051
and
Figure BDA0003779164800000052
in the formula, x s 、y s Respectively an X-axis coordinate system of the sensor for the target measurement point in a plane rectangular coordinate system,Y-axis coordinate, e r 、e θ The system errors of the sensor in the distance dimension and the azimuth angle dimension are measured on the target respectively.
The measurement of the sensor to the target contains zero-mean random measurement noise and stable system error, which are respectively expressed as the discrete distribution degree of a measurement point set and the deviation degree of a measurement value and a true value, and the two are mutually independent.
As shown in fig. 2, each scatter point represents a measurement result of the sensor on the target by the above formula, and together form an integral point set of the target. Based on the space nearest neighbor criterion, an integral point set envelope circle taking the measured mean value as the center of a circle is constructed, and the position relation between the integral point set envelope circle and the target truth value represents the discrete distribution degree and the deviation truth value degree of the integral point set.
S3, estimating a system error: and calculating to obtain system error estimation by adopting a minimum mean square error estimation algorithm based on a measurement point set of a cooperative target (cooperative target).
Based on the set of measurement points for the same cooperative target, the m-time repeated measurement set Z is:
Z＝{z i,1 ,z i,2 ,...,z i,m }；
obtaining the estimated value of the system error by solving by adopting a minimum mean square error estimation algorithm
Figure BDA0003779164800000061
Optimal estimation of established system errors
Figure BDA0003779164800000062
E is the mathematical expectation symbol, and the right end of the equation indicates that the deviation between the estimated systematic error value and the actual systematic error value under the condition of the known measurement set is minimal. The larger the number m of times is, the optimal estimation of the system error is
Figure BDA0003779164800000063
Closer to system error e i 。
S4, target real-time track prediction: and substituting the target track state estimation and the error covariance thereof into a maneuvering target track state equation to calculate based on the target track state estimation at the last moment k-1, so as to realize the real-time track prediction of the target.
The target track state estimation at the previous moment meets a time updating equation:
Figure BDA0003779164800000064
the error covariance at the previous time instant satisfies the time update equation:
P(k|k-1)＝A(k)P(k-1)A T (k)+Q；
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003779164800000065
p (k-1) is the covariance of the track state estimation error at the previous time,
Figure BDA0003779164800000066
and P (k | k-1) is the covariance of the prediction error of the track state at the current moment.
S5, track filtering updating: and adopting a Kalman filtering algorithm, performing iterative solution after the target is measured by the sensor, and outputting the target track state estimation and the error covariance thereof at the current moment.
Wherein, the Kalman filtering state update equation comprises:
Figure BDA0003779164800000071
Figure BDA0003779164800000072
after the measurement of the sensor on the target is obtained, iterative solution is carried out:
Figure BDA0003779164800000073
P(k)＝[I-G(k)*H i (k)]P(k|k-1)
wherein res i (k) G (k) is the filter residual, and G (k) is the filter gain;
Figure RE-GDA0003981348980000074
and P (k) is a target track state estimation value at the current moment, P (k) is a target track state estimation error covariance at the current moment, and I is an identity matrix of a corresponding order.
S6, compensating a system error: and (3) subtracting the system error estimation value from the target measurement by the sensor to realize system error compensation, and substituting the compensated target measurement into a track filtering residual error calculation formula again to obtain an unbiased tracking result of the target track.
The specific process comprises the following steps:
the compensated target is measured as
Figure BDA0003779164800000076
The compensated filter residual is
Figure BDA0003779164800000077
After the measurement after spatial registration is substituted into the track filtering residual, the target track state estimated value at the current moment is
Figure BDA0003779164800000078
And finally obtaining an unbiased tracking result of the target track.
Compared with the prior art, the method provided by the application realizes effective identification and estimation of the inherent regularity system error of the sensor, guarantees the unbiased characteristic of target track tracking, improves the precision and guarantees the global consistency of target track tracking.
Referring to fig. 3, fig. 3 is a schematic view of an embodiment of an electronic device or an onboard device according to an embodiment of the present disclosure.
As shown in fig. 3, the embodiment of the present application provides an electronic device 500, which includes a memory 510, a processor 520, and a computer program 511 stored in the memory 520 and capable of running on the processor 520, and the processor 520 executes the computer program 511 to implement the following steps:
constructing an equation for describing a maneuvering target track state, wherein the equation for describing the maneuvering target track state is expressed by a linear recursion equation, and the linear recursion equation contains zero-mean random measurement noise and system errors;
constructing an equation for describing the measurement of the sensor on the target;
calculating by adopting a minimum mean square error estimation method based on the measurement point set of the synthetic target to obtain system error estimation;
substituting the target track state estimation and the error covariance thereof at the previous moment into a maneuvering target track state equation to calculate so as to realize real-time track prediction of the target;
adopting a Kalman filtering algorithm, and carrying out track filtering updating after obtaining the measurement of the target by the sensor, thereby obtaining the target track state estimation and the error covariance thereof at the current moment;
and subtracting the system error estimation from the sensor target measurement to realize system error compensation, substituting the compensated target measurement into the track filtering residual error again to obtain a target track state estimation value at the current moment, and finally obtaining an unbiased tracking result of the target track.
Referring to fig. 4, fig. 4 is a schematic diagram of an embodiment of a computer-readable storage medium according to an embodiment of the present application.
As shown in fig. 4, the embodiment of the present application provides a computer-readable storage medium 600, on which a computer program 611 is stored, wherein the computer program 611 implements the following steps when being executed by a processor:
constructing an equation for describing a maneuvering target track state, wherein the equation of the maneuvering target track state is expressed by a linear recursion equation, and the linear recursion equation contains zero-mean random measurement noise and system errors;
constructing an equation for describing the measurement of the sensor on the target;
calculating by adopting a minimum mean square error estimation method based on the measurement point set of the synthetic target to obtain system error estimation;
substituting the target track state estimation and the error covariance thereof at the previous moment into a maneuvering target track state equation to calculate so as to realize real-time track prediction of the target;
adopting a Kalman filtering algorithm, and carrying out track filtering updating after obtaining the measurement of the target by the sensor, thereby obtaining the target track state estimation and the error covariance thereof at the current moment;
and subtracting the system error estimation from the sensor target measurement to realize system error compensation, substituting the compensated target measurement into the track filtering residual error again to obtain a target track state estimation value at the current moment, and finally obtaining an unbiased tracking result of the target track.
It should be noted that, in the foregoing embodiments, the description of each embodiment has an emphasis, and reference may be made to the related description of other embodiments for a part that is not described in detail in a certain embodiment.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (10)

1. A method for sensor error registration based on an iterative nearest integer point set, the method comprising:
constructing an equation for describing a maneuvering target track state, wherein the equation of the maneuvering target track state is expressed by a linear recursion equation, and the linear recursion equation contains zero-mean random process noise;
constructing an equation for describing the measurement of the sensor to the target, wherein the equation for measuring the target by the sensor contains volume mean value random measurement noise and system error;
calculating by adopting a minimum mean square error estimation method based on the measurement point set of the synthetic target to obtain system error estimation;
substituting the target track state estimation and the error covariance thereof at the previous moment into a maneuvering target track state equation to calculate so as to realize real-time track prediction of the target;
adopting a Kalman filtering algorithm, and carrying out track filtering updating after obtaining the measurement of the target by the sensor, thereby obtaining the target track state estimation and the error covariance thereof at the current moment;
and subtracting the system error estimation from the sensor target measurement to realize system error compensation, substituting the compensated target measurement into the track filtering residual error again to obtain a target track state estimation value at the current moment, and finally obtaining a target track unbiased tracking result.
2. The method for sensor error registration based on the set of iterative nearest integer points of claim 1, wherein the linear recurrence equation is: x (k) = A (k) x (k-1) + w (k)
In the formula, k is a sampling time, x (k) and x (k-1) are respectively the target motion states of the current time k and the last time k-1, A (k) is a state matrix, and w (k) is random process noise with zero mean and covariance of Q.
3. The method of iterative nearest integer point set based sensor error registration according to claim 2, wherein the equation for the sensor to target measure is:
z i (k)＝H i (k)x(k)+e i +v i (k)
wherein i is a sensor number, z i (k) For the target measurement, H i (k) To measure the matrix, v i (k) Random measurement noise with zero mean and covariance R, e i Is the systematic error.
4. The method of claim 3 for sensor error registration based on a set of iterative nearest integer pointsWherein, in the two-dimensional plane, the measurement matrix is for the distance measurement and angle measurement characteristics
Figure FDA0003779164790000021
The system error is
Figure FDA0003779164790000022
Wherein x is s 、y s Respectively as the X-axis coordinate and the Y-axis coordinate of the sensor to the target measurement point in a plane rectangular coordinate system r 、e θ Respectively, the sensor measures the systematic error of the target in the distance dimension and the azimuth dimension.
5. The iterative nearest integer point set-based sensor error registration method of claim 4, wherein obtaining the systematic error estimate comprises:
based on the set of metrology points for the same cooperative target, the m-time repeated metrology set Z is Z = { Z = { (Z) } i,1 ,z i,2 ,...,z i,m }；
Obtaining the estimated value of the system error by solving by adopting a minimum mean square error estimation algorithm
Figure FDA0003779164790000023
Optimal estimation of established system errors
Figure FDA0003779164790000024
E is a mathematical expectation symbol, and the right end of the equation indicates that the deviation degree between the estimated value of the systematic error and the actual value of the systematic error under the condition of the known measurement set is minimum.
6. The method for sensor error registration based on the set of iterative nearest integer points according to claim 5, wherein in the real-time track prediction for achieving the target, the target track state estimation at the last time k-1 satisfies a time update equation:
Figure FDA0003779164790000025
the error covariance at the last time k-1 satisfies the time update equation: p (k | k-1) = a (k) P (k-1) a T (k)+Q；
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003779164790000026
p (k-1) is the covariance of the track state estimation error at the previous time,
Figure FDA0003779164790000027
and P (k | k-1) is the covariance of the prediction error of the track state at the current moment.
7. The method for registering the sensor errors based on the iterative closest-to-integer point set according to claim 6, wherein in the kalman filtering algorithm, a kalman filtering state update equation is as follows:
Figure RE-FDA0003981348970000031
Figure RE-FDA0003981348970000032
the target track state estimation and the error covariance thereof at the current moment are respectively as follows:
Figure RE-FDA0003981348970000033
P(k)＝[I-G(k)*H i (k)]P(k|k-1)
wherein res i (k) G (k) is the filter residual, and G (k) is the filter gain;
Figure RE-FDA0003981348970000034
and P (k) is a target track state estimation value at the current moment, P (k) is a target track state estimation error covariance at the current moment, and I is a unit matrix of a corresponding order.
8. The method of claim 7, wherein the compensated target metric is based on an iterative nearest integer point set
Figure FDA0003779164790000036
Compensated filtered residual
Figure FDA0003779164790000037
After the flight path filtering residual equation is substituted into the flight path filtering residual equation again, the target flight path state estimated value at the current moment is as follows:
Figure FDA0003779164790000038
and finally obtaining an unbiased tracking result of the target track.
9. An apparatus, characterized in that the apparatus comprises:
a memory for storing a computer software program;
a processor for reading and executing the computer software program, thereby implementing the sensor error registration method based on the set of iterative nearest integer points according to any of claims 1 to 8.
10. A non-transitory computer-readable storage medium, characterized in that the storage medium has stored therein a computer software program for implementing the iterative closest-to-integer-point-set-based sensor error registration method according to any one of claims 1 to 8.
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