CN116626666A - Maneuvering target tracking method based on interactive multi-model - Google Patents

Maneuvering target tracking method based on interactive multi-model Download PDF

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CN116626666A
CN116626666A CN202310540702.8A CN202310540702A CN116626666A CN 116626666 A CN116626666 A CN 116626666A CN 202310540702 A CN202310540702 A CN 202310540702A CN 116626666 A CN116626666 A CN 116626666A
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state
maneuvering target
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徐敏
王鹏
杨娜
占凯
周焯
刘爱华
谷宇杰
马婷婷
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Shanghai Radio Equipment Research Institute
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Abstract

The invention discloses a maneuvering target tracking method based on interactive multiple models, which is characterized in that a model set covering the movement characteristics of a target is selected, the filtering value weights of various models are adaptively adjusted according to the change of model transition probability, and finally, the filtering results of the models are interactively fused to realize the optimal filtering estimation of the target, so that the maneuvering target is stably tracked. The invention is applied to the missile-borne seeker, and can effectively improve the tracking capability of the missile-borne radar on the maneuvering target.

Description

Maneuvering target tracking method based on interactive multi-model
Technical Field
The invention relates to the technical field of maneuvering target tracking of missile-borne seekers, in particular to a maneuvering target tracking method based on an interactive multi-model.
Background
Maneuvering target tracking is a research focus in the field of target tracking, and has the core of performing state estimation under the conditions of complex interference environment and dense targets and estimating target motion trajectories and related parameters in a control area, so that a filtering algorithm is needed, and the commonly used filtering algorithm comprises kalman filtering, least square filtering and the like. The Kalman filtering is a time domain filtering method based on a state space model, and has the advantages that the filtering algorithm is recursive and is widely applied to engineering. When the assumed target motion model accords with the real target motion model, the filtering result is close to the real value, and the error between the filtering result and the real value is smaller along with the increase of the filtering time; however, when the assumed target motion model does not match the real model, a filter divergence phenomenon occurs. The Kalman filtering is based on a target motion model, but when a target moves, the motion mode in the process changes into various modes such as uniform speed, uniform acceleration, maneuvering turning and the like, the Kalman filtering can only track the target of the moving target in a single mode, the tracking performance of the maneuvering target in various modes is poor, and the problem of maneuvering target tracking cannot be solved by simple Kalman filtering.
Disclosure of Invention
The invention aims to provide an interactive multi-model-based maneuvering target tracking method, which solves the problems that Kalman filtering can only track a single-mode target and has poor maneuvering target tracking performance on the interactive multi-model.
In order to solve the technical problems, the invention is realized by the following technical scheme:
an interactive multi-model-based maneuvering target tracking method, comprising: s1, selecting a model set covering a moving model of a moving target; the conversion between the maneuvering target motion models accords with a Markov chain, and the state estimation of each maneuvering target at the previous moment is interacted to obtain the input state estimation and the state covariance of each maneuvering target motion model filter at the current moment. And S2, performing extended Kalman filtering on each maneuvering target motion model based on the input state estimation and the state covariance of each maneuvering target motion model filter at the current moment to obtain the state estimation and the state covariance of each maneuvering target motion model at the current moment. And step S3, updating the probability of each maneuvering target motion model based on the innovation and innovation covariance of each maneuvering target motion model. And S4, carrying out weighted summation on the state estimation and the state covariance according to the probability on the basis of the state estimation and the state covariance of each maneuvering target motion model at the current moment and the probability of each maneuvering target motion model to obtain the state estimation and the state covariance of the maneuvering target combination so as to realize tracking of the maneuvering target.
Optionally, the step S1 includes: step S1.1, a priori given Markov state transition matrix pi ij Calculating the probability u of transition of the maneuvering target motion model i to the maneuvering target motion model j k-1|k-1 (i|j)：
Wherein u is k-1 (j) Probability of maneuver target motion model j at time k-1, and i, j=1, 2, …, N;representing the sum of probabilities of all models being transferred to the model j as a normalization parameter for probability calculation; u (u) k-1 (i) The probability of the maneuvering target motion model i at the moment k-1.
Step S1.2, estimating the state of the maneuvering target motion model j at the moment k-1And State covariance->The input state estimation of each maneuvering target motion model filter at the current moment is obtained through interaction according to the following formula>Sum-state covariance P oj (k-1|k-1)：
Wherein P is i (k-1|k-1) represents the state estimation covariance corresponding to the model, i=1, 2, …, N.
Optionally, the specific implementation process of performing extended kalman filtering on each maneuvering target motion model in step S2 is as follows: step S2.1, one-step prediction state estimation of the maneuvering target motion model j is calculatedAnd state estimation covariance P j (k|k-1)：
P j (k|k-1)＝F j (k-1)P oj (k-1|k-1)F j (k-1) T +Q j (k-1) T
Wherein F is j (k-1) state transition matrix for maneuver object motion model j, Q j (k-1) is the process noise covariance.
Step S2.2 one step of pre-heatingState estimationConverting into measurement predicted values, wherein the relation between measurement and target states in the North east geographic coordinate system satisfies the relation:
in the method, in the process of the invention,the state vector is a state vector of the maneuvering target and respectively represents the position, the speed and the acceleration of X, Y, Z in three directions; h is a r (X k ) For radial shot distance X k Relation of (h) b (X k ) Is azimuth angle and X k Relation of (h) e (X k ) Is pitch angle and X k Relation of (h) D (X k ) For playing the radial velocity of the eye and X k Is a relationship of (2); h (X) k ) To measure the transfer function, the measurement and target state X is represented k Is a conversion relation of (a).
Because the conversion between the measurement and the target state is nonlinear, taylor expansion is carried out on the conversion between the measurement and the target state, the first-order truncation is carried out, and the corresponding Jacobin matrix is calculated, so that the measurement predicted value is obtained
Step S2.3, calculating the information(difference between measured and measured predicted values) and innovation covariance->The formula is as follows:
wherein Z (k) is a measurement taken at time k,for measuring the predicted value at k time, R j (k) Measuring the noise covariance; h j (k) The measurement conversion matrix representing the maneuver object motion model j at the k moment is a measurement conversion function h (X k ) Predicting +.>First order taylor expansion at.
Step S2.4, calculate kalman gain K j (k)：
In the method, in the process of the invention,and (5) representing an innovation covariance inverse matrix of the k-moment model j.
Step S2.5 using kalman gain K j (k) And new informationCorrecting the predicted value of the one-step state, estimating the state of the maneuvering target motion model j at the moment k>Sum-state covariance P j (k|k) is:
P j (k|k)＝(I-K j (k)H j (k))P j (k|k-1)
wherein I represents an identity matrix.
Optionally, the step S3 includes: step S3.1, calculating the likelihood of each model, namely the likelihood function lambda, based on the innovation and innovation covariance of each maneuver target motion model j (k) The formula is as follows:
s3.2, weighting the interaction probability of each maneuvering target motion model by the model probability, and carrying out normalization processing to obtain the probability u of the maneuvering target motion model at the current moment j (k) The formula is as follows:
wherein, lambda i (k) A probability density function representing model i;representing the model transition probability of model i.
Optionally, the step S4 includes: weighting and combining the state estimation and covariance of the N maneuvering target motion models according to the probability of the updated maneuvering target motion models to obtain final target state estimationAnd a state covariance P (k|k), the formula is as follows:
in the method, in the process of the invention,state estimation of a k moment model i is represented; p (P) i (k|k) represents the state estimation covariance of the k-moment model i, i=1, 2, …, N.
In another aspect, the present invention also provides an electronic device, including: a processor and a memory, the memory having stored thereon a computer program which, when executed by the processor, implements a method as described above.
In yet another aspect, the present invention also provides a readable storage medium having stored therein a computer program which, when executed by a processor, implements a method as described above.
The invention has at least one of the following technical effects:
according to the invention, the multi-model set covering the target movement mode is set, the filtering value weights of various models are adaptively adjusted according to the change of the model transition probability, and finally, the filtering results of the models are interactively fused to realize the optimal filtering estimation of the target, so that the stable tracking of the maneuvering target is realized, the tracking precision of the maneuvering target is greatly improved, the real-time performance of the target tracking is met, and the method is applied to a missile-borne seeker, and the performance of the missile-borne radar for tracking the maneuvering target can be effectively improved. The invention can well track the maneuvering targets of the interactive multi-model, and solves the problems that Kalman filtering can only track the targets of a single mode and the maneuvering targets of the interactive multi-model have poor tracking performance.
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FIG. 1 is a schematic flow chart of a maneuvering target tracking method based on an interactive multi-model according to an embodiment of the invention;
fig. 2 is a schematic diagram of multi-model filtering interaction of a maneuvering target tracking method based on an interactive multi-model according to an embodiment of the invention.
Detailed Description
The following describes a maneuvering target tracking method based on interactive multi-model according to the present invention in further detail with reference to the accompanying drawings and the detailed description. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are in a very simplified form and are all to a non-precise scale, merely for the purpose of facilitating and clearly aiding in the description of embodiments of the invention. For a better understanding of the invention with objects, features and advantages, refer to the drawings. It should be understood that the structures, proportions, sizes, etc. shown in the drawings are for illustration purposes only and should not be construed as limiting the invention to the extent that any modifications, changes in the proportions, or adjustments of the sizes of structures, proportions, or otherwise, used in the practice of the invention, are included in the spirit and scope of the invention which is otherwise, without departing from the spirit or essential characteristics thereof.
As shown in fig. 1, the present embodiment provides a maneuvering target tracking method based on an interactive multi-model, including: s1, selecting a model set covering a moving model of a moving target; the conversion between the maneuvering target motion models accords with a Markov chain, and the state estimation of each maneuvering target at the previous moment is interacted to obtain the input state estimation and the state covariance of each maneuvering target motion model filter at the current moment.
And S2, performing extended Kalman filtering on each maneuvering target motion model based on the input state estimation and the state covariance of each maneuvering target motion model filter at the current moment to obtain the state estimation and the state covariance of each maneuvering target motion model at the current moment.
And step S3, updating the probability of each maneuvering target motion model based on the innovation and innovation covariance of each maneuvering target motion model.
And S4, carrying out weighted summation on the state estimation and the state covariance according to the probability on the basis of the state estimation and the state covariance of each maneuvering target motion model at the current moment and the probability of each maneuvering target motion model to obtain the state estimation and the state covariance of the maneuvering target combination so as to realize tracking of the maneuvering target.
According to the method, the device and the system, the multi-model set covering the target movement mode is set, the filtering value weights of various models are adaptively adjusted according to the change of the model transfer probability, and finally, the filtering results of the models are integrated in an interactive mode to achieve optimal filtering estimation of the target, so that stable tracking of the maneuvering target is achieved, the tracking precision of the maneuvering target is greatly improved, the real-time performance of target tracking is met, the method and the system are applied to a missile-borne seeker, and the performance of tracking the maneuvering target by the missile-borne radar can be effectively improved. The embodiment can well track the maneuvering targets of the interactive multi-model, and solves the problems that Kalman filtering can only track the targets of a single mode and has poor tracking performance on maneuvering targets of the interactive multi-model.
As shown in fig. 1 and 2, the step S1 includes: the model set covering the moving target motion model comprises a constant speed model, a uniform acceleration model and 3 constant speed turning models with different turning rates, wherein the number of the models in the model set is N, and model input interactions of the N models are shown in figure 2.
Step S1.1, the conversion among the models meets the Markov chain, and the Markov state transition matrix pi is given according to priori ij Calculating the probability u of transition of the maneuvering target motion model i to the maneuvering target motion model j k-1|k-1 (i|j)：
Wherein u is k-1 (j) Probability of maneuver target motion model j at time k-1, and i, j=1, 2, …, N;representing the sum of probabilities of all models being transferred to the model j as a normalization parameter for probability calculation; u (u) k-1 (i) The probability of the maneuvering target motion model i at the moment k-1.
With continued reference to FIG. 2, step S1.2, for time k-1, the state estimation of maneuver object motion model jAnd State covariance->The input state estimation of each maneuvering target motion model filter at the current moment is obtained through interaction according to the following formula>Sum-state covariance P oj (k-1|k-1)：
In the method, in the process of the invention,representing the state estimate, P, of the k-1 time model i i (k-1|k-1) represents the state estimation covariance corresponding to the model i, i=1, 2, …, N.
With continued reference to fig. 2, the step S2 includes: filtering is performed on each maneuvering target motion model respectively, and 5 filtering models (cooperative turning models with uniform speed, uniform acceleration and 3 turning rates) are set in the embodiment, so that a corresponding state transition matrix F is calculated according to the motion process of each maneuvering target motion model j (k-1), process noise covariance matrix Q j (k-1)。
Step S2.1, one-step prediction state estimation of the maneuvering target motion model j is calculatedAnd state estimation covariance P j (k|k-1)：
P j (k|k-1)＝F j (k-1)P oj (k-1|k-1)F j (k-1) T +Q j (k-1) T (5)
Wherein F is j (k-1) state transition matrix for maneuver object motion model j, Q j (k-1) is the process noise covariance. One-step prediction state estimationIt can be understood that the state at time k is predicted from the estimated value at time k-1.
Step S2.2, estimating the one-step prediction stateConverting into measurement predicted values, wherein the relation between measurement and target states in the North east geographic coordinate system satisfies the relation:
in the method, in the process of the invention,state vector, x, for maneuver target k Represents the position in the X direction, < >>Represents the velocity in the X direction, +.>Representing acceleration in the X direction;
y k the position in the Y-direction is indicated,represents the velocity in the Y direction, +.>Indicating acceleration in the Y direction; z k Represents the position in the Z direction, +.>Indicating the speed in the Z direction, +.>Indicating acceleration in the Z direction; h is a r (X k ) For radial shot distance X k Relation of (h) b (X k ) Is azimuth angle and X k Relation of (h) e (X k ) Is pitch angle and X k Relation of (h) D (X k ) For playing the radial velocity of the eye and X k Is a relationship of (2); h (X) k ) To measure the transfer function, the measurement and target state X is represented k Is a conversion relation of (a).
Because the conversion between the measurement and the target state is nonlinear, taylor expansion is carried out on the conversion between the measurement and the target state, the first-order truncation is carried out, and the corresponding Jacobin matrix is calculated, so that the measurement predicted value is obtained
Step S2.3, calculating the information(difference between measured and measured predicted values) and innovation covariance->The formula is as follows:
wherein Z (k) isThe measurements taken at time k are taken,for measuring the predicted value at k time, R j (k) Measuring the noise covariance; h j (k) The measurement conversion matrix representing the maneuver object motion model j at the k moment is a measurement conversion function h (X k ) Predicting +.>First order taylor expansion at.
Step S2.4, calculate kalman gain K j (k)：
In the method, in the process of the invention,and (5) representing an innovation covariance inverse matrix of the k-moment model j.
Step S2.5 using kalman gain K j (k) And new informationCorrecting the predicted value of the one-step state, estimating the state of the maneuvering target motion model j at the moment k>Sum-state covariance P j (k|k) is:
P j (k|k)＝(I-K j (k)H j (k))P j (k|k-1) (11)
wherein I represents an identity matrix.
The step S3 is to update the model probability of each model, and comprises the following specific steps:
step S3.1, calculating the likelihood of each model, namely the likelihood function lambda, based on the innovation and innovation covariance of each maneuver target motion model j (k) The formula is as follows:
s3.2, weighting the interaction probability of each maneuvering target motion model by the model probability, and carrying out normalization processing to obtain the probability u of the maneuvering target motion model at the current moment j (k) The formula is as follows:
wherein, lambda i (k) A probability density function representing model i;representing the model transition probability of model i.
With continued reference to fig. 2, the step S4 includes: weighting and combining the state estimation and covariance of the N maneuvering target motion models according to the probability of the updated maneuvering target motion models to obtain final target state estimationAnd a state covariance P (k|k), the formula is as follows:
in the method, in the process of the invention,representing the state of the model i at time kEstimating; p (P) i (k|k) represents the state estimation covariance of the k-moment model i, i=1, 2.
An interactive multi-model based object tracking method (IMM) is a structural adaptive algorithm with markov transition probabilities that supports multiple object models to work in parallel, transitions between models with probabilities, and object states are the result of multiple filter interactions. The tracking performance of the algorithm on the maneuvering target is greatly improved.
In another aspect, the present embodiment further provides an electronic device, including: a processor and a memory, the memory having stored thereon a computer program which, when executed by the processor, implements a method as described above.
In yet another aspect, the present embodiment also provides a readable storage medium having stored therein a computer program which, when executed by a processor, implements a method as described above.
In summary, in this embodiment, by setting the multi-model set covering the target movement mode, and adaptively adjusting the filtering value weights of various models according to the change of the model transition probability, and finally, the filtering results of the models are interactively fused to realize the optimal filtering estimation of the target, so that the stable tracking of the maneuvering target is realized, the tracking precision of the maneuvering target is greatly improved, the real-time performance of the target tracking is satisfied, and the method is applied to the missile-borne seeker, and the performance of the missile-borne radar for tracking the maneuvering target can be effectively improved. The embodiment can well track the maneuvering targets of the interactive multi-model, and solves the problems that Kalman filtering can only track the targets of a single mode and has poor tracking performance on maneuvering targets of the interactive multi-model.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
It should be noted that the apparatus and methods disclosed in the embodiments herein may be implemented in other ways. The apparatus embodiments described above are merely illustrative, for example, flow diagrams and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments herein. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, the functional modules in the embodiments herein may be integrated together to form a single part, or the modules may exist alone, or two or more modules may be integrated to form a single part.
While the present invention has been described in detail through the foregoing description of the preferred embodiment, it should be understood that the foregoing description is not to be considered as limiting the invention. Many modifications and substitutions of the present invention will become apparent to those of ordinary skill in the art upon reading the foregoing. Accordingly, the scope of the invention should be limited only by the attached claims.

Claims (7)

1. An interactive multi-model-based maneuvering target tracking method is applied to an missile-borne seeker, and is characterized by comprising the following steps:
s1, selecting a model set covering a moving model of a moving target; the conversion between the moving models of all the moving targets accords with a Markov chain, and the state estimation of each moving target at the previous moment is interacted to obtain the input state estimation and the state covariance of the moving model filter of each moving target at the current moment;
step S2, based on the input state estimation and state covariance of each maneuvering target motion model filter at the current moment, performing extended Kalman filtering on each maneuvering target motion model to obtain the state estimation and state covariance of each maneuvering target motion model at the current moment;
step S3, updating the probability of each maneuvering target motion model based on the innovation and innovation covariance of each maneuvering target motion model;
and S4, carrying out weighted summation on the state estimation and the state covariance according to the probability on the basis of the state estimation and the state covariance of each maneuvering target motion model at the current moment and the probability of each maneuvering target motion model to obtain the state estimation and the state covariance of the maneuvering target combination so as to realize tracking of the maneuvering target.
2. The method for tracking a maneuvering target based on an interactive multi-model according to claim 1, wherein the step S1 comprises:
step S1.1, a priori given Markov state transition matrix pi ij Calculating the probability u of transition of the maneuvering target motion model i to the maneuvering target motion model j k-1|k-1 (i|j)：
Wherein u is k-1 (j) Probability of maneuver target motion model j at time k-1, and i, j=1, 2, …, N;representing the sum of probabilities of all models being transferred to the model j as a normalization parameter for probability calculation; u (u) k-1 (i) The probability of the maneuvering target motion model i at the moment k-1.
Step S1.2, estimating the state of the maneuvering target motion model j at the moment k-1Sum state covarianceThe input state estimation of each maneuvering target motion model filter at the current moment is obtained through interaction according to the following formula>Sum-state covariance P oj (k-1|k-1)：
In the method, in the process of the invention,representing the state estimate, P, of the k-1 time model i i (k-1|k-1) represents the state estimation covariance corresponding to the model i,i＝1,2,…,N。
3. the maneuvering target tracking method based on the interactive multi-model according to claim 1, wherein the specific implementation process of performing extended kalman filtering on each maneuvering target motion model in the step S2 is as follows:
step S2.1, one-step prediction state estimation of the maneuvering target motion model j is calculatedAnd state estimation covariance P j (k|k-1)：
P j (k|k-1)＝F j (k-1)P oj (k-1|k-1)F j (k-1) T +Q j (k-1) T
Wherein F is j (k-1) state transition matrix for maneuver object motion model j, Q j (k-1) is a process noise covariance;
step S2.2, estimating the one-step prediction stateConverting into measurement predicted values, wherein the relation between measurement and target states in the North east geographic coordinate system satisfies the relation:
in the method, in the process of the invention,the state vector is a state vector of the maneuvering target and respectively represents the position, the speed and the acceleration of X, Y, Z in three directions; h is a r (X k ) For radial shot distance X k Relation of (h) b (X k ) Is azimuth angle and X k Relation of (h) e (X k ) Is pitch angle and X k Relation of (h) D (X k ) For playing the radial velocity of the eye and X k Is a relationship of (2); h (X) k ) To measure the transfer function, the measurement and target state X is represented k Is a conversion relation of (a);
because the conversion between the measurement and the target state is nonlinear, taylor expansion is carried out on the conversion between the measurement and the target state, the first-order truncation is carried out, and the corresponding Jacobin matrix is calculated, so that the measurement predicted value is obtained
Step S2.3, calculating the information(difference between measured and measured predicted values) and innovation covariance->The formula is as follows:
wherein Z (k) is a measurement taken at time k,for measuring the predicted value at k time, R j (k) Measuring the noise covariance; h j (k) The measurement conversion matrix representing the maneuver object motion model j at the k moment is a measurement conversion function h (X k ) Predicting state estimation in one step->First order taylor expansion at the site;
step S2.4, calculate kalman gain K j (k)：
In the method, in the process of the invention,an innovation covariance inverse matrix of the k moment model j is represented;
step S2.5 using kalman gain K j (k) And new informationCorrecting the predicted value of the one-step state, estimating the state of the maneuvering target motion model j at the moment k>Sum-state covariance P j (k|k) is:
P j (k|k)＝(I-K j (k)H j (k))P j (k|k-1)
wherein I represents an identity matrix.
4. The method for tracking a maneuvering target based on an interactive multi-model according to claim 1, wherein the step S3 comprises:
step S3.1, calculating the likelihood of each model, namely the likelihood function lambda, based on the innovation and innovation covariance of each maneuver target motion model j (k) The formula is as follows:
s3.2, weighting the interaction probability of each maneuvering target motion model by the model probability, and carrying out normalization processing to obtain the probability u of the maneuvering target motion model at the current moment j (k) The formula is as follows:
wherein, lambda i (k) A probability density function representing model i;representing the model transition probability of model i.
5. The method for tracking a maneuvering target based on an interactive multi-model according to claim 1, wherein the step S4 comprises:
weighting and combining the state estimation and covariance of the N maneuvering target motion models according to the probability of the updated maneuvering target motion models to obtain final target state estimationAnd a state covariance P (k|k), the formula is as follows:
in the method, in the process of the invention,state estimation of a k moment model i is represented; p (P) i (k|k) represents the state estimation of the k-moment model iCovariance is calculated, i=1, 2, …, N.
6. An electronic device comprising a processor and a memory, the memory having stored thereon a computer program which, when executed by the processor, implements the method of any of claims 1 to 5.
7. A readable storage medium, characterized in that the readable storage medium has stored therein a computer program which, when executed by a processor, implements the method of any one of claims 1 to 5.
CN202310540702.8A 2023-05-12 2023-05-12 Maneuvering target tracking method based on interactive multi-model Pending CN116626666A (en)

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