CN114494340B - KL interactive multi-model underwater target tracking method - Google Patents

KL interactive multi-model underwater target tracking method Download PDF

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CN114494340B
CN114494340B CN202111659699.9A CN202111659699A CN114494340B CN 114494340 B CN114494340 B CN 114494340B CN 202111659699 A CN202111659699 A CN 202111659699A CN 114494340 B CN114494340 B CN 114494340B
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闫永胜
韩世华
王海燕
申晓红
张天佑
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Abstract

The invention provides a KL interactive multi-model underwater target tracking method, which aims at the interference of physical characteristics of a seawater medium on measurement information, introduces KL divergence to calculate a model probability weighting coefficient, uses the KL divergence to calculate the matching degree of a certain motion model and a target real motion mode in a motion model set, and combines a model probability updating method based on an innovation likelihood function in a standard IMM algorithm to enable the model to select a real motion model which is more attached to the target, thereby improving the position estimation precision of the target. The invention not only can be used for describing complex and changeable motion states of the maneuvering target, but also can be used for meeting the requirements of small calculated amount and easy processing.

Description

KL interactive multi-model underwater target tracking method
Technical Field
The invention belongs to the field of underwater acoustic sensor network target tracking, and relates to statistical signal processing, information fusion and target tracking theory, which are used for tracking an underwater target in an underwater complex environment with high precision.
Background
Underwater target tracking technology has become a very leading field of research. The underwater target tracking technology has great strategic significance in the fields of underwater operations, submarine target monitoring, ocean resource development and the like. Whether in the military national defense field or the common civil field, ensuring high reliability and high precision target tracking is a main index for designing and improving a target tracking system. Modeling target motion is a very important part of a target tracking system.
Blom and Bar-Shalm propose that the interactive multi-model (Interacting Multiple Model, IMM) algorithm has great advantages in strong maneuver object tracking, and in the standard IMM algorithm, the model transition probability and the choice of model probability are key factors for adjusting IMM performance.
Xu Dengrong et al propose an adaptive transition probability IMM algorithm, which uses a strong tracking correction input estimation (STMIE) model and a uniform motion model as a model set of the IMM algorithm, and utilizes the tracking capability of the STMIE algorithm to a high maneuvering target and the tracking precision of a CV model to a non-maneuvering target to achieve comprehensive adaptive tracking to the target, but the algorithm has large calculation amount.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a KL interactive multi-model underwater target tracking method, aiming at the interference of physical characteristics of a seawater medium on measurement information, KL (Kullback-Leiber) divergence is introduced to calculate a model probability weighting coefficient, the KL divergence is used to calculate the matching degree of a certain motion model and a target real motion mode in a motion model set, and a model probability updating method based on a new likelihood function in a standard IMM algorithm is combined, so that the model selects a real motion model which is more attached to the target, and the position estimation precision of the target is further improved. The invention not only can be used for describing complex and changeable motion states of the maneuvering target, but also can be used for meeting the requirements of small calculated amount and easy processing.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
step 1, constructing a model set M of an IMM model, wherein the model set comprises a plurality of motion sub-models;
step 2, performing interactive operation on the initial states of all the motion sub-models according to the model transition probability to obtain target mixed state input
Figure BDA0003449393890000021
And covariance matrix->
Figure BDA0003449393890000022
Figure BDA0003449393890000023
Wherein N represents the number of motion sub-models in the model set M, < ->
Figure BDA0003449393890000024
And->
Figure BDA0003449393890000025
Respectively the target state and covariance matrix of the ith motion sub-model in the model set M at k time points,/I>
Figure BDA0003449393890000026
Converting the probability for the predictive model;
step 3, when the target enters the monitoring area, waking up the sensor nodes in the sensing area, and the woken-up sensor nodes perform TOA measurement on the target to obtain measurement data Z k+1 ；
Step 4, mixing the target state vector
Figure BDA0003449393890000027
Covariance matrix->
Figure BDA0003449393890000028
And measurement information Z k+1 Performing conditional filtering prediction and estimation as input of an extended Kalman filter under a corresponding ith motion sub-model, and calculating target state estimation +_ under the ith motion sub-model at the moment k+1>
Figure BDA0003449393890000029
And covariance matrix estimation->
Figure BDA00034493938900000210
Step 5, constructing a likelihood function matched with the ith motion sub-model at the moment k+1
Figure BDA00034493938900000211
Wherein (1)>
Figure BDA00034493938900000212
And->
Figure BDA00034493938900000213
Respectively expanding a Kalman filter intermediate product innovation and innovation covariance matrix; likelihood function through the ith motion sub-model +.>
Figure BDA00034493938900000214
Determining the probability of the k+1 moment model i>
Figure BDA00034493938900000215
Step 6, calculating a motion sub-model in the model set M
Figure BDA00034493938900000216
And a true motion pattern s k KL divergence between
Figure BDA00034493938900000217
Get->
Figure BDA00034493938900000218
Is used as a coefficient for adjusting the model probability, so that the model matching degree gets a new model probability +.>
Figure BDA00034493938900000219
Step 7, utilizing the updated model probability
Figure BDA00034493938900000220
State estimation for each sub-filter output of step 4
Figure BDA00034493938900000221
Weighted summation is carried out to obtain the fused target state estimation and covarianceA matrix.
In the step 6, the motion sub-model in the model set M
Figure BDA00034493938900000222
And a true motion pattern s k KL divergence between
Figure BDA00034493938900000223
Wherein n represents the measurement data Z k+1 Dimension, Z of k+1 Model in model set M +.>
Figure BDA00034493938900000224
The mean and covariance below are denoted +.>
Figure BDA0003449393890000031
And
Figure BDA0003449393890000032
in a real movement pattern s k The mean and covariance below are denoted +.>
Figure BDA0003449393890000033
And->
Figure BDA0003449393890000034
The beneficial effects of the invention are as follows:
1) The KL divergence is introduced to calculate the module distribution weighting coefficient, so that the matching degree between the assumed motion model and the real motion mode is improved, the accuracy of target tracking is improved compared with a standard IMM algorithm, and meanwhile, the method is convenient to process and small in calculation amount.
2) In the principle of the standard IMM algorithm, the process of performing motion model conversion by the model probability conversion matrix is delayed relative to the conversion of the real motion state of the target, and the model probability matching of the KL-IMM algorithm is faster than that of the standard IMM, so that the error is reduced.
Drawings
Fig. 1 is a flowchart of the KL-IMM algorithm of the present invention.
Fig. 2 is a schematic diagram of an underwater target motion track and a target state estimation result.
Fig. 3 is a schematic diagram of the distance RMSE and PCRLB for both algorithms.
Fig. 4 is a schematic diagram of probability of each moment of each model of the standard IMM algorithm.
Fig. 5 is a schematic probability diagram of each moment of each model of the KL-IMM algorithm.
Detailed Description
The invention will be further illustrated with reference to the following figures and examples, which include but are not limited to the following examples.
The technical scheme adopted by the invention comprises the following steps:
step 1: construction of IMM model
Assuming that a model set M of the IMM model comprises various motion sub-models such as uniform linear motion, uniform turning motion and the like in the model set, and initial probability distribution mu 0 The target state of the ith sub-model in the model set M at the moment k of the state transition matrix pi
Figure BDA0003449393890000035
And covariance matrix->
Figure BDA0003449393890000036
Step 2: input interaction operation
Performing interactive operation on the initial states of all the sub-models according to the model transition probability to obtain target mixed state input
Figure BDA0003449393890000037
And covariance matrix->
Figure BDA0003449393890000038
The following are provided:
Figure BDA0003449393890000039
Figure BDA00034493938900000310
in the formula (2) (. Cndot. T Representing a matrix transpose, N representing the number of models in model set M,
Figure BDA0003449393890000041
probabilities are transformed for the predictive model.
Step 3: obtaining an observed value of a target
When the target enters the monitoring area, the sensor nodes in the sensing range are awakened, and the awakened sensor nodes perform TOA measurement on the target to obtain measurement data Z k+1 。
Step 4: state filtering
Mixing the target state vectors
Figure BDA0003449393890000042
Covariance matrix->
Figure BDA0003449393890000043
And measurement information Z k+1 Performing conditional filtering prediction and estimation as input of an extended Kalman filter under a corresponding ith sub-model, and calculating target state estimation +.>
Figure BDA0003449393890000044
And covariance matrix estimation->
Figure BDA0003449393890000045
Step 5: calculating model probabilities
Utilization of extended kalman filter intermediate innovation in step 4
Figure BDA0003449393890000046
And a new covariance matrix->
Figure BDA0003449393890000047
The likelihood function of the matching of the k+1 moment model i is constructed as follows:
Figure BDA0003449393890000048
in the formula (3) |·| represents modulo.
Likelihood function through the ith sub-model
Figure BDA0003449393890000049
Determining the probability of the k+1 moment model i>
Figure BDA00034493938900000410
Step 6: computing KL divergence and model probability updates
Sub-models in a computation model set M
Figure BDA00034493938900000411
And a true motion pattern s k KL divergence between the two is expressed as follows:
Figure BDA00034493938900000412
in the formula (4), n represents the measurement data Z k+1 Where tr (. Cndot.) represents the trace of the matrix, Z k+1 Models in model set M
Figure BDA00034493938900000413
Lower mean->
Figure BDA00034493938900000414
Sum of covariance->
Figure BDA00034493938900000415
In a real movement pattern s k Lower mean->
Figure BDA00034493938900000416
Sum of covariance->
Figure BDA00034493938900000417
The KL criterion is used for obtaining
Figure BDA00034493938900000418
Is a non-negative number, the smaller the value is, the higher the degree of matching is. Thus, take
Figure BDA00034493938900000419
The inverse is used as a coefficient for adjusting the model probability, so that the model matching degree obtains a new model probability such as +.>
Figure BDA00034493938900000420
Step 7: state estimation fusion output
Updated model probabilities
Figure BDA0003449393890000051
State estimation for each sub-filter output of step 4 +.>
Figure BDA0003449393890000052
Weighted summation is carried out to obtain the fused target state estimation +.>
Figure BDA0003449393890000053
And covariance matrix->
Figure BDA0003449393890000054
Figure BDA0003449393890000055
The KL-IMM algorithm flow provided by the embodiment of the invention is shown in figure 1. The solid line indicates the data flow at time k and the dashed line indicates that the value at time k+1 is to be replaced by the value at time k.
Assume a target initial state X 0 ＝[500，10，500，10] T According to a certain rule. For example: 1-30 s: the target moves linearly at a uniform speed; 31-60 s: target advanceUniform cornering motion (ω= -0.1); 61-90 s: the target moves linearly at a uniform speed; 9-120 s: the target makes uniform turning movement (omega= -0.08); 121-150 s: the target moves linearly at a uniform speed. The sampling period is t=1s. The track is shown in FIG. 2
The method comprises the following steps:
step 1: initializing and constructing IMM model
The IMM model set M is constructed as { constant speed turning model (omega= -0.1), constant speed motion model, constant speed turning model (omega= -0.08) }, and the model initial probability distribution is as follows
Figure BDA0003449393890000056
Wherein each element takes the value randomly, and the initial value does not influence the final result.
μ k ＝μ 0 ＝[0.2，0.6，0.2]；
The model probability transition matrix pi is:
Figure BDA0003449393890000057
the ith row and jth column elements in pi represent the probability of transitioning under sub-model i to sub-model j, where pi belongs to a priori knowledge. Make the initial state of all sub-models proceed
Figure BDA0003449393890000058
Initial noise covariance matrix
Figure BDA0003449393890000059
Step 2: initial state of all sub-models
Figure BDA00034493938900000510
Performing interactive operation according to the model transition probability to obtain a target mixed state input +.1 at the moment k->
Figure BDA00034493938900000511
And covariance matrix->
Figure BDA00034493938900000512
X is the initial state of the submodel 0 。
Figure BDA0003449393890000061
Figure BDA0003449393890000062
In (7)
Figure BDA0003449393890000063
Representing the transition probability of the predictive model, i.e. +.>
Figure BDA0003449393890000064
The probability of the k moment model i to the k+1 moment model j is represented, and the formula is as follows: />
Figure BDA0003449393890000065
Pi in (8) ij The i-th row and j-th column of the state transition matrix pi represent the probability of the model i being converted to the model j.
Step 3: the target enters the monitoring area, the sensor nodes in the sensing range are awakened, TOA measurement is carried out on the target by the awakened sensor nodes, the obtained measurement information is obtained, and the coordinates of the sensor nodes are [ x ] i ，y i ]＝[700，500]Measurement information Z obtained by a sensor k+1 The expression is as follows:
Figure BDA0003449393890000066
in the formula (9) (x k+1 ，y k+1 ) Representing the position coordinates of the target at the moment k+1; v k+1 Is the noise observed by TOA, v k+1 Obeying a gaussian distribution with a mean of 0 and a variance of 100.
Step 4: state filtering; obtaining an extended Kalman filter using the model i to obtain a target state estimate under the model i
Figure BDA0003449393890000067
And covariance matrix estimation->
Figure BDA0003449393890000068
Suppose Q k ＝diag([1，0.01，1，0.01])，/>
Figure BDA0003449393890000069
Expanding a constant motion model state transition matrix in Kalman:
Figure BDA00034493938900000610
constant speed turning model (ω= -0.1/ω= -0.08) } state transition matrix:
Figure BDA00034493938900000611
extended kalman prediction for model i:
Figure BDA0003449393890000071
Figure BDA0003449393890000072
extended kalman update of model i:
Figure BDA0003449393890000073
Figure BDA0003449393890000074
new information
Figure BDA0003449393890000075
New information covariance matrix->
Figure BDA0003449393890000076
Is calculated as follows:
Figure BDA0003449393890000077
Figure BDA0003449393890000078
target state estimation under Kalman filter corresponding to model i
Figure BDA0003449393890000079
Covariance matrix->
Figure BDA00034493938900000710
/>
Figure BDA00034493938900000711
Figure BDA00034493938900000712
Step 5: after the last step of filtering, calculating an innovation covariance matrix to obtain a likelihood function at the moment k+1:
Figure BDA00034493938900000713
the probability of the k+1 moment model i is determined by a likelihood function:
Figure BDA00034493938900000714
wherein the method comprises the steps of
Figure BDA00034493938900000715
C is the normalization constant: />
Figure BDA00034493938900000716
Step 6: calculation model
Figure BDA00034493938900000717
And a true motion pattern s k KL divergence between them, and for the information obtained in step 5
Figure BDA00034493938900000718
Its corresponding covariance->
Figure BDA00034493938900000719
Probability of each model->
Figure BDA00034493938900000720
The updating and correcting process is as follows:
in practice due to
Figure BDA00034493938900000721
And->
Figure BDA00034493938900000722
Respectively represent Z k+1 In pattern s k The mean and covariance under the condition that the real mode of the system is unknown, only the online information at the time of k+1, namely the model set M and all measurement vector sequences Z at the time of the previous k, can be utilized 1：k To approximate Z k+1 In pattern s k Lower mean->
Figure BDA0003449393890000081
Sum of covariance->
Figure BDA0003449393890000082
The expression is as follows:
Figure BDA0003449393890000083
Figure BDA0003449393890000084
in the formulas (20) and (21),
Figure BDA0003449393890000085
model representing time k+1->
Figure BDA0003449393890000086
Measurement prediction value of->
Figure BDA0003449393890000087
Representing a corresponding metrology prediction covariance; />
Figure BDA0003449393890000088
Representation model->
Figure BDA0003449393890000089
The model transition probability of (2) is calculated as follows:
Figure BDA00034493938900000810
Figure BDA00034493938900000811
Figure BDA00034493938900000812
Z k+1 in the model
Figure BDA00034493938900000813
Lower mean->
Figure BDA00034493938900000814
Sum of covariance->
Figure BDA00034493938900000815
Expressed as follows, use the overall estimate +.>
Figure BDA00034493938900000816
And->
Figure BDA00034493938900000817
Instead of history information M and Z at the previous k times 1：k 。
Figure BDA00034493938900000818
Figure BDA00034493938900000819
/>
From the true pattern s k The average value of
Figure BDA00034493938900000820
Sum of covariance->
Figure BDA00034493938900000821
Model->
Figure BDA00034493938900000822
Lower mean->
Figure BDA00034493938900000823
Sum of covariance->
Figure BDA00034493938900000824
Calculation model->
Figure BDA00034493938900000825
And true motionPattern s k KL divergence between:
Figure BDA00034493938900000826
in equation (27), the new model probabilities are as follows:
Figure BDA0003449393890000091
step 7: with updated model probabilities
Figure BDA0003449393890000092
To measure the matching degree of the sub-model and the real motion state at the current moment, the state estimation of each sub-filter output at the current moment is carried out>
Figure BDA0003449393890000093
Weighted summation is carried out to obtain the fused estimated state +.>
Figure BDA0003449393890000094
And covariance matrix->
Figure BDA0003449393890000095
Figure BDA0003449393890000096
Figure BDA0003449393890000097
Simulation results: fig. 2 is a target motion and tracking trajectory, fig. 3 is distances RMSE and PCRLB of two algorithms, and fig. 4 and 5 are probabilities of each moment of each model of the standard IMM algorithm and KL-IMM algorithm, respectively. According to simulation results, the interactive multi-model underwater target tracking method based on the joint KL divergence and likelihood function has the advantages of wide application range and high tracking precision. And fifthly, the probability matching degree of the model is improved, so that the tracking precision is higher and the method is more practical.

Claims (2)

1. The KL interactive multi-model underwater target tracking method is characterized by comprising the following steps of:
step 1, constructing a model set M of an IMM model, wherein the model set comprises a plurality of motion sub-models;
step 2, performing interactive operation on the initial states of all the motion sub-models according to the model transition probability to obtain target mixed state input
Figure FDA0004151481150000011
And covariance matrix->
Figure FDA0004151481150000012
Figure FDA0004151481150000013
Wherein N represents the number of motion sub-models in the model set M, < ->
Figure FDA0004151481150000014
And->
Figure FDA0004151481150000015
Respectively the target state and covariance matrix of the ith motion sub-model in the model set M at k time points,/I>
Figure FDA0004151481150000016
Converting the probability for the predictive model;
step 3, when the target enters the monitoring area, waking up the sensor nodes in the sensing area, and the woken-up sensor nodes perform TOA measurement on the target to obtain measurement data Z k+1 ；
Step 4, mixing the target state vector
Figure FDA0004151481150000017
Covariance matrix->
Figure FDA0004151481150000018
And measurement information Z k+1 Performing conditional filtering prediction and estimation as input of an extended Kalman filter under a corresponding ith motion sub-model, and calculating target state estimation +_ under the ith motion sub-model at the moment k+1>
Figure FDA0004151481150000019
And covariance matrix estimation->
Figure FDA00041514811500000110
Step 5, constructing a likelihood function matched with the ith motion sub-model at the moment k+1
Figure FDA00041514811500000111
Wherein (1)>
Figure FDA00041514811500000112
And->
Figure FDA00041514811500000113
Respectively expanding a Kalman filter intermediate product innovation and innovation covariance matrix; likelihood function through the ith motion sub-model +.>
Figure FDA00041514811500000114
Determining the probability of the k+1 moment model i>
Figure FDA00041514811500000115
Step 6, calculating a motion sub-model in the model set M
Figure FDA00041514811500000116
And a true motion pattern s k KL divergence between->
Figure FDA00041514811500000117
Get->
Figure FDA00041514811500000118
Is used as a coefficient for adjusting the model probability, so that the model matching degree gets a new model probability +.>
Figure FDA00041514811500000119
The new model probabilities are as follows:
Figure FDA00041514811500000120
step 7, utilizing the updated model probability
Figure FDA00041514811500000121
State estimation for each sub-filter output of step 4 +.>
Figure FDA00041514811500000122
And carrying out weighted summation to obtain the fused target state estimation and covariance matrix.
2. The KL interactive multi-model underwater target tracking method according to claim 1, wherein in step 6, the motion sub-model in the model set M
Figure FDA0004151481150000021
And a true motion pattern s k KL divergence between
Figure FDA0004151481150000022
Wherein n represents the measurement data Z k+1 Dimension, Z of k+1 Model in model set M +.>
Figure FDA0004151481150000027
The mean and covariance below are denoted +.>
Figure FDA0004151481150000023
And
Figure FDA0004151481150000024
in a real movement pattern s k The mean and covariance below are denoted +.>
Figure FDA0004151481150000025
And->
Figure FDA0004151481150000026
/>
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