CN114494340B - KL interactive multi-model underwater target tracking method - Google Patents
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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
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
And covariance matrix->
Wherein N represents the number of motion sub-models in the model set M, < ->
And->
Respectively the target state and covariance matrix of the ith motion sub-model in the model set M at k time points,/I>
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
Covariance matrix->
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>
And covariance matrix estimation->
Step 6, calculating a motion sub-model in the model set M
And a true motion pattern s k KL divergence between
Get->
Is used as a coefficient for adjusting the model probability, so that the model matching degree gets a new model probability +.>
Step 7, utilizing the updated model probability
State estimation for each sub-filter output of step 4
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
And a true motion pattern s k KL divergence between
Wherein n represents the measurement data Z k+1 Dimension, Z of k+1 Model in model set M +.>
The mean and covariance below are denoted +.>
And
in a real movement pattern s k The mean and covariance below are denoted +.>
And->
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
And covariance matrix->
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
And covariance matrix->
The following are provided:
in the formula (2) (. Cndot. T Representing a matrix transpose, N representing the number of models in model set M,
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
Covariance matrix->
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 +.>
And covariance matrix estimation->
Step 5: calculating model probabilities
Utilization of extended kalman filter intermediate innovation in step 4
And a new covariance matrix->
The likelihood function of the matching of the k+1 moment model i is constructed as follows:
in the formula (3) |·| represents modulo.
Likelihood function through the ith sub-model
Determining the probability of the k+1 moment model i>
Step 6: computing KL divergence and model probability updates
Sub-models in a computation model set M
And a true motion pattern s k KL divergence between the two is expressed as follows:
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
Lower mean->
Sum of covariance->
In a real movement pattern s k Lower mean->
Sum of covariance->
The KL criterion is used for obtaining
Is a non-negative number, the smaller the value is, the higher the degree of matching is. Thus, take
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 +.>
Step 7: state estimation fusion output
Updated model probabilities
State estimation for each sub-filter output of step 4 +.>
Weighted summation is carried out to obtain the fused target state estimation +.>
And covariance matrix->
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
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:
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
Initial noise covariance matrix
Step 2: initial state of all sub-models
Performing interactive operation according to the model transition probability to obtain a target mixed state input +.1 at the moment k->
And covariance matrix->
X is the initial state of the submodel 0 。
In (7)
Representing the transition probability of the predictive model, i.e. +.>
The probability of the k moment model i to the k+1 moment model j is represented, and the formula is as follows: />
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:
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
And covariance matrix estimation->
Suppose Q k ＝diag([1，0.01，1，0.01])，
Expanding a constant motion model state transition matrix in Kalman:
constant speed turning model (ω= -0.1/ω= -0.08) } state transition matrix:
extended kalman prediction for model i:
extended kalman update of model i:
new information
New information covariance matrix->
Is calculated as follows:
target state estimation under Kalman filter corresponding to model i
Covariance matrix->
Step 5: after the last step of filtering, calculating an innovation covariance matrix to obtain a likelihood function at the moment k+1:
the probability of the k+1 moment model i is determined by a likelihood function:
wherein the method comprises the steps of
C is the normalization constant:
Step 6: calculation model
And a true motion pattern s k KL divergence between them, and for the information obtained in step 5
Its corresponding covariance->
Probability of each model->
The updating and correcting process is as follows:
in practice due to
And->
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->
Sum of covariance->
The expression is as follows:
in the formulas (20) and (21),
model representing time k+1->
Measurement prediction value of->
Representing a corresponding metrology prediction covariance;
Representation model->
The model transition probability of (2) is calculated as follows:
Z k+1 in the model
Lower mean->
Sum of covariance->
Expressed as follows, use the overall estimate +.>
And->
Instead of history information M and Z at the previous k times 1：k 。
From the true pattern s k The average value of
Sum of covariance->
Model->
Lower mean->
Sum of covariance->
Calculation model->
And true motionPattern s k KL divergence between:
in equation (27), the new model probabilities are as follows:
step 7: with updated model probabilities
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>
Weighted summation is carried out to obtain the fused estimated state +.>
And covariance matrix->
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
And covariance matrix->
Wherein N represents the number of motion sub-models in the model set M, < ->
And->
Respectively the target state and covariance matrix of the ith motion sub-model in the model set M at k time points,/I>
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
Covariance matrix->
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>
And covariance matrix estimation->
Step 5, constructing a likelihood function matched with the ith motion sub-model at the moment k+1
Wherein (1)>
And->
Respectively expanding a Kalman filter intermediate product innovation and innovation covariance matrix; likelihood function through the ith motion sub-model +.>
Determining the probability of the k+1 moment model i>
Step 6, calculating a motion sub-model in the model set M
And a true motion pattern s k KL divergence between->
Get->
Is used as a coefficient for adjusting the model probability, so that the model matching degree gets a new model probability +.>
The new model probabilities are as follows:
step 7, utilizing the updated model probability
State estimation for each sub-filter output of step 4 +.>
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
And a true motion pattern s k KL divergence between
Wherein n represents the measurement data Z k+1 Dimension, Z of k+1 Model in model set M +.>
The mean and covariance below are denoted +.>
And
in a real movement pattern s k The mean and covariance below are denoted +.>
And->
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