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The random matrix (RM) method is widely applied for group target tracking. The assumption that the group extension keeps invariant in conventional RM method is not yet valid, as the orientation of the group varies rapidly while it is maneuvering; thus, a new approach with group extension predicted is derived here. To match the group maneuvering, a best model augmentation (BMA) method is introduced. The existing BMA method uses a fixed basic model set, which may lead to a poor performance when it could not ensure basic coverage of true motion modes. Here, a maneuvering group target tracking algorithm is proposed, where the group extension prediction and the BMA adaption are exploited. The performance of the proposed algorithm will be illustrated by simulation.

Groups are structured objects and formations of entities moving in a coordinated manner [

The methods for group target tracking mainly include tracking via Poisson likelihoods [

IMM approach is one of the most wildly used tracking algorithms for maneuvering target; with the interacting of models, fusion estimation for maneuvering target was obtained. With a fixed structure, many more models are needed for an efficient tracking performance, as the target maneuverings in a more complex mode, which will lead to an increase in computation burden and model competition consequently. One of the variable structure multiple model (VSMM) methods called best model augmentation (BMA) was proposed in [

The paper is organized as follows. Section

Considering a target group with an ellipsoidal shape, we use a SPD random matrix

It is assumed that in each scan

In a Bayesian view, a group target tracking algorithm is an iterative updating scheme for conditional probability densities

or

with its Bayes’ formula as

With the assumption that the extension does not tend to change over time in [

The prediction of kinematic state and extension can be expressed, respectively, as follows.

(A) Kinematic state is as follows:

(B) Extension is as follows:

In reality, the assumption that extension does not tend to change over time is not so valid in many situations, for example, when the group target is moving in a turning mode, the orientation of the group extension will change timely; a proper prediction to the extension may improve the tracking performance.

It can be learned heuristically from [

While the group target has a relatively large extension and a dense scattering, the kinematic state may have little influence on the extension. So, posterior probability density of the extension is nearly independent from the kinematic state, but mainly dependent on the measurement. Thus we make the following assumption.

The posterior probability density of extension can be approximated by marginal probability

It can be learned from (

Naval vessels, Submarines, or ground moving convoys show a clear orientation [

With the regularities of distribution being invariant, the state update procedure is similar to [

Models with fixed parameter are used to form the candidate model set of BMA, whose structure is different from that of the basic model set. The model who can best match the true motion mode of the target in the candidate model set will be activated. Moreover, the activated model will be selected to form a state estimation model set (SEMS) of a particular moment combination with the basic model set. All the estimations of the models in SEMS are fused to output the final estimation [

Assume that

In order to select the model to be activated

The discrepancy of model

If

As shown in Section

With the basic model set selected offline, more prior knowledge is needed to ensure a basic coverage of true modes, which is a difficult task in practice.

To cover a complicate maneuvering mode, the basic model set should be augmented, which will make only a part of model efficiently match the maneuvering at each moment; the other models just do little help in improving the tracking performance, moreover, will bring a heavy burden in computation and model competition.

To overcome the drawbacks of BMA method mentioned above, an adaptive structure is considered for a better performance in maneuvering tracking. Suppose that

The metric

If

Otherwise, the activated model is

The model eliminated from SEMS

② Mixed estimation is

② Likelihood function is

Here

③ state and covariance update is as follows.

The estimations

With

④ Model probability update is as follows:

Assume that the initial kinematic state of the group is

Measurement of group target.

Basic model set is composed of 13 CV models. Candidate model set is composed of 8 CT models. The dynamic model, model parameters, transform matrix, and the process noise matrix are the same as in [

RMSE of extended state.

RMSE of centroid position.

RMSE of centroid velocity.

ANEES of kinematics.

ANEES of extension.

In Figures

Figures

Moreover, it can be seen from Figures

As to BMA13+1+A, it can be seen from Figures

The proposed algorithm BMA13+1+New, with extension predicted in orientation, can improve the estimation performance of extension obviously, especially when it is maneuvered; moreover, an adaptive structure of BMA improves the performance of its kinematic state estimation; thus the proposed algorithm can improve the overall performance of group target tracking compared with the original BMA13+1.

Figures

① ANEES of kinematics is

② ANEES of extension is

It can be learned from Figures

A comparison is presented in Table

A comparison on average performance.

IMM13 | IMM21 | IMM13+1 | IMM13+1+A | IMM13+1+New | |
---|---|---|---|---|---|

Average time (s) | 0.0217 | 0.0493 | 0.0283 | 0.0324 | 0.0325 |

Position RMSE (m) | 14.2303 | 5.5390 | 8.2438 | 6.4474 | 6.4699 |

Velocity RMSE (m/s) | 19.9825 | 7.3435 | 12.9626 | 8.9902 | 8.8283 |

Extension RMSE (m^{2}) |
551.6187 | 214.2907 | 237.3733 | 214.2780 | 161.2098 |

This article focuses on the maneuvering group target tracking based on random matrix method. As the group target’s motion shows a clear orientation in many occasions, a random matrix approach is derived based on Bayesian theory for maneuvering target tracking, which does have a prediction on target extension, and the assumption that the extension keeps invariant is eliminated. Then, the model set of BMA is adjusted in real time and improves the algorithm’s tracking ability for target maneuvering. Finally, a comparison is presented by simulation, and the results shows that the proposed algorithm can gain an obvious improvement in tracking accuracy in both kinematic state and extension estimation with a relatively small computation cost. As the work of this paper only focuses on the group target with ellipse extension, the future work should pay more attention to group target with a more general extension appearance.

The authors declare that there are no conflicts of interest regarding the publication of this paper.