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In order to solve the tracking problem of radar maneuvering target in nonlinear system model
and non-Gaussian noise background, this paper puts forward one interacting multiple model (IMM) iterated extended

In the field of manoeuvring target tracking, IMM [

Recently, particle filter (PF) [

However, in IMM-PF, the particles in each mode are drawn according to the prior density without any consideration of current measurements, which have a large deviation with the particles generated from the true posteriori density. Particularly in the case of the measurement model with high accuracy or target maneuvering, this issue will be more serious. To import the current measurements into the particle sampling process, an EKPF and an UPF were applied in each mode of the IMM algorithm presented in [

On the other hand, over the past decades, considerable attention has been devoted to

In this paper, we propose to combine IMM with IEHPF (IMM-IEHPF) for the tracking problem of maneuvering target in nonlinear non-Gaussian system. The filter accuracy of IEHF is higher than that of EKF and UKF, and IEHF is insensitive to the exact knowledge of the noise processes, therefore the importance density function generated by it is more approximate to the true state posteriori density.

The structure of this paper is as follows. Section

Consider the following discrete nonlinear time-varying systems for maneuvering target tracking:

The state estimation problem of system described in (

It is well known that Kalman filter can get the optimal state estimation in the linear Gaussian system. However, in practice, most cases belong to nonlinear non-Gaussian system, so the analytic expression of posteriori density

IMM-IEHPF algorithm proposed in this paper, in fact, is the combination of IMM algorithm and IEHPF algorithm. Compared with IMM-PF, IMM-IEHPF has considered the latest measurements in the particle sampling process by utilizing the prediction and updating mechanism of IEHF. Therefore, the distribution of particles is more approximate to the true state posteriori density and the filter accuracy can be enhanced. We first briefly describe the

Consider the following state space model of linear time-varying system:

Suboptimal

For a given

The covariance updating is

So, the state updating equation of

Although EHF can adapt to the case of system noise with non-Gaussian distribution, it also will face the problem of model linearisation error. Therefore, to further enhance the degree of linearisation approximation of nonlinear system, this paper makes improvements on model linearisation technique and proposes IEHF algorithm. Its fundamental idea is as below.

Given the filtered estimation

It is not difficult to see that

Linearize the dynamical model at the smoothed value

Linearize the measurement model at the filtered value

In order to further improve the filtering accuracy, the linearisation technique can be repeated many times at one step. All these contribute to IEHF algorithm. However, for many nonlinear filtering problems, the performance is not significantly improved after repeating iterations. Usually it ends after two or three times of iterations. According to the above thoughts, the implementation steps of IEHF algorithm are as follows.

Assume that the iterative filtering value

The smoothing value required by

On the basis of IMM-PF [

Calculate the mixing probability

Calculate the particle weights [

Normalizing

(4) State estimation of each mode

Covariance estimation

Particle residual of each mode

Covariance of residual

Mode likelihood function

Mode probability

Combination

In order to validate the filtering performance of IMM-IEHPF algorithm, this paper compares standard IMM, IMM-PF, and IMM-IEHF algorithm. The experiment scene is designed as follows. Radar scanning interval is

Mode

Mode

Mode

We measure the range and bearing, and the measurement function

Measurement noise standard deviations are

Figure

Position estimate.

As seen from Figure

To compare the filtering accuracy of the previous four methods, Figure

Position RMSE.

The IMM-IEHPF algorithm, however, can deal with target maneuvering and we see that the filter also performs well after

To quantitatively analyse the filtering performances of the four methods, Table

Mean and variance of RMSE under different measurement bearing deviations.

Algorithm | Bearing standard deviations |
Mean | Variance |
---|---|---|---|

IMM | 2 | 9.7293 | 98.2215 |

IMM-IEHF | 2 | 4.0394 | 5.6625 |

IMM-PF | 2 | 4.1397 | 2.4750 |

IMM-IEHPF | 2 | 2.7593 | 0.3633 |

| |||

IMM | 5 | 12.794 | 159.49 |

IMM-IEHF | 5 | 6.5694 | 7.5583 |

IMM-PF | 5 | 5.2413 | 2.9841 |

IMM-IEHPF | 5 | 5.3559 | 1.1192 |

| |||

IMM | 10 | 18.421 | 333.87 |

IMM-IEHF | 10 | 8.6552 | 10.3592 |

IMM-PF | 10 | 8.3949 | 8.2179 |

IMM-IEHPF | 10 | 7.7631 | 3.4886 |

This paper has investigated the problem of maneuvering target tracking in the nonlinearities of the dynamic state-space and the non-Gaussian measurement noise. We have presented a new IEHPF method in the IMM framework. The performance of the proposed method is evaluated via simulations and compared with IMM, IMM-IEHF, and IMM-PF, which illustrates that the tracking performance of our proposed method is superior to the others. We have also provided insight into the influence of various bearing standard deviations. Three bearing standard deviations are given for comparing the performance of our proposed method with the other methods. We have found that IMM-IEHPF is weakly sensitive to noise levels. The simulation results have well verified the validity of the proposed method.

This paper only considers a maneuvering target appearing in the scanned region of radar at whole time step. However, in actual radar target tracking, target may disappear at any time step. Therefore in future work, we will study how to construct a suitable model to describe target appearance or disappearance in maneuvering target tracking under a low SNR environment.

The authors thank the referees for their careful reading, invaluable comments, and suggestions on improving the quality of this paper. This work is supported in part by the National Natural Science Foundation of China under Grant nos. 61179014 and 60872156.