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In this paper, a novel robust Student’s

To obtain the reliable and precise information, multisensor systems have become more and more popular in a wide range of applications such as cooperative tracking, autonomous navigation, signal processing, and guidance [

To apply the KF in nonlinear system and improve the accuracy of nonlinear approximation, the first order linearization-based extended Kalman filter (EKF) [

To tackle the heavy-tailed non-Gaussian noise, some Huber-based information filters have been proposed by minimizing a cost function which is a combined

Since the Student’s

To cope with the nonlinear multisensor estimation problem with heavy-tailed process and measurement noises, a novel robust Student’s

The rest of the paper is organized as follows. In Sec. II, the problem is formulated. Sec. III gives the derivation of the proposed filter. The simulations are conducted in Sec. IV, and the conclusions are drawn in Sec. V.

Consider a discrete-time stochastic nonlinear system described by

Since

Based on the measurement equation and the distribution of measurement noise, the likelihood PDF

Due to the heavy-tailed process noise, the predictive PDF

Based on the state model given by (

Then, the updated information matrix

To get the approximate solution of posterior PDF

Since the process noise is a zero mean vector with nominal covariance

To accurately describe the predictive PDF, the VB approximation method is applied to dynamically estimate the scale matrix

Then,

According to the property of inverse Wishart distribution, we have

To capture the statistics of

Based on the (

Note that we consider the case that the heavy-tailed process noise statistics, i.e., the scale matrix

To estimate the state

Minimizing (

Since the PDF given by (

Substituting (

Then,

By updating one element of

Let

And the initial value of iteration is set as

Contrasting (

Let

The

Contrasting (

Let

Contrasting (

Let

According to the Bayesian theory, the posterior PDF can be approximated by

Exploiting (

Since Gaussian distribution can approximate the posterior PDF more accurate than the Student’s

According to the basic equations of information filter, we have

Based on the linear error propagation, the cross covariance

Multiplying

Using (

The predicted measurement

Based on the information contributions given by (

Then, the estimated state and covariance can be recovered as

After the iterations, the approximate PDFs given in (

The main advantage of the IF is its ability to fuse multisource measurements simply by adding the information contributions to the information matrix and state. Suppose

Then, the information matrix and information state can be updated by

To better illustrate the proposed filtering algorithm, the computational procedures are summarized in Figure

Diagram of the proposed NRSTCIF.

To demonstrate the feasibility of the proposed algorithm, a target tracking problem is investigated in this section. The target moves in a plane with an unknown speed and unknown constant turn rate, it is observed by multiple radars in clutter. Due to the rapid motion and clutter, the heavy-tailed noises are introduced.

The state equation is given by

The measurement equation of

The locations of the four sensors are given as

The initial state estimation

In the simulation, the dof parameter, tuning parameter, and NOI of the proposed filter are set as

Tracking performance of four filters; (a) Position estimation error, (b) Velocity estimation error, (c) Turn rate estimation error.

The average computational costs of the various filters for each Monte-Carlo run are given in Table

Computational time comparisons.

Filter | CIF | HCIF | STCIF | NRSTCIF |
---|---|---|---|---|

Time(s) | 0.11 | 0.19 | 0.24 | 0.5 |

To clarify the relation between estimation accuracy and NOI, another 1000 independent Monte Carlo simulation runs with different NOIs are conducted based on the proposed filter, and the simulation results are summarized in Figure

Averaged RMSEs with different NOIs.

Figure

Performance comparison of three filters with different probabilities of outlier. (a) Position estimation error. (b) Velocity estimation error. (c) Turn rate estimation error.

In this paper, a novel robust Student’s

There is no underlying data related to the submission.

The authors declare that there is no conflict of interest regarding the publication of this paper.