Taking into account the difficulty of shape estimation for the extended targets, a novel algorithm is proposed by fitting the B-spline curve. For the single extended target tracking, the multiple frame statistic technique is introduced to construct the pseudomeasurement sets and the control points are selected to form the B-spline curve. Then the shapes of the extended targets are extracted under the Bayes framework. Furthermore, the proposed shape estimation algorithm is modified suitably and combined with the probability hypothesis density (PHD) filter for multiple extended target tracking. Simulations show that the proposed algorithm has a good performance for shape estimate of any extended targets.

In the traditional low resolution sensor system, each target is tracked as a single point source; that is, its extension is assumed to be neglectable in comparison with sensor resolution. With the increase of the resolution of modern radars and other detection equipment, the echo signal of a target may be distributed in a different range resolution cell; thus, the measurement is no longer equivalent to a point; that is, a single target may generate multiple measurements. Such target is referred to as an extended target in [

In the conventional extended target tracking, the measurements are modeled as a spatial distribution model in [

To solve the aforementioned problem, a novel shape estimation algorithm based on the B-spline curve fitting is proposed in this paper, and then the proposed shape estimation method is integrated into the framework of extended target probability hypothesis density (ET-PHD) filter for multiple extended target tracking [

Assume the state equation and the measurement equation of a single target in two-dimensional plane are given by

Suppose that

Prediction of state and covariance:

Calculating gain:

Update of state and covariance:

Assume that readers are familiar with the concepts of B-spline curves. A smooth subsection curve can be obtained by fitting the control point set. The B-spline curve of order

In this section, the Bayesian filter framework is introduced for single extended target state and shape estimates. Assume the state equation and the measurement equation are the same as (

At time

When

prediction of the state and covariance according to (

update of the state by the latest measurement set

Construct a new pseudomeasurement set

Let

Set

Update the shape of the extended target by the pseudomeasurement set

(4.1) Divide the interval

(4.2) Calculate

(4.3) Shape estimation by implementing the one-dimension (1-D) KF: assume the shape control matrix

Prediction:

Update:

Angle interval partition.

Shape estimation according to

Map the control points to the Cartesian coordinates by

Produce a closed control point set by adding the element

The standard PHD filter for single measurement target tracking has been described in [

In this section, we combine the proposed shape estimation algorithm into the framework of ET-GM-PHD filter, which can effectively achieve the multiple extended target tracking with different shape estimation. We refer to this algorithm as Shape-ET-GM-PHD, and its steps are as follows.

In the following subsections, assume that the current estimated PHD

Notice that the D-distance partition method [

Finally, shapes of multiple extended targets are extracted according to

Assume that there is an extended target making a uniform motion in a two-dimensional simulation scenario, and the state equation and the measurement equation are the same as (

Figure

Shape estimation by the proposed algorithm and the RM method.

Figure

The real measurements of the extended target (1~20 frames).

Figure

Average shape estimate.

Figure

Shape estimation by the proposed algorithm and the RM method.

The real measurements of the extended target (1~20 frames).

Average shape estimate.

The scenario of multiple extended target tracking is the same as that of [

The intensity of the spawned targets is

Figure

Shape estimate results.

Measurements and tracking results

Shape estimates of Targets 1 and 2

Shape estimates of cross targets

Shape estimates of the spawned target

Figure

Number estimates.

OSPA distance.

In this paper, a novel shape estimation algorithm is proposed based on the B-spline curve fitting. The multiple frame statistic technique is introduced to construct the pseudomeasurement sets. The selected control points are used to form the B-spline curve, and then the curve yields the shapes of the extended targets. Moreover, the proposed shape estimation algorithm is modified suitably and combined with the probability hypothesis density (PHD) filter for multiple extended target tracking. Simulations show that the proposed algorithm has a good performance for shape estimates of extended targets.

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

This paper is supported by the National Natural Science Foundation of China (nos. 61305017 and 61304264) and the Natural Science Foundation of Jiangsu Province (no. BK20130154).