*2.2. Target Tracking with a Bistatic Compact HFSWR*

Once the plot data sequence is consecutively obtained with each plot being denoted by a measured state vector [*R<sup>m</sup> <sup>R</sup> <sup>θ</sup><sup>m</sup> <sup>R</sup> <sup>v</sup><sup>m</sup> dR*], a multi-target tracking method is required to produce target tracks. The proposed MTT algorithm was modified from the method presented in [11], which is developed from Converted Measurement Kalman Filter (CMKF) and a data association method based on minimal cost. In this method, data association, state prediction, and state estimation are three key steps, where data association is performed in the polar coordinate with the receiving radar site as its origin, while state prediction and estimation are implemented in a Cartesian coordinate.

The state prediction and estimation using the CMKF method are implemented by a linear Kalman filter, which is based on a specific dynamic model and an observation model. Taking the motion characteristic of large vessels into consideration, the target dynamic model is defined in a Cartesian coordinate as

$$\mathbf{x}\_k = \mathbf{F}\mathbf{x}\_{k-1} + \omega\_{k'} \tag{6}$$

where **x***<sup>k</sup>* = [*xk*, *vxk* , *yk*, *vyk* ] *<sup>T</sup>* is the true state vector at time *k* in the Cartesian coordinate with the boresight of the receiving array 2 as its x-axis, the direction perpendicular to the radar boresight as the y-axis. *xk* and *yk* denote the true target position components, *vxk* and *vyk* denote the corresponding true velocity components along *x* and *y* directions. [·] *<sup>T</sup>* denotes the transpose operator. *ω<sup>k</sup>* represents the Gaussian process noise with zero mean and covariance matrix **Q***k*. **F** is the state transition matrix defined as

$$\mathbf{F} = \begin{bmatrix} 1 & T & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & T \\ 0 & 0 & 0 & 1 \end{bmatrix}' $$

where *T* denotes the sampling time.

The observation model is also defined in the Cartesian coordinate as

$$\mathbf{z}\_k = \mathbf{H}\mathbf{x}\_k + \mathbf{v}\_{k\prime} \tag{7}$$

where **z***<sup>k</sup>* = [*x*˜*k*, *v*˜*xk* , *y*˜*k*, *v*˜*yk* ] *<sup>T</sup>* is a measured state vector at time *k*, *x*˜*<sup>k</sup>* and *y*˜*<sup>k</sup>* denote the measured target position components, *v*˜*xk* and *v*˜*yk* are the corresponding measured velocity components along *x* and *y* directions, respectively. **v***<sup>k</sup>* represents measurement noise following Gaussian distribution with zero mean and covariance matrix **R***k*. **H** is the measurement matrix and it is an identity matrix here.

The difference in the tracking procedure between a monostatic and a bistatic HFSWR lies in that the measured state vector [*R<sup>m</sup> <sup>R</sup> <sup>θ</sup><sup>m</sup> <sup>R</sup> <sup>v</sup><sup>m</sup> dR*] instead of [*R<sup>m</sup> <sup>T</sup> <sup>θ</sup><sup>m</sup> <sup>T</sup> <sup>v</sup><sup>m</sup> dT*] is used. On one hand, the accuracy of *R<sup>m</sup> <sup>R</sup>* , which is related to the coarsely estimated azimuth as shown in Equation (2), is lower than *<sup>R</sup><sup>m</sup> T* . On the other hand, the elliptical Doppler velocity *v<sup>m</sup> dR* that is along the bistatic bisector is used here, and it is assumed that the elliptical Doppler velocity of a target does not change much during a coherent

integration time. Thus, the data association procedure is modified by using different target parameters, validation gate thresholds, and association weights. Based on the above analysis, the proposed target tracking procedure for a bistatic compact HFSWR, including three parallel sub-procedures, i.e., track initiation, track maintenance, and track termination, is summarized as follows.
