*2.3. Fusion Center*

We assume that the radar network adopts an indirect centralized fusion method. Specifically, each radar illuminates the assigned target, extracts the measurement information from the echo signal, and transmits the distance and azimuth information to the fusion center through a radio frequency (RF) stealth data link for processing. In this system, suppose that the fusion center can make full use of the original measurement data without any loss of information, and thus the fusion results are the optimal. Therefore, the measurement information about the target *q* at time index *k* can be formulated as:

$$\mathbf{Z}\_{k}^{q} = \left[ \begin{bmatrix} 1,1 \end{bmatrix}^{\mathrm{T}} \otimes \mathbf{u}\_{k}^{q} \right] \odot \left[ \left[ \left( \mathbf{R}\_{k}^{q} \right)^{\mathrm{T}}, \left( \Theta\_{k}^{q} \right)^{\mathrm{T}} \right]^{\mathrm{T}} + \left[ \left( \Delta \mathbf{R}\_{k}^{q} \right)^{\mathrm{T}}, \left( \Delta \Theta\_{k}^{q} \right)^{\mathrm{T}} \right]^{\mathrm{T}} \right] \tag{15}$$

where **R***<sup>q</sup> <sup>k</sup>* <sup>=</sup> *Rq* 1,*k* ,*R<sup>q</sup>* 2,*k* , ... ,*Rq N*,*k* <sup>T</sup> and <sup>θ</sup>*<sup>q</sup> <sup>k</sup>* <sup>=</sup> θ*q* 1,*k* , θ*q* 2,*k* , ... , θ*<sup>q</sup> N*,*k* <sup>T</sup> denotes the sets of the distance and azimuth measurement parameters of target *q* at time index *k*, respectively, Δ**R***<sup>q</sup> <sup>k</sup>* <sup>=</sup> Δ*Rq* 1,*k* , Δ*Rq* 2,*k* , ... , Δ*R<sup>q</sup> N*,*k* <sup>T</sup> and <sup>Δ</sup>θ*<sup>q</sup> <sup>k</sup>* <sup>=</sup> Δθ*<sup>q</sup>* 1,*k* , Δθ*<sup>q</sup>* 2,*k* , ... , Δθ*<sup>q</sup> N*,*k* <sup>T</sup> are the sets of the distance and azimuth measurement parameter errors, respectively. In (15), the term **u***<sup>q</sup> <sup>k</sup>* represents the radar allocation index set of target *q* at time index *k*, ⊗ is the matrix direct product operation, and is the matrix dot product.

It is assumed that the measurement errors of each radar are independent of each other's, so the *q*th target's measurement noise covariance matrix **G***<sup>q</sup> <sup>k</sup>* can be given by:

$$\mathbf{G}\_k^q = \text{diag}\left\{ u\_{1,k}^q \sigma\_{R\_{i,k}^q}^2, u\_{2,k}^q \sigma\_{R\_{i,k}^q}^2, \dots, u\_{N,k}^q \sigma\_{R\_{i,k}^q}^2, u\_{1,k}^q \sigma\_{\theta\_{i,k}^q}^2, u\_{2,k}^q \sigma\_{\theta\_{i,k}^q}^2, \dots, u\_{N,k}^q \sigma\_{\theta\_{i,k}^q}^2 \right\} \tag{16}$$

where diag{·} denotes diagonal matrix.

Since the fusion center receives the measurement information from all of the radars in the network on each target, the total number of samples that need to be processed can be calculated as follows:

$$N\_k = \sum\_{q=1}^{Q} \sum\_{i=1}^{N} N\_{i,q,k} \tag{17}$$
