*3.2. Selection of Validated Measurements*

Since it is computationally inefficient to use all measurements in the entire surveillance region, the validation gate [2,3] is generated around the track predicted position, and the track is updated using only the measurements that exist inside the gate. If the measurement **z***k*,*<sup>i</sup>* satisfies the following equation for track *τ*, **z***k*,*<sup>i</sup>* is regarded as a validated measurement. Otherwise, it is not used for updating the states of track *τ*.

$$(\mathbf{z}\_{k,i} - \mathbf{H}\hat{\mathbf{x}}\_{k|k-1}^{\tau})^{\top}(\mathbf{S}\_{k|k-1}^{\tau})^{-1}(\mathbf{z}\_{k,i} - \mathbf{H}\hat{\mathbf{x}}\_{k|k-1}^{\tau}) < \tau\_{\mathbf{G}\prime} \tag{14}$$

with:

$$\mathbf{S}\_{k|k-1}^{\tau} = \mathbf{H} \mathbf{P}\_{k|k-1}^{\tau} \mathbf{H}^{\top} + \mathbf{R}\_{k\prime} \tag{15}$$

where <sup>√</sup>*τ<sup>G</sup>* is the size of the validation gate. The set of validated measurements selected by track *<sup>τ</sup>* and the number of validated measurements are denoted by **Z***<sup>τ</sup> <sup>k</sup>* and *<sup>m</sup><sup>τ</sup> <sup>k</sup>* , respectively.
