The effect of noise-only tracks on the performance of a combined detection and tracking algorithm

The effect of the number of noise-only tracks is examined for a combined detection and tracking algorithm. Specifically we find the signal-to-noise ratio (SNR) required to ensure that the track containing the target produces the maximum integrator output with a given probability P_c when the number of noise-only tracks is allowed to vary over many orders of magnitude. We use numerical integration and a function solver in MATLAB to evaluate the formulas derived. The SNR required for large track trials is more modest than might be thought; in fact, it is found that for P_c=0.99, the required SNR increases only 2 dB as the number of noise-only tracks increases from 10² to 10⁷.