Applying detection theory to define stopping criteria for the Signal Decomposition and Parameterization Algorithm

The Signal Decomposition and Parameterization Algorithm (SDPA) offers a way to obtain direct path and multipath ray waveform parameter estimates from real world recorded data. Using the SDPA, ray parameters are obtained that can then be used in the modeling and generation of simulated GNSS signals that showcase the local environmental effects impacting the recorded GNSS signal. The algorithm works by iteratively decomposing the search space to obtain ray estimates, determining estimate error, making a decision on whether to further iterate, and if so, determine where to place the next trial ray waveforms. Ideally, the stopping criteria would continue iteration until the error between the estimate and true (no noise) search spaces is minimized. Previously, the SDPA continued to decompose and parameterize until the error between the received and estimate search spaces could no longer be reduced. This paper outlines how the optimum SDPA processing stopping criteria is established, supplementing signal detection theory with an optimization criteria that minimizes the error between the true iteration after which to halt processing and the realized iteration after which to halt as dictated by a threshold.