Wald Sequential Detection with Non-Gaussian Pulse Radar Using the Zakai Equation

The "optimal" Wald sequential hypthesis test for diffusion signals is presented. The result is a threshold test with explicitly computable thresholds. Five possible schemes for a numerical implementation of the test are given. A comparison of the different implementations and analysis of the detectors performance is done for the radar problem of ship versus chaff target discrimination using lognornal and Rayleigh models respectively. Parameter estimation for the lognormal and Rayleigh cases are also studies. Finally, a signal estimation scheme is presented utilizing the conditional expectation of the signal computed from the conditional density of the underlying state, which is the solution to the Zakai equation.