Convergence Properties of Recursive Projection Algorithm for System Identification with Binary-Valued Observations

This paper studies the identification problem for FIR (finite impulse response) systems with binary-valued observations. The recursive projection algorithm was proposed in [9] to estimate the unknown parameter. We prove that the convergence rate of the recursive projection algorithm can achieve
$O(1/k)$
(the same order as the CR (Cramer-Rao) lower bound), which is faster than that in the previous work. By using the properties of higher moment of the estimation error, we prove that the convergence rate is obtained under a more intuitive condition. Numerical examples were given to demonstrate the theoretical results.