Recursive identification of FIR systems with binary-valued observations

This paper investigates the identification of the finite impulse response (FIR) systems with binary-valued observations. Combining with the stochastic gradient algorithm and statistical property of the system noise, a recursive projection algorithm is proposed to estimate the unknown parameters. Under some mild conditions on the a priori knowledge of the unknown parameters and inputs, the algorithm is proved to be convergent in the almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates of estimation errors are also obtained, and the schemes of selecting the quantization value are provided to ensure such rates. A numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained.