Identification of FIR Systems With Binary Input and Output Observations

Alex S. Leong, Erik Weyer, Girish N. Nair

Abstract: This article considers the identification of finite-impulse response systems, where information about the inputs and outputs of the system undergoes quantization into binary values before transmission to the estimator. In the case where the thresholds of the input and output quantizers can be adapted, we propose identification schemes that are strongly consistent for Gaussian distributed inputs and noises. The algorithms are based on the idea that certain joint probabilities of the unquantized signals can be estimated from the binary signals, and the system parameters can then be inferred from these estimates. The algorithms and their properties are illustrated in simulation examples.