On Iterative Parameter Identification of FIR Systems With Batched Possibly Incorrect Binary-valued Observations

This paper considers the problem of parameter identification for a binary output finite impulse response (FIR) system with measurement error, where the measurement error makes the binary measurement values take opposite values with a certain probability. First, the maximum likelihood estimation (MLE) of the parameters is given and an iterative algorithm with projection based on the Expectation-Maximization algorithm is presented to calculate the MLE. Furthermore, the necessary and sufficient condition for the likelihood function to have a unique maximum point is obtained. It is proved that the iterative estimation error converges to zero at an exponential rate under persistently excitation input conditions. Finally, some numerical simulation results based on a typical system show the effectiveness of the proposed algorithm.