State estimation with quantised innovations and communication channels

This study considers the minimum mean-squared error (MMSE) state estimation for the discrete linear stochastic systems subject to both the quantisation and the communication unreliability. Based on the binary quantised innovation and a binary symmetric channel, the recursive MMSE estimator is established, and its performance is analysed. It is also discussed how the quantisation scheme and the communication uncertainty jointly affect the estimation quality. Consequently, the related results are extended to the case of the time-invariant discrete memoryless channel. Numerical simulations are included to illustrate the main results obtained.