IIR deconvolution from noisy observations using Kalman filtering

In this paper, we reconstruct the input signal of an IIR filter from the noise corrupted output signal. We perform two operations parallely. One deconvolution and the other, noise removal. We show how to use Kalman filter to perform this task. We develop theory for a very general scenario of reconstructing an ARMA process from its noise corrupted IIR filtered output. We develop augmented state space equations combining the state space equations of the ARMA process and the IIR filter, which are required to apply Kalman filter. The simulation results show clear improvement in the signal-to-noise ratio.