Detection and estimation of a Bernoulli-Gauss process for linear discrete-time systems

This paper is concerned with the deconvolution of impulsive noise, i.e. the estimation of the arrival lime and amplitude of a Bernoulli-Gauss process for a linear discrete-time system in the presence of noise. A crude approximate algorithm coupled with both event detection and amplitude estimation is developed by using two Kalman filters. An honest algorithm that involves 2(2^L — I) Kalman filters, event detection and amplitude estimation is also developed (Ldenotes the smoothing lag of a Bernoulli process). Moreover, to save CPU time and to simplify the structure of the honest algorithm, a fast algorithm that includes 2^L Kalman filters is derived. Digital simulation studies and comparison with other algorithms are included.