MULTIRATE MODELING OF AR/MA STOCHASTIC SIGNALS AND ITS APPLICATION TO THE COMBINED ESTIMATION INTERPOLATION PROBLEM

The use of the Kalman filter is investigated in this work for interpolating and estimating values of an AR or MA stochastic signal when only a noisy, down-sampled version of the signal can be measured. A multirate modeling theory of the ARIMA stochastic signals is first derived from a block state-space viewpoint. The missing samples are embedded in the state vector so that missing signal reconstruction problem becomes a state estimation scheme. Next, Kalman state estimation theory is introduced to treat the combined problem. Some extensions are also discussed for variations of the original basic problem. The proposed Kalman reconstruction filter can be also applied toward recovering missing speech packets in a packet switching network with packet interleaving configuration. By analysis of state estimation theory, the proposed Kalman reconstruction filters produce minimum-variance estimates of the original signals, Simulation results indicate that the multirate Kalman reconstruction filters possess better estimation/interpolation performances than a Wiener reconstruction filter under adequate numerical complexity.