(Preprint) AAS BATCH-FORM SOLUTIONS TO OPTIMAL INPUT SIGNAL RECOVERY IN THE PRESENCE OF NOISES

This paper studies the problem of optimally recovering the input signals to a linear time-invariant system when both input and measurement noises are present. We focus on batch-form solutions which are suitable for applications that deal with short-duration events. The system, the input and measurement noise covariances, the noise-corrupted output signals are assumed known, and we seek to recover the input signals that enter the system prior to being corrupted by input noise. The proposed solution works through a Kalman filter to characterize the input and measurement noise statistics. The input signal recovery is optimal in the sense that the Kalman filter residual is correctly recovered from the given information about the model and the output measurements. A weighted least-squares solution is found to be both simple and useful in acoustic signal recovery applications.