Batch-Form Solutions to Optimal Input Signal Recovery in the Presence of Noises

Abstract

This paper studies the problem of optimally recovering the input signals to a linear time-invariant system in the presence of input and measurement noises. The emphasis is on batch-form solutions which are suitable for short-duration large-domain signal propagation applications. 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 input signal recovery is optimal in the sense that the optimal Kalman filter residual is correctly recovered from the given information. Various solution techniques are considered and a weighted least-squares solution is found to be the simplest and most practical in short-duration signal recovery applications.