A Linear Optimal Transversal Filter for Time-Varying Receiver Channels

Abstract

Discrete linear optimal and unbiased transversal filters are proposed for onboard receiver channels to estimate continuous/discrete time-varying state-space signal models. The solutions are first found in the batch form. For optimal filtering, the mean square initial state function is determined a posteriori by the discrete algebraic Riccati equation. The unbiased filter is also represented in the iterative Kalman-like form with no requirements for noise and initial state. The filtering error bound is found in the three-sigma sense via the noise power gain (NPG). A fast iterative algorithm for NPG is also supplied. A comparison with the Kalman channel is given employing the harmonic two-state space model.