Estimation of signal subspace-constrained inputs to linear systems

Estimation of inputs to deterministic linear systems is of interest in applications from target tracking to sound resynthesis. Considering prior information about inputs, such as the time-limited nature of striking a musical instrument, estimates may be made to meet known constraints. This paper presents a method of estimating, based on noisy observations, inputs in terms of a basis expansion, where the inputs are known a priori to be constrained to a signal subspace. It is shown how input estimates may be obtained via least-squares estimation, including recursive algorithms. Simulation results are given to show the improvement of estimation where constraints are known. Additionally, application to sound resynthesis is presented.