Iterative state estimation

Iterative solvers allow for a trade-off between speed and accuracy. We propose an iterative method for the estimation of the internal states of a given discrete-time linear state-space model from a series of noisy measurements. In particular we identify the MAP estimate of those states as being the solution of a sparse system of linear equations and derive an iterative solver based on the conjugate gradient method. We derive convergence results to quantify the trade-off between speed and accuracy and finally apply the method to channel estimation where it is shown to outperform Kalman smoothing complexity-wise.