An application of receding horizon control to estimation with quantized coefficients

A methodology for designing optimal finite impulse response estimators with quantized coefficients is proposed. The problem of minimizing the covariance of the estimation error is translated into a constrained quadratic regulator problem, where the inputs need to be chosen from a finite set. Solving it has a computational complexity which is exponential in the filter impulse response length. To overcome the associated computational burden, we propose an approximate algorithm using receding horizon ideas borrowed from the model predictive control framework. This approach can be independently motivated without utilizing the control analogy. We present a closed form expression for the exact solution to the problem. An example illustrates the trade-off that arises between computational time and performance.