A general hankel-norm approximation scheme for linear recursive filtering

Let {x(t)} and {y(t)} be stochastic processes which are weakly stationary and stationarily correlated. We consider the problem of finding an approximate recursive low-dimensional filter of x(t), based on the observation of the past of y(t), using Hankel-norm techniques. Several estimation problems have been investigated in the past using these techniques. We present here a general framework which includes many of these approaches as special cases. We also discuss some new applications. The approximate filter so constructed allows for an a priori bound on the estimation error.