Smoothly time varying systems and least squares system identification

This paper considers the significance of smoothness from a somewhat broader perspective. Three issues are involved. The first is the ability of the identification algorithm to track a smooth model when the order is estimated appropriately. The second is to find circumstances under which the estimates themselves will be smooth. The third is to find circumstances under which a smooth model of a given order can be fit to a set of input/output data. The first two are considered here. Before the identification algorithm can even be applied, it is necessary to have an estimate of the system order. However, a unique order for a time-varying system is not a well defined concept. In fact, any pair of input and output sequences, u t and y t can be realized by a zero order time-varying system.