Analysis, design, and performance limitations of H2 optimal filtering in the presence of an additional input with known frequency

The standard H2 optimal filtering problem considers the estimation of a certain output based on the measured output when the input is a zero mean white noise stochastic process of known intensity. In this paper, the inputs are considered to be of two types. The first type of input, as in standard H2 optimal filtering, is a zero mean wide sense stationary white noise, while the second type is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. Under such inputs, a generalized H2 optimal filtering problem is formulated here. As in the standard H2 optimal filtering problem, the generalized H2 optimal filtering problem seeks to find a linear stable unbiased filter (called the generalized H2 optimal filter) that estimates a desired output while utilizing the measured output such that the H2 norm of the transfer matrix from the white noise input to the estimation error is minimized. The analysis, design, and performance limitations of generalized H2 optimal filters are presented here.