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

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. The generalized H₂ optimal filtering problem seeks to find a linear stable filter that estimates a desired output such that the H₂ norm of the transfer matrix from the white noise input to the estimation error is minimized subject to the constraint that the mean of the error converges to zero for all initial conditions of the given system and filter and for all possible external sinusoidal signals. The analysis, design, and performance limitations of generalized H₂ optimal filters are presented here.