Signal recognition without state space expansion based on observations containing a singular interference: the case of nonlinear parameters of basis functions

This paper proposes a novel method for recognizing a set of signals with linearly and nonlinearly included parameters from a given ensemble of signals under essential a priori uncertainty. Due to this uncertainty, well-known statistical methods become inapplicable. Signals may be present in an additive mixture containing an observation noise and a singular interference; the distribution law of the noise is unknown, and only its correlation matrix is specified. The novel method is invariant to this interference, does not require traditional state-space expansion, and ensures the decomposition and parallelization of the computational procedure. The signals and interference are represented using conventional linear spectral decompositions with unknown coefficients and given basis functions. Random and methodological errors, as well as the resulting computational effect, are analyzed. An illustrative example is provided.