Worst-case estimation of unknown sinusoids contained in corrupted measurement data

We present an H_∞-type approach to the problem of estimation of sinusoids from noisy measurements. In this context, estimation of sinusoids means simultaneous estimation of frequencies, amplitudes, and phase angles of all sinusoidal components contained in the measured data. The estimation problem is formulated as a minimax optimization problem for minimization of estimation error in the presence of the worst-case noise of unknown statistics. The necessary conditions for the best sinusoids and the worst-case noise are derived. These conditions are given in terms of a nonlinear two-point-boundary-value problem which can be solved using numerical methods. Simulation results show a high estimation accuracy even in the presence of multiple sinusoids