Kalman-based multiple sinusoids identification from intermittently missing measurements of the superimposed signal

We consider the problem of stochastic identification of multiple sinusoids from intermittently missing measurements of superimposed signal. An alternate problem formulation is presented as estimation of amplitude and frequency of the sinusoids from missing measurements. The popularly known estimation methods, such as the extended Kalman filter (EKF) and cubature Kalman filter (CKF) may fail or suffer from poor accuracy if the measurements are missing. In this paper, we redesign the EKF to handle this irregularity in measurements and apply the modified EKF for the formulated estimation problem. In this regard, we introduce a modified measurement model incorporating the possibility of missing measurements. Subsequently, we rederive the relevant parameters of the EKF, such as measurement estimate, measurement error covariance, and state-measurement cross-covariance, for the modified measurement model. Furthermore, we rederive the posterior covariance with minimized trace and study the stability of the resulting extension of the EKF. The results reveal the superior performance of the modified EKF compared with the ordinary Gaussian filters and existing filters-based estimation of the sinusoids in the presence of intermittently missing measurements.