A signal processing device includes a prediction and correction engine configured to receive a signal including a target signal, and to execute a single-moment filter, based on a current measurement sample of the signal and a model of the target signal, to obtain a single-moment state estimate and a single-moment state estimate error covariance for the target signal, a covariance renormalizer configured to determine a multi-moment state estimate error covariance for the target signal based on a prior single-moment state estimate error covariance, corresponding to a sample prior to the current measurement sample, and the single-moment state estimate error covariance, and a multi-moment prediction and correction engine configured to execute a multi-moment filtering extension based on the current measurement sample and the multi-moment state estimate error covariance to obtain a multi-moment state estimate, and further configured to determine an estimate for the target signal based on the multi-moment state estimate.