We describe methods for applying Monte Carlo filtering and smoothing for estimation of unobserved states in a nonlinear state-space model. By exploiting the statistical structure of the model, we develop a Rao–Blackwellized particle smoother. Due to the lengthy nature of real signals, we suggest processing the data in blocks, and a block-based smoother algorithm is developed for this purpose. A...

Several groups have proposed the state-space approach to tracking time-varying frequencies of multiharmonic quasiperiodic signals. The extended Kalman filter/smoother (EKF/EKS) is one of the common frequency tracking approaches seen in the literature. We introduce a multiharmonic frequency tracker based on the forward-backward statistical linearized Sigma-Point Kalman smoother (FBSL-SPKS) and c...

It is formally proved that the general smoother for nonlinear dynamics can be formulated as a sequential method, that is, observations can be assimilated sequentially during a forward integration. The general filter can be derived from the smoother and it is shown that the general smoother and filter solutions at the final time become identical, as is expected from linear theory. Then, a new sm...

The Kalman Filter (KF) is a powerful tool in the analysis of the evolution of a dynamical model in time. The filter provides with a flexible manner to obtain recursive estimation of the parameters, which are optimal in the mean square error sense. The properties of KF along with the simplicity of the derived equations make it valuable in the analysis of signals. In this chapter an overview of t...

A photoplethysmography (PPG) signal provides very useful information about a subject's hemodynamic status in a hospital or ubiquitous environment. However, PPG is very vulnerable to motion artifacts, which can significantly distort the information belonging to the PPG signal itself. Thus, the reduction of the effects of motion artifacts is an important issue when monitoring the cardiovascular s...

The augmented, iterated Kalman smoother is applied to system identification for inverse problems in evolutionary differential equations. In the augmented smoother, the unknown, time-dependent coefficients are included in the state vector, and have a stochastic component. At each step in the iteration, the estimate of the time evolution of the coefficients is linear. We update the slowly varying...

The xed lag Kalman smoother was proposed recently as a framework for providing retrospective data assimilation capability in atmospheric reanalysis projects Cohn et al Mon Wea Rev Retrospective data assimilation refers to the dynamically consistent incorporation of data observed well past each analysis time into each analysis Like the Kalman lter the xed lag Kalman smoother requires statistical...