The Rauch-Tung-Striebel (RTS) smoother is an algorithm for computing state estimates in time series using noisy measurements from all time steps. The RTS smoother works by first filtering the state when measurements arrive and then using a backward pass to obtain the smoothed state estimates for all time steps that use measurement information from all time steps as well. The backward pass goes through all time steps for which a filtering estimate were obtained in backward order. We propose a smoother that does the backward pass using only a fraction of the time steps and provides the same results as the conventional RTS smoother for these time steps. This reduces computational complexity and required memory significantly as only data for these interesting time steps need to be stored. We also propose the extension of the reduced sampling-rate smoother for non-linear systems. We show an example application involving position estimation using a state space model that uses a high filtering rate, but where it is suitable to present the final smoothed route with a considerably lower rate. In a second example, we show how the reduced rate smoother works in a nonlinear case.

The Kalman Filter (KF) is a classical algorithm that was developed for estimating a state that evolves in time based on noisy measurements by assuming linear state transition and measurements models. There exist various KF extensions for non-linear situations, but they are not exact and provide different linearization errors. The Iterated Posterior Linearization Filter (IPLF) does the linearizations iteratively to achieve better linearizations. However, it is possible that some measurements cannot be well linearized using the current knowledge, but their linearization may be better after more measurements are available. Thus, we propose an algorithm that can store the older state elements and measurements when their linearization error is high. The resulting algorithm, the Stacked Iterated Posterior Linearization Filter (S-IPLF), is based on linear dynamic models and uses information from multiple time instances to make the linearization of the measurement function. Results show that the proposed algorithm outperforms traditional KF extensions when some of the measurements cannot be well linearized with the current knowledge, but can be when future information is available.