Sigma-point Kalman smoothing: algorithms and analysis with applications to indoor tracking

The sigma‑point Kalman filter (SPKF) offers improved accuracy over the extended Kalman filter for nonlinear state estimation, yet nonlinear smoothing methods based on sigma‑point techniques remain limited. This work introduces new fixed‑interval and fixed‑lag sigma‑point Kalman smoothers (SPKS) using forward‑backward and Rauch‑Tung‑Striebel frameworks. To enable backward propagation, we use weighted statistical linear regression to generate pseudo‑linearized dynamics compatible with the SPKF. The proposed smoothers are evaluated in applications such as indoor localization and multiharmonic frequency tracking, showing strong performance. We also extend the theoretical foundations of the SPKF by deriving mean‑square error lower bounds and stability‑based upper bounds, and verify these results experimentally.