Description
The Kalman filter is the optimal linear-Gaussian recursive Bayesian estimator. It maintains a Gaussian posterior over the state and updates it with each new measurement in closed form. Extended (EKF) and unscented (UKF) variants linearise / sample for nonlinear systems. In indoor positioning and CSI tracking it is the natural default when noise is approximately Gaussian and the dynamics are smooth.
When it's used
- Smoothing CSI-derived state estimates (occupancy counts, positions)
- BLE / IMU / CSI fusion when Gaussian noise is a good fit
- Online state tracking with limited compute
Limitations
- Suboptimal under heavy-tailed or multi-modal posteriors
- Requires good linearisation in EKF / UKF
- Process / measurement noise covariances must be tuned