NormsKF

NormsKF is a family of robust Kalman filtering methods designed to improve state estimation in the presence of outliers and non-Gaussian noise. Building on the classical Kalman filter, NormsKF modifies the treatment of residuals (innovations) by using norm-based loss functions rather than the standard squared error, which enhances resilience to atypical measurements while preserving usefulness for regular data.

In terms of method, NormsKF replaces or augments the conventional quadratic loss with robust alternatives such as L1, Huber, or other non-quadratic penalties on the innovation sequence. This leads to a data assimilation problem that is effectively solved through techniques like iterative reweighted least squares or robust statistics within the prediction-correction cycle. For linear systems, some formulations resemble a weighted Kalman filter with data-dependent covariances; for nonlinear systems, NormsKF can be embedded in extended or unscented Kalman filter frameworks.

Implementation considerations include selecting an appropriate robust loss function and tuning parameters that govern the balance between robustness and efficiency. Computational cost may exceed that of standard Kalman filters, due to iterative steps or more complex weighting schemes. Convergence properties depend on the chosen loss and problem structure.

Applications of NormsKF span areas where measurements exhibit outliers or heavy-tailed noise, such as mobile robotics, navigation, target tracking, and aerospace systems. Performance is typically evaluated against conventional Kalman filters using metrics like root-mean-square error, robustness to outliers, and sensitivity to noise characteristics, across both simulated and real-world datasets.

See also: Kalman filter, Extended Kalman Filter, Unscented Kalman Filter, robust statistics, iterative reweighted least squares.