LooprekKF

LooprekKF is a class of state estimation algorithms that extend the classical Kalman filter by incorporating looping, iterative updates within each filtering step. The name is a portmanteau of loop and KF, reflecting the central idea: after an initial Kalman update, the algorithm performs one or more inner iterations to refine the state estimate and its covariance by re-evaluating residuals and, if needed, re-linearizing the process and measurement models. The inner loop continues until a convergence criterion is satisfied or a preset iteration limit is reached. This approach aims to improve robustness in the presence of model errors, time-varying dynamics, or nonlinearity.

LooprekKF can be formulated for linear systems as an augmented or iterated Kalman filter, and for nonlinear systems it can be integrated with extended or unscented Kalman filter frameworks, where inner iterations are used to tighten linearization or sigma-point approximations. In practice, looprekKF trades lower bias and better consistency for higher computational cost and potential stability concerns; proper tuning of convergence thresholds, initialization, and max iterations is essential.

Applications include robotics, autonomous navigation, sensor fusion, and target tracking, especially in scenarios with model mismatch or rapid environmental changes. The method is often implemented as a modular layer atop existing KF codebases, allowing practitioners to activate inner iterations selectively based on observed residuals or predicted innovation statistics.

Limitations include the risk of non-convergence, increased latency, and sensitivity to tuning parameters. As with other iterative estimation techniques, thorough validation on representative datasets is recommended before deployment.