Tram Localization using Soft-Constrained Iterated Kalman Filter with Optimal Step Size Control

The paper describes a way to incorporate soft constraints to iterated Kalman filter and its application to tram localization. The localization task is motivated by a suboptimal performance of a currently used hard-constrained localization solution and is then tackled by introducing a framework allowing to insert various constraints into the Kalman filter scheme. The filtering (data update) step of the iterated Kalman filter is interpreted as an instance of a non-linear least squares problem for which the step size in each iteration can be chosen in the optimal manner, improving the overall state estimate convergence. The described estimation framework is showcased on real-life data and compared against a hard-constrained Kalman filter scheme which resembles the one originally motivating the task. While the presented solution does not provide a substantial quantifiable improvement in quality of estimate in this particular case, it is much more versatile and does not require prior specific choice of tramway tracks. Finally, the introduced scheme is employed on the motivating example with a discussion of possible further enhancements.