2021/02/28 by Anna Kutschireiter, Luke Rast, Luke I. Rast +1
Computer Science · Mathematics · #Algorithm #Angular velocity #Artificial intelligence #Blind Source Separation Techniques #Computer science #Computer vision #Control theory (sociology) #Filter (signal processing) #Kalman filter #Mathematics #Nonlinear system #Probabilistic logic #Target Tracking and Data Fusion in Sensor Networks #Time Series Analysis and Forecasting #cs.RO #stat.ME
paper · pdf · doi:10.1109/tsp.2022.3143471
published as IEEE Transactions on Signal Processing (2022) · 15 pages, 3 figures, accepted at IEEE Transactions on Signal Processing
openalex publication_date 2022/01/01 · arxiv created 2022/01/18 · arxiv updated 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Angular path integration is the ability of a system to estimate its own heading direction from potentially noisy angular velocity (or increment) observations. Non-probabilistic algorithms for angular path integration, which rely on a summation of these noisy increments, do not appropriately take into account the reliability of such observations, which is essential for appropriately weighing one's current heading direction estimate against incoming information. In a probabilistic setting, angular path integration can be formulated as a continuous-time nonlinear filtering problem (circular filtering) with observed state increments. The circular symmetry of heading direction makes this inference task inherently nonlinear, thereby precluding the use of popular inference algorithms such as Kalman filters, rendering the problem analytically inaccessible. Here, we derive an approximate solution to circular continuous-time filtering, which integrates state increment observations while maintaining a fixed representation through both state propagation and observational updates. Specifically, we extend the established projection-filtering method to account for observed state increments and apply this framework to the circular filtering problem. We further propose a generative model for continuous-time angular-valued direct observations of the hidden state, which we integrate seamlessly into the projection filter. Applying the resulting scheme to a model of probabilistic angular path integration, we derive an algorithm for circular filtering, which we term the circular Kalman filter. Importantly, this algorithm is analytically accessible, interpretable, and outperforms an alternative filter based on a Gaussian approximation.