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Projection Filtering with Observed State Increments with Applications in Continuous-Time Circular Filtering.

Anna Kutschireiter¹, Luke Rast¹, Jan Drugowitsch¹

¹Department of Neurobiology, Harvard Medical School, Boston MA, United States.

IEEE Transactions on Signal Processing : a Publication of the IEEE Signal Processing Society

|November 7, 2022

Summary

This study introduces the circular Kalman filter for accurate heading direction estimation using noisy angular data. This probabilistic approach improves angular path integration by properly weighting observational reliability.

Keywords:

Bayesian methods circular filtering continuous-time estimation nonlinear filtering sensor fusion stochastic processes

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Area of Science:

Robotics
Navigation Systems
Probabilistic Inference

Background:

Angular path integration estimates heading direction from noisy angular velocity.
Non-probabilistic methods fail to weigh observation reliability, crucial for accurate estimates.
Probabilistic formulation treats angular path integration as nonlinear circular filtering.

Purpose of the Study:

Develop a probabilistic solution for continuous-time circular filtering.
Address the nonlinear nature of heading direction estimation.
Create an analytically accessible and interpretable algorithm for angular path integration.

Main Methods:

Extended the projection-filtering method to handle observed state increments.
Developed a generative model for continuous-time angular-valued observations.
Derived the circular Kalman filter algorithm for probabilistic angular path integration.

Main Results:

The proposed circular Kalman filter provides an approximate solution to circular continuous-time filtering.
The algorithm integrates state increment observations effectively.
It outperforms Gaussian approximation-based filters in accuracy and interpretability.

Conclusions:

The circular Kalman filter offers an analytically accessible and interpretable method for angular path integration.
This probabilistic approach enhances heading direction estimation accuracy.
The derived filter is suitable for systems requiring reliable navigation from noisy angular data.