The State Space Subdivision Filter for Estimation on SE(2)

Florian Pfaff,Uwe D Hanebeck,Kailai Li

doi:10.3390/s21186314

Abstract

The domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

Highlights

The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle
The results of the second evaluation, in which we considered different numbers of particles for the particle filter (PF) and areas for the S3F, are given in the second subsection
While some existing approaches, such as the unscented Kalman filter on manifolds (UKF-M) and the ProgSE2BF, use a fixed number of parameters, the number of parameters can be increased to arbitrary numbers in the S3F and the PF

Summary

Introduction

The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. When tracking vehicles or robots that are only capable of planar motion within rooms or on plains, their pose can be described by a two-dimensional position and a heading angle. Such filters are generally suboptimal since they cannot fully take the periodicity of the angle

Objectives

Discussion

Conclusion