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

Area of Science:

• Robotics and Control Systems
• State Estimation and Filtering Theory
• Computational Geometry and Manifold Theory

Background:

• The Special Euclidean group SE(2) is crucial for describing planar object motion, encompassing both position and orientation.
• The inherent nonlinearity and periodicity of the angle in SE(2) present significant challenges for traditional filtering techniques.
• Existing methods often struggle with computational complexity or accuracy when dealing with correlated position and orientation states.

Purpose of the Study:

• To introduce a novel filtering approach designed for the SE(2) domain that addresses its inherent nonlinearities.
• To develop a filter that efficiently handles correlated position and orientation states in planar tracking scenarios.
• To demonstrate superior performance compared to existing state-of-the-art filters in terms of accuracy and computational efficiency.

Main Methods:

• A novel filter is proposed that decomposes the joint probability density into a marginalized density for the periodic angle and a conditional density for the linear position.
• The state space is discretized along the periodic dimension, with each segment represented by Gaussian parameters and a grid value.
• This representation allows for the approximation of functions on SE(2) by weighting Gaussians with grid values, effectively interweaving a grid filter with a Kalman filter.

Main Results:

• The proposed filter demonstrates comparable complexity to grid filters for circular domains while accommodating varying numbers of parameters.
• In simulated tracking scenarios, the filter significantly outperformed the unscented Kalman filter for manifolds and a dual quaternion-based progressive filter.
• The filter achieved higher accuracy than a particle filter with one million particles, operating over an order of magnitude faster.

Conclusions:

• The novel SE(2) filter offers a computationally efficient and highly accurate solution for planar tracking problems with correlated position and orientation.
• This approach provides a significant advancement over existing filtering techniques, particularly in real-time applications requiring high performance.
• The method's ability to balance accuracy and speed makes it a valuable tool for robotics and autonomous systems operating in 2D environments.