Portrait of James Richard Forbes

James Richard Forbes

Associate Academic Member
Full Professor, McGill University, Department of Mechanical Engineering
Research Topics
Applied Machine Learning
Autonomous Robotics Navigation
Information Theory
Lie Group Theory
Optimization
Robotics
Website
Google Scholar
LinkedIn

Publications

The Harmonic Exponential Filter for Nonparametric Estimation on Motion Groups
Miguel Saavedra-Ruiz
Steven A. Parkison
Ria Arora
James Richard Forbes
Liam Paull
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from nois… (see more)y sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing nonparametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. This paper introduces a novel approach to nonparametric Bayesian filtering on motion groups, designed to handle multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and asymptotically exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's performance compared with established nonparametric filtering methods across simulated and real-world localization tasks.
2025-02-01
IEEE Robotics and Automation Letters (published)
doi.org
arxiv.org
The Harmonic Exponential Filter for Nonparametric Estimation on Motion Groups
Miguel Saavedra-Ruiz
Steven A. Parkison
Ria Arora
James Richard Forbes
Liam Paull
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from nois… (see more)y sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing nonparametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. This paper introduces a novel approach to nonparametric Bayesian filtering on motion groups, designed to handle multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and asymptotically exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's performance compared with established nonparametric filtering methods across simulated and real-world localization tasks.
2024-08-01
ArXiv (preprint)
doi.org
arxiv.org
The Harmonic Exponential Filter for Nonparametric Estimation on Motion Groups
Miguel Saavedra-Ruiz
Steven A. Parkison
Ria Arora
James Richard Forbes
Liam Paull
Bayesian estimation is a vital tool in robotics as it allows systems to update the belief of the robot state using incomplete information fr… (see more)om noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are all unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing non-parametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. In this paper, we introduce a novel approach to nonparametric Bayesian filtering to cope with multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's superior performance compared with established nonparametric filtering methods across a range of simulated and real-world localization tasks.
2024-08-01
ArXiv (preprint)
doi.org
arxiv.org
The Harmonic Exponential Filter for Nonparametric Estimation on Motion Groups
Miguel Saavedra-Ruiz
Steven A. Parkison
Ria Arora
James Richard Forbes
Liam Paull
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from nois… (see more)y sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing nonparametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. This paper introduces a novel approach to nonparametric Bayesian filtering on motion groups, designed to handle multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and asymptotically exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's performance compared with established nonparametric filtering methods across simulated and real-world localization tasks.
2024-08-01
ArXiv (preprint)
doi.org
arxiv.org
The Harmonic Exponential Filter for Nonparametric Estimation on Motion Groups
Miguel Saavedra-Ruiz
Steven A. Parkison
Ria Arora
James Richard Forbes
Liam Paull
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from nois… (see more)y sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are all unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing nonparametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. This letter introduces a novel approach to nonparametric Bayesian filtering on motion groups, designed to handle multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and asymptotically exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's superior performance compared with established nonparametric filtering methods across a range of simulated and real-world localization tasks.
2024-08-01
ArXiv (preprint)
doi.org
arxiv.org