Multi-modal filtering for non-linear estimation

Multi-modal densities appear frequently in time series and practical applications. However, they are not well represented by common state estimators, such as the Extended Kalman Filter and the Unscented Kalman Filter, which additionally suffer from the fact that uncertainty is often not captured sufficiently well. This can result in incoherent and divergent tracking performance. In this paper, we address these issues by devising a non-linear filtering algorithm where densities are represented by Gaussian mixture models, whose parameters are estimated in closed form. The resulting method exhibits a superior performance on nonlinear benchmarks. © 2014 IEEE

Multi-modal filtering for non-linear estimation

Multi-modal densities appear frequently in time series and practical applications. However, they are not well represented by common state estimators, such as the Extended Kalman Filter and the Unscented Kalman Filter, which additionally suffer from the fact that uncertainty is often not captured sufficiently well. This can result in incoherent and divergent tracking performance. In this paper, we address these issues by devising a non-linear filtering algorithm where densities are represented by Gaussian mixture models, whose parameters are estimated in closed form. The resulting method exhibits a superior performance on nonlinear benchmarks

Invertible Particle Flow-based Sequential MCMC with extension to Gaussian Mixture noise models

Sequential state estimation in non-linear and non-Gaussian state spaces has a wide range of applications in statistics and signal processing. One of the most effective non-linear filtering approaches, particle filtering, suffers from weight degeneracy in high-dimensional filtering scenarios. Several avenues have been pursued to address high-dimensionality. Among these, particle flow particle filters construct effective proposal distributions by using invertible flow to migrate particles continuously from the prior distribution to the posterior, and sequential Markov chain Monte Carlo (SMCMC) methods use a Metropolis-Hastings (MH) accept-reject approach to improve filtering performance. In this paper, we propose to combine the strengths of invertible particle flow and SMCMC by constructing a composite Metropolis-Hastings (MH) kernel within the SMCMC framework using invertible particle flow. In addition, we propose a Gaussian mixture model (GMM)-based particle flow algorithm to construct effective MH kernels for multi-modal distributions. Simulation results show that for high-dimensional state estimation example problems the proposed kernels significantly increase the acceptance rate with minimal additional computational overhead and improve estimation accuracy compared with state-of-the-art filtering algorithms

Atmospheric tomography with separate minimum variance laser and natural guide star mode control

This paper introduces a novel, computationally efficient, and practical atmospheric tomography wavefront control architecture with separate minimum variance laser and natural guide star mode estimation. The architecture is applicable to all laser tomography systems, including multi conjugate adaptive optics (MCAO), laser tomography adaptive optics (LTAO), and multi object adaptive optics (MOAO) systems. Monte Carlo simulation results for the Thirty Meter Telescope (TMT) MCAO system demonstrate its benefit over a previously introduced “ad hoc” split MCAO architecture, calling for further in-depth analysis and simulations over a representative ensemble of natural guide star (NGS) asterisms with optimized loop frame rates and modal gains