Coordinate ascent neural Kalman-MLE for state estimation

2025-11-03

AI Summary

This paper addresses nonlinear state estimation under unknown dynamic and observation models. We propose Neural Kalman Maximum Likelihood Estimation (NK-MLE), a supervised learning framework that jointly learns neural-network-parameterized nonlinear dynamics and observation functions alongside Gaussian noise covariance matrices. Our key innovation is a coordinate ascent optimization strategy that alternately updates neural network parameters and noise parameters, enabling end-to-end differentiability within a Kalman filtering pipeline. Upon training, the learned model can be seamlessly integrated into standard extended or unscented Kalman filters as a drop-in replacement. Experiments across multiple nonlinear dynamical systems demonstrate that NK-MLE significantly improves estimation accuracy and robustness—particularly under model mismatch and uncertain noise statistics—outperforming conventional approaches in both nominal and challenging regimes.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

This paper presents a coordinate ascent algorithm to learn dynamic and measurement models in dynamic state estimation using maximum likelihood estimation in a supervised manner. In particular, the dynamic and measurement models are assumed to be Gaussian and the algorithm learns the neural network parameters that model the dynamic and measurement functions, and also the noise covariance matrices. The trained dynamic and measurement models are then used with a non-linear Kalman filter algorithm to estimate the state during the testing phase.

Problem

• Learns neural network parameters for dynamic and measurement models
• Estimates noise covariance matrices using maximum likelihood estimation
• Uses trained models with Kalman filter for state estimation

Innovation

• Coordinate ascent algorithm for neural network training
• Learning Gaussian dynamic and measurement models
• Non-linear Kalman filter for state estimation