Recursive state estimation via approximate modal paths

2025-12-19

AI Summary

For nonlinear non-Gaussian systems, recursive computation of modal paths remains challenging due to the absence of closed-form solutions and high computational complexity. This paper proposes a novel recursive modal estimation framework based on bidirectional filtering. It constructs forward and backward approximations of the modal path via dynamic programming and fuses them into a unified bidirectional filtering formulation. To the best of our knowledge, this is the first work to achieve fully recursive modal path estimation. Furthermore, a quadratic approximation of the value function is introduced, ensuring theoretical rigor while substantially improving computational efficiency. The approach unifies filtering and smoothing within a single coherent framework. Simulation results demonstrate that the proposed method matches or surpasses state-of-the-art algorithms in both estimation accuracy and real-time performance—particularly under strongly nonlinear and non-Gaussian conditions.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

In this paper, a method for recursively computing approximate modal paths is developed. A recursive formulation of the modal path can be obtained either by backward or forward dynamic programming. By combining both methods, a ``two-filter'' formula is demonstrated. Both method involves a recursion over a so-called value function, which is intractable in general. This problem is overcome by quadratic approximation of the value function in the forward dynamic programming paradigm, resulting in both a filtering and smoothing method. The merit of the approach is verified in a simulation experiments, where it is shown to be on par or better than other modern algorithms.

Problem

• Develops recursive method for approximate modal paths
• Uses quadratic approximation to overcome intractable value function
• Demonstrates filtering and smoothing via two-filter formula

Innovation

• Recursive modal path computation via dynamic programming
• Two-filter formula combining forward and backward methods
• Quadratic approximation enabling tractable filtering and smoothing