Design of robust Gaussian approximate filter and smoother with latency probability identification

Area of Science:

• Control Systems Engineering
• Signal Processing
• Statistical Inference

Background:

• Kalman filters assume Gaussian noise and accurate measurements, which are often violated in real-world scenarios.
• Heavy-tailed measurement noise (HMN) and one-step randomly delayed measurements (ORDMs) with unknown latency probability (LP) degrade the performance of standard estimators.
• Nonlinear systems present additional challenges for state estimation.

Purpose of the Study:

• To develop robust Gaussian approximate (GA) filters and smoothers for nonlinear systems.
• To address the challenges posed by heavy-tailed measurement noise (HMN) and unknown latency probability (LP) in state estimation.
• To provide a general estimation framework adaptable to various nonlinear estimation techniques.

Main Methods:

• Modeling the one-step predicted probability density function (PDF) as Gaussian.
• Utilizing a Normal-Gamma-Beta (NGBM) distribution for the likelihood PDF.
• Applying variational Bayesian techniques to derive novel robust GA filters and smoothers.

Main Results:

• The proposed robust GA filter and smoother demonstrate superior performance in estimating states of nonlinear systems.
• Effectiveness validated through applications in a nonstationary growth model, passive ranging, and target tracking.
• Achieved higher estimation precision compared to existing algorithms, with a marginal increase in computational complexity.

Conclusions:

• The developed robust GA filters and smoothers offer a general and effective framework for state estimation under HMN and ORDMs.
• The variational Bayesian approach provides a powerful tool for robust nonlinear state estimation.
• The proposed methods enhance estimation accuracy in practical scenarios where traditional filters fail.