Maximum likelihood-based iterated divided difference filter for nonlinear systems from discrete noisy measurements.

Area of Science:

• State estimation
• Nonlinear systems
• Numerical algorithms

Background:

• Nonlinear state estimation often suffers from low accuracy due to large initial errors and complex measurement equations.
• Existing methods like UKF, DDF, IUKF, and IDDF have limitations in handling these challenges effectively.

Purpose of the Study:

• To develop a novel filter, the Maximum Likelihood-based Iterated Divided Difference Filter (MLIDDF), for improved nonlinear state estimation.
• To address the limitations of existing filters in scenarios with significant initial estimation errors and nonlinear measurement models.

Main Methods:

• The MLIDDF is a derivative-free algorithm relying solely on functional evaluations.
• It incorporates an iterative measurement update using the current measurement and a maximum likelihood-based termination criterion.
• The algorithm is designed to ensure estimates ascend the maximum likelihood surface.

Main Results:

• Simulations show MLIDDF reduces accumulated mean-square root error in position by 63% compared to UKF and DDF.
• MLIDDF demonstrates a 7% improvement over IUKF and IDDF in position error.
• The algorithm exhibits enhanced state estimation accuracy and a faster convergence rate.

Conclusions:

• The MLIDDF offers superior performance in nonlinear state estimation compared to established filters.
• Its derivative-free nature and maximum likelihood criterion contribute to improved accuracy and convergence.
• MLIDDF presents a promising advancement for applications requiring precise state estimation in challenging nonlinear systems.