A Variance-Constrained Approach to Recursive Filtering for Nonlinear 2-D Systems With Measurement Degradations

Area of Science:

• Control Systems Engineering
• Signal Processing
• Stochastic Systems

Background:

• Recursive filtering is crucial for estimating system states from noisy measurements.
• Nonlinear 2-D time-varying systems present unique challenges due to their complexity and evolving dynamics.
• Measurement degradation, occurring randomly, further complicates accurate state estimation.

Purpose of the Study:

• To design a recursive filter for nonlinear 2-D time-varying systems with stochastic measurement degradation.
• To guarantee and minimize the upper bound of the estimation error variance.
• To develop a filter suitable for recursive online computation.

Main Methods:

• Taylor expansion is used to handle system nonlinearities, with linearization errors treated as norm-bounded uncertainties.
• Mathematical induction and Riccati-like difference equations are employed to derive an upper bound for the estimation error variance.
• Filter gain parameters are optimized at each time step to minimize the derived error bound.

Main Results:

• An upper bound for the estimation error variance is derived and minimized.
• The designed filter parameters are suitable for recursive online computation.
• The impact of stochastic measurement degradation on filtering performance is analyzed.

Conclusions:

• The proposed filter effectively minimizes the estimation error variance for nonlinear 2-D systems with degraded measurements.
• The developed method provides a computationally efficient approach for online recursive filtering.
• The study demonstrates the filter's effectiveness through a simulation example.