Fast Kalman-like optimal FIR filter for time-variant systems with improved robustness

Area of Science:

• Control Systems Engineering
• Signal Processing
• Dynamic Systems Analysis

Background:

• Linear time-varying (LTV) systems require efficient filtering techniques.
• Traditional batch algorithms can be computationally intensive for real-time applications.
• The Kalman filter (KF) is a benchmark for linear filtering but has limitations for certain LTV systems.

Purpose of the Study:

• To propose a fast Kalman-like iterative algorithm for discrete-time filtering of LTV systems.
• To demonstrate the uniqueness and computational efficiency of the proposed OFIR filter.
• To evaluate the performance and robustness of the iterative OFIR filter in practical applications.

Main Methods:

• Re-derivation of the batch Optimal Finite Impulse Response (OFIR) filter to establish its uniqueness.
• Development of a computationally efficient iterative form of the OFIR filter using recursions.
• Formulation of each recursion in a Kalman filter (KF) predictor/corrector format with N-point initial conditions.
• Consideration of the KF as a limiting case of the iterative OFIR filter (N → ∞).

Main Results:

• The proposed iterative OFIR algorithm is significantly faster than the batch OFIR filter.
• The algorithm exhibits computational complexity suitable for real-time applications.
• Increasing the number of states enhances the OFIR filter's robustness against model uncertainties and noise statistic errors.
• Simulations and experimental results validate the algorithm's performance.

Conclusions:

• The fast iterative OFIR algorithm provides an efficient and effective solution for discrete-time filtering of LTV systems.
• The algorithm's KF-like structure and N-point initialization offer flexibility and robustness.
• The proposed method is well-suited for real-time control and tracking applications, such as target tracking and hover systems.