A Two-Filter Approach for State Estimation Utilizing Quantized Output Data.

Area of Science:

• Control Systems Engineering
• Signal Processing
• Data Analysis

Background:

• Filtering and smoothing algorithms are crucial for decision-making and parameter identification in diverse fields like economics and control systems.
• Noisy measurements from cost-effective sensors or digitalization processes often lead to significant information loss, complicating accurate state estimation.
• Developing robust algorithms is essential for reliable system analysis and control under practical measurement constraints.

Purpose of the Study:

• To develop advanced Gaussian sum filtering and smoothing algorithms specifically designed for quantized and noisy measurements.
• To address the challenge of information loss in real-world sensor data and communication channels.
• To improve the accuracy and computational efficiency of state estimation techniques.

Main Methods:

• Characterization of the probability mass function of quantized output using an integral equation.
• Approximation of the integral equation via Gauss-Legendre quadrature to obtain a Gaussian mixture model.
• Development of filtering and smoothing algorithms based on the derived Gaussian mixture model.

Main Results:

• The proposed Gaussian sum filtering and smoothing algorithms effectively handle quantized and noisy measurements.
• Numerical simulations demonstrate significant improvements in estimation accuracy compared to existing methods.
• The developed algorithms offer a favorable balance between estimation accuracy and computational cost.

Conclusions:

• Gaussian sum filtering and smoothing provide a robust framework for state estimation with quantized measurements.
• The Gauss-Legendre quadrature approximation enables efficient processing of quantized data within a Gaussian mixture structure.
• This approach offers practical benefits for applications requiring accurate state estimation under measurement limitations.