An FPGA-Based Trigonometric Kalman Filter Approach for Improving the Measurement Quality of a Multi-Head Rotational Encoder

Abstract

This article introduces an advanced theoretical approach, named the Trigonometric Kalman Filter (TKF), to enhance measurement accuracy for multi-head rotational encoders. Leveraging the processing capabilities of a Field-Programmable Gate Array (FPGA), the proposed TKF algorithm uses trigonometric functions and sophisticated signal fusion techniques to provide highly accurate real-time angle estimation with rapid response. The inclusion of the Coordinate Rotation Digital Computer (CORDIC) algorithm enables swift and efficient computation of trigonometric values, facilitating precise tracking of angular position and rotational speed. This approach represents a notable advancement in control systems, where high accuracy and minimal latency are essential for optimal performance. The paper addresses key challenges in angle measurement, particularly the signal fusion inaccuracies that often impede precision in high-demand applications. Implementing the TKF with an FPGA-based pure fixed-point method not only enhances computational efficiency but also significantly reduces latency when compared to conventional software-based solutions. This FPGA-based implementation is particularly advantageous in real-time applications where processing speed and accuracy are critical, and it demonstrates the effective integration of hardware acceleration in improving measurement fidelity. To validate the effectiveness of this approach, the TKF was rigorously tested on a precision drive control system, configured for a direct PMSM drive in an astronomical telescope mount equipped with a standard 0.5m telescope frequently used by astronomers. This real-world application highlights the TKF’s ability to meet the stringent positioning and measurement accuracy requirements characteristic of astronomical observation, a field where minute angular adjustments are critical. The FPGA-based design enables high-frequency updates, essential for managing the minor, precise adjustments required for telescope control. The study includes a comprehensive computational analysis and experimental testing on an Altera Stratix FPGA board, presenting a detailed comparison of the TKF’s performance with other known methods, including fusion techniques such as differential methods, α–β filters, and related Kalman filtering applied to one sensors. The study demonstrates that the four-head fusion configuration of the TKF outperforms traditional methods in terms of measurement accuracy and responsiveness.