Research on an adaptive dynamic compensation method for cumulative noise in displacement sensors utilizing error-state Kalman filtering and dual-parameter adaptive adjustment

Grating displacement sensors are vulnerable to various factors, including mechanical vibrations and temperature fluctuations. These influences can result in cumulative errors in displacement measurements, ultimately compromising the accuracy of the measurements. To address the challenge of time-varying accumulated errors in dynamic measurements using high-precision optical fringe displacement sensors, this paper proposes a dynamic fusion algorithm that integrates Error State Kalman Filtering (ESKF) with dual-parameter adaptive tuning, denoted as ADA-ESKF. This algorithm dynamically tracks and estimates the cumulative error in the measurement process, perceives the residual change trend in real time, and dynamically adjusts the size of the dual noise parameters, achieving adaptive filtering of dynamic noise. This article constructs a dynamic cumulative error compensation model based on error-state Kalman filtering and dual-parameter adaptive adjustment. A comprehensive simulation study, including scenarios with white Gaussian noise and impulsive disturbances, demonstrates that ADA-ESKF outperforms both the Maximum Correntropy Kalman Filter and graph-based optimization in terms of estimation accuracy and robustness to abrupt noise variations, while maintaining computational efficiency suitable for real-time applications. The experimental results show that in multiple sets of displacement measurement experiments with continuous measurement at 20 mm, this algorithm has good real-time predictability for cumulative errors. The corrected root mean square error was reduced on average from 1.362 to 0.432 μm, with an average decrease of 68.92%. The maximum absolute error was reduced on average from 2.438 to 0.690 μm, with an average decrease of 72.25%. Additional tests under varying velocities (0.5-3.0 mm/s) and extended ranges (up to 40 mm) confirm the algorithm's adaptability and long-term stability. The proposed ADA-ESKF thus provides an efficient, accurate, and robust solution for real-time cumulative error compensation in high-precision displacement sensors.