Robust Kalman Filter with Continuous Outlier Insensitivity

This paper introduces a robust Kalman filter implementation that demonstrates insensitivity to continuous outliers. The filter's performance was validated through simulations documented in a Tsinghua University journal article, showing its effectiveness in eliminating consecutive outliers while maintaining estimation accuracy. The implementation typically involves modifying the measurement update step using robust statistical approaches like Huber functions or adaptive tuning of innovation covariance matrices. The core algorithm maintains the standard prediction-correction structure while incorporating outlier detection mechanisms that weigh measurements based on their statistical likelihood. We provide detailed explanations of the robust Kalman filter's underlying principles and practical application scenarios, offering valuable references for researchers in related fields. The implementation often features adaptive thresholding mechanisms that dynamically adjust to outlier patterns, using innovation sequences to detect abnormalities. Key functions may include covariance inflation techniques when outliers are detected, or switching between multiple models for different data quality conditions. Finally, we discuss the filter's limitations regarding computational complexity and parameter sensitivity, along with future research directions focusing on real-time adaptation and machine learning enhancements. Potential improvements could involve automated tuning of robustness parameters using optimization algorithms or hybrid approaches combining traditional Kalman filtering with modern anomaly detection techniques.