Auto‐calibration Kalman filters for non‐linear systems with direct feedthrough

Abstract The problem of state estimation for non‐linear systems with unknown inputs is discussed. The objective is to construct a non‐linear filter where the unknown input affects both the state equation and measurement equation. An auto‐calibration Kalman filter is proposed with three stages, where the first and second stages are the extension of the two‐stage Kalman filter in non‐linear system cases, and the third stage is the extended Kalman filter with correlated noise. Compared with the two‐stage extended Kalman filter, the presented algorithm conducts a more reasonable linearization of the measurement equation in the third stage. As a result, auto‐calibration is realized and more accurate and more stable state estimation can be obtained. Simulative and practical examples both demonstrate the validity and superiority of the presented auto‐calibration Kalman filter. Furthermore, positioning experiments illustrate that the auto‐calibration Kalman filter can obtain an accurate long‐term heading estimation in pedestrian navigation and is easy to apply in engineering applications