# A Robust Extended Kalman Filter Algorithm Based on a Sliding Window Fractional-Order Grey Prediction Model and Its Application in MINS/GNSS

## TL;DR

This paper introduces a new robust filtering algorithm to improve navigation accuracy when GPS signals are slightly faulty.

## Contribution

A novel robust extended Kalman filter algorithm using a sliding window fractional-order grey prediction model is proposed.

## Key findings

- The proposed algorithm improves velocity and position accuracy by over 50% and 80% during GPS faults.
- Simulation and vehicle experiments confirm the algorithm's effectiveness in handling small amplitude faults.

## Abstract

To address the issue of reduced accuracy or even divergence in micro-electro-mechanical inertial navigation systems’/global navigation satellite systems’ (MINSs’/GNSSs’) integrated navigation systems caused by small amplitude fault in GNSS measurement information, this paper proposes a robust extended Kalman filter algorithm based on a sliding window fractional-order grey prediction model (SWFGM(1,1)-REKF). When GNSS signals are disrupted, this algorithm first detects system faults through a weighted index sequential probability ratio test (SPRT) detection. Then, it uses GNSS measurements predicted by a sliding window fractional-order grey prediction model (FGM(1,1)) to replace the faulty GNSS data and integrates them with MINSs. Finally, it combines robust estimation to construct a robust extended Kalman filter to correct the integrated information. Simulation and vehicle experiment results show the advancement of SWFGM(1,1)-REKF. When GNSS measurements experience small amplitude abrupt faults, compared with traditional robust extended Kalman filter algorithm based on a chi-square test, the proposed algorithm improves filtering accuracy of velocity and position. In the vehicle small amplitude mutation fault experiment, the velocity and position accuracy are increased by more than 50% and 80% respectively.