A robust total Kalman filter algorithm with numerical evaluation

In this study, the observation model of Kalman Filter (KF) is extended to an errors-in-variables (EIV) model because the observations may exist in the design matrix of the observation model. Then, a robust total least squares method (RTLS) is introduced into the KF, and a robust total Kalman filter (RTKF) algorithm is derived. The RTKF is a simple, flexible and effective algorithm. It is simple because its computational formulae are similar to the computational formulae of a standard KF; it is flexible because it can be used in a wide range of applications; it is effective because the influence of outliers on estimated results is weakened. Finally, the simulated example of the indoor location and the empirical example of pseudorange differential positioning are used to demonstrate the performance of the RTKF algorithm. The results prove the validity, robustness, and reliability of the RTKF in dealing with the outliers that exist in both observation vector and design matrix of the EIV model. Furthermore, the results of the empirical example show that the RTKF improves the precision of a pseudorange differential positioning compared with KF and robust Kalman filter (RKF) algorithms regardless the observation model has outliers or not in this empirical example.