A Robust Extended Kalman Filter Applied to Ultrawideband Positioning

Abstract

Ultrawideband (UWB) is well-suited for indoor positioning due to its high resolution and good penetration through objects. The observation model of UWB positioning is nonlinear. As one of nonlinear filter algorithms, extended Kalman filter (EKF) is widely used to estimate the position. In practical applications, the dynamic estimation is subject to the outliers caused by gross errors. However, the EKF cannot resist the effect of gross errors. The innovation will become abnormally large and the performance and the reliability of the filter algorithm are inevitably influenced. In this study, a robust EKF (REKF) method accompanied by hypothesis test and robust estimation is proposed. To judge the validity of model, the global test based on Mahalanobis distance is implemented to assess whether the test statistical term exceeds the threshold for outlier detection. To reduce and eliminate the effects of the individual outlier, the robust estimation using scheme III of the Institute of Geodesy and Geophysics of China (IGGIII) based on local test of the normalized residual is performed. Meanwhile, three kinds of stochastic models for outliers are expressed by modeling the contaminated distributions. Furthermore, the simulation and measurement experiments are performed to verify the effectiveness and feasibility of the proposed REKF for resisting the outliers. Simulation experiment results are given to demonstrate that the outliers following all the three kinds of contaminated distributions can be detected. The proposed REKF can effectively control the influences of the outliers being treated as systematic errors and large variance random errors. When the outliers come from the thick-tailed distribution, the robust estimation does not play a role, and the REKF are equivalent to the EKF method. The measured experiment results show that the outliers will be generated in the nonline-of-sight environment whose impact is abnormally serious. The robust estimation can provide relatively reliable optimized residuals and control the influences of the outliers caused by gross errors. We can believe that the proposed REKF is effective to resist the effects of outliers and improves the positioning accuracy compared with least-squares (LS) and EKF method. Moreover, the adaptive filter and ranging error model should be considered to compensate the state model errors and ranging systematic errors respectively. Then, the measurement outliers will be detected more correctly, and the robust estimation will be used effectively.

Robust Simultaneous Localization and Mapping Using Range and Bearing Estimation of Radio Ultra High Frequency Identification Tags

“…The range and bearing estimation through MHEKF is affected by outliers that do not fulfill the assumed stochastic model of EFK, so this can be a potential problem for parameters estimation as also mentioned in [25]. In order to resist the effects of the outliers, a resilient EFK has been designed.…”

“…where j is the j th element in the state vector and a 0 , a 1 are the robust constants of the Kalman gain, usually determined based on the objective requirements. In (27) the factor (a 1 −w i )/(a 1 −a 0 ) is raised to third power, which differs from the implementation of the IGGIII scheme presented in [25] where the same factor is raised to the second power. The reason for this choice is that we want to further decrease the robust Kalman gain factor when the normalized measurement residual is in the range (a 0 , a 1 ].…”

“…Moreover, the identification (ID) of the RFID tags is known and this provides a straightforward hardware solution to the data association problem, which may afflict other kinds of sensors. Finally, the Manuscript received 25 Fabrizio Romanelli and Francesco Martinelli are with the Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, 00133 Rome, Italy (e-mail: fabrizio.romanelli@uniroma2.it; francesco.martinelli@uniroma2.it).…”

A Closed-Loop Output Error Approach for Physics-Informed Trajectory Inference Using Online Data

“…Kalman filter [5], [6] and its variants is one of the most important algorithms, and widely used in industry, for trajectory and state estimation based on Gaussian distribution assumption [7], [8] at the prior model and sensor noise. The algorithm merges two sources of information: prior knowledge of the dynamics of the system and the posterior estimation such that the mean between these two state estimation almost matches with the exact mean of the posterior distribution.…”

A Novel Ultra-Wideband Double Difference Indoor Positioning Method with Additional Baseline Constraint

“…For example, Cui et al [32] proposed a LOS/NLOS identification method based on a Morlet wave transform and convolutional neural networks. As for the processing of UWB error (including NLOS), a robust and adaptive Kalman filter was often utilized [33][34][35]. In addition, Xia et al [36] applied a particle swarm optimization (PSO) algorithm for UWB positioning.…”