An Ultra-Wideband Indoor Localization Algorithm with Improved Cubature Kalman Filtering Based on Sigmoid Function

Abstract

In this paper, an improved cubature Kalman filtering (CKF) is proposed using the Sigmoid function to address the problems of positioning accuracy degradation and large deviations in ultra-wideband (UWB) indoor positioning in non-line-of-sight environments. The improved CKF is based on the squared range difference (SRD) model of the time difference of arrival (TDOA) algorithm. The inaccurate impact of model estimation under non-Gaussian noise is reduced by updating the measurement noise matrix in real time. The covariance matrix is estimated using singular value decomposition (SVD) to solve the problem of degraded state estimation performance. The filtering effect of the improved CKF algorithm is evaluated by referring to the checkpoints in the dynamic trajectory. The experimental results show that the proposed algorithm effectively mitigates the impact of UWB ranging outliers in the occluded experimental environment, which makes the dynamic positioning trajectory smoother, better fitted, and more stable. The algorithm improves the positioning accuracy by up to 39.29% compared with the SRD model used alone.

Refined Aircraft Positioning Based on Stochastic Hybrid Estimation with Adaptive Square-Root Unscented Particle Filtering

“…The fundamental square root unscented Kalman filtering algorithm, from which the ASR-UPF is derived, is described as follows. The SR-UKF is initialized according to Equation (19).…”

“…Further, we obtain the filtering values for each mode using the ASR-UPF filter based on Equation (19):…”

“…In cooperation with state estimation algorithms, this system can carry out state estimation based on the stochastic hybrid dynamic model with coupled discrete and continuous states. The extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF) based on KF have limited improvement of estimation accuracy for nonlinear systems [17][18][19], while particle filter could effectively solve this problem using sequential Monte Carlo sampling with the appropriate number of particles [20,21]. However, the importance of sampling distribution commonly uses a particle filter, which is generally a prior distribution, instead of using the posterior probability distribution corrected by measurement data, which would cause issues of low efficiency and sensitivity to singular points and would not effectively utilize measurement data [22].…”