Improved adaptive Kalman filtering algorithm for vehicular positioning

Robust adaptive cubature Kalman filter for tracking manoeuvring target by wireless sensor network under noisy environment

“…Because the subtraction operation for the matrix will make the measurement noise covariance lose the positive definiteness and process noise covariance lose the non-negative definiteness, this unbiased NSE is not robust. To ensure that the NSE is robust, a fault-tolerant NSE composed of the unbiased and biased NSEs is established [23].…”

“…Because the subtraction operation for the matrix will make the measurement noise covariance lose the positive definiteness and process noise covariance lose the non‐negative definiteness, this unbiased NSE is not robust. To ensure that the NSE is robust, a fault‐tolerant NSE composed of the unbiased and biased NSEs is established [23]. $$${\mathbf{R}}_{k+1}=\left\{\begin{array}{l}{\mathbf{R}}_{k+1}\,\text{if}\,{\mathbf{R}}_{k+1}\,\text{is}\,\text{positive}\,\text{definite}\\ \begin{array}{l}\left(1-{d}_{k}\right){\mathbf{R}}_{k}+{d}_{k}\left[{\varepsilon }_{k}{\varepsilon }_{k}^{T}\right]\\ \text{otherwise}\hfill \end{array}\end{array}\right.,$$$ $$${\mathbf{Q}}_{k+1}=\left\{\begin{array}{l}{\mathbf{Q}}_{k+1}\,\mathrm{i...$$…”

“…The different types of AKFs must comprise noise statistic estimators (NSE) with the corresponding accuracy of the Taylor series expansions, that is, the adaptive EKF (AEKF) requires a first-order NSE, the adaptive UKF (AUKF) requires a secondorder NSE, and the adaptive CKF (ACKF) requires a thirdorder NSE [19][20][21]. At present, the NSEs for an AKF are mainly divided into two types: unbiased and biased [22,23]. Generally, an unbiased NSE can only sense one of process noise and measurement noise, and cannot perceive two types of noise simultaneously.…”