Considering that the external hostile environment will lead to rapid attenuation of sensor signals, which will make the noise parameters we set different from the actual noise parameters. In this letter, a novel online adaptive Kalman filter (AKF) is investigated with the main focus on inaccurate nonzero mean Gaussian white noise inherent in the filtering model. In the proposed AKF, we employed the expectation maximization algorithm to construct the noise parameter iteration expressions and obtain an approximate solution of the noise parameter. Finally, the derived AKF can effectively estimate the one-step prediction mean vector, the one-step prediction error covariance matrix, and the measurement noise covariance matrix. A classical target tracking simulation results show the effectiveness and stability of the derived AKF.

The strap‐down inertial navigation system (SINS) is a commonly used sensor for autonomous underground navigation, which can be used for shearer positioning under a coal mine. During the process of initial alignment, inaccurate or time‐varying noise covariance matrices will significantly degrade the accuracy of the initial alignment of the shearer. To overcome the performance degradation of the existing initial alignment algorithm under complex underground environment, a novel adaptive filtering algorithm is proposed by the integration of the strong tracking Kalman filter and the sequential filter for the initial alignment of the shearer with complex underground environment. Compared with the traditional multiple fading factor strong tracking Kalman filter (MSTKF) method, the proposed MSTSKF algorithm integrates the advantage of strong tracking Kalman filter and sequential filter, and multiple fading factor and forgetting factor for east and north velocity measurement are designed in the algorithm, respectively, which can effectively weaken the coupling relationship between the different states and increase strong robustness against process uncertainties. The simulation and experiment results show that the proposed MSTSKF method has better initial alignment accuracy and robustness than existing strong tracking Kalman filter algorithm.

We consider that existing nonlinear state estimators cannot always yield a satisfactory performance when the distribution of the measurement noise deviates from the assumed Gaussian distribution. This paper investigates the non-linear robust fixed-interval smoothing problem where the measurement vectors are partially disturbed by outliers. The proposed smoother employs a binary indicator variable modelled with a beta-Bernoulli distribution to determine whether the measurement vector is an outlier. Moreover, to address the inaccurate process noise covariance matrix, an inverse Wishart distribution was chosen as the conjugate prior of the process noise covariance matrix. Then, the variational Bayesian inference method was applied to estimate the state trajectory, inaccurate process noise covariance matrix, and a set of binary indicator variables. Traditional target tracking simulation results indicate the effectiveness and stability of the derived smoother, and the proposed smoother has demonstrated a marked improvement in estimation accuracy and robustness