A new Gaussian approximate filter with colored non-stationary heavy-tailed measurement noise

A new Gaussian–Student's t mixing distribution‐based Kalman filter with unknown measurement random delay rate

“…According to (), the optimal solution of () satisfies 2,28,30,31 $$$$ \kern0.5em \log {q}_a\left({x}_t^e\right)={\mathrm{E}}_{{{\boldsymbol{\Xi}}_t}^{\left(-\theta \right)}}\left[\log p\left({\boldsymbol{\Xi}}_t,{y}_{1:t}^a\right)\right]+{c}_{\theta }, $$$$ where $$$ {{\boldsymbol{\Xi}}_t}^{\left(-\theta \right)} $$$ represents the set of all elements in $$$ {\boldsymbol{\Xi}}_t $$$ except for $$$ \theta $$$, and $$$ {c}_{\theta } $$$ denotes a constant related only to the variable $$$ \theta $$$.…”

A meticulous covariance adaptive Kalman filter for satellite attitude estimation

“…For example, numerous scholars in the literature have studied the fading memory filters [17,18], adaptive kinematics-aided Kalman filter [6], filters with both adaptivity and robustness [19,20], and adaptive gain complementary filter [21], respectively. Recently, the robust Kalman filters based on the state-space model constructed by student-t have been widely studied for the heavytailed noises problem [22,23]. Additionally, several widely used and improved adaptive filters include the Sage-Husa adaptive Kalman filters [24,25], and adaptive filters based on innovation or residual covariance matching [26][27][28][29]19] proposed an adaptive robust Kalman filter with both adaptive and robust performance, the algorithm recursively makes a choice among the standard, robust, and adaptive strategies, taking into account abnormal innovation sequences and incorporating observations from the next moment, realizing the improvement of the attitude estimation accuracy in multiple cases; the best invariant quadratic unbiased estimation is introduced to adaptively tune and estimate the local components of the system's covariance at each step, thereby further enhancing the accuracy of attitude determination [6]; for the small-area or full-area infrared interference faced by the system, literature [30] proposes an adaptive fault-tolerant extended Kalman filter (AFTEKF), which adjusts the values of the relevant parameters by counting the number of faulty points diagnosed by the fault diagnostic algorithm, which ultimately improving the adaptive capability to infrared disturbances; recently [31], introduced a strong tracking filter in the multiplicative MRPs-based unscented Kalman filter to enhance the robustness of the satellite attitude system to model uncertainties; literature [32] used short-term sequences of the residual to represent the measurement disturbances, and developed an hidden Markov model recognizer for identifying the measurement disturbances and adaptively adjust the noise covariance of the MEKF, this process aims to improve the stability and accuracy of the attitude estimation system.…”

Method for measuring non-stationary motion attitude based on MEMS-IMU array data fusion and adaptive filtering

“…Through simulation experiments, it has been proven that the proposed filter has better performance and estimation accuracy in dealing with the nonlinear filtering problem of NSHTMN [15,16]. Huang et al proposed a novel robust GSTM distribution Kalman filter, which can adapt to NSHTMN by using adaptive learning of mixed probabilities, thereby improving estimation accuracy.…”