Yue Yang

Yue Yang, Ryan Martin

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes approach has recently been proposed, featuring thin-tailed conjugate priors with data-driven centers. While conjugate priors ease some of the computational burden, Markov chain Monte Carlo methods are still needed, which can be expensive when dimension is high. In this paper, we develop a variational approximation to the empirical Bayes posterior that is fast to compute and retains the optimal concentration rate properties of the original. In simulations, our method is shown to have superior performance compared to existing variational approximations in the literature across a wide range of high-dimensional settings.

Yue Yang

The accurate Attitude Heading Reference System(AHRS) is an important apart of the UAV reliable flight system. Aiming at the application scenarios of near ground navigation of small-UAV, this paper establishes a loose couple error model of the gyroscope/accelerometer/magnetometer, and presents an improved FastEuler Double-Layer Kalman Filter algorithm. Using low-cost devices which include MEMS Inertial Measurement Units(IMU) and magnetometers, this paper constructs the AHRS hardware and software systems of UAV, and designs the offline and real-time verification platforms. Moreover, the attitude changes of UAV is analyzed by the simulation and flight test, respectively. In addition, an adaptive factor is used to adjust the measurement noise covariance in order to eliminate the harmful effects of linear acceleration in the accelerometer, which is solved the roll and ptich angle. The experimental comparison with the Complementary Filter shows that the proposed algorithm can provide accurate attitude information when UAV is flying, which improves the accuracy and reliability of attitude solution, and removes the influence the gyro bias for the attitude estimation.

Yue Yang

In this paper, we present a Singular Value Decomposition Cubature Kalman Filter(SVDCKF) fusion algorithm based on the improved nonlinear FastEuler Attitude and Heading Reference and System(AHRS) estimation model for small-UAV attitude. The contributions of this work are the derivation of the low-cost IMU/MAG integrated AHRS model combined with the quaternion attitude determination, and use the FastEuler to correct the gyroscope attitude update, which can increase the real-time solution. In addition, the SVDCKF algorithm is fused the various raw sensors data in order to improve the filter accuracy compared with the CKF. The simulation and experiment results demonstrate the proposed algorithm has the more excellent attitude solution accuracy compared with the CKF in the low and high dynamic flight conditions.

Yue Yang

Aimed at solving the problem of Attitude and Heading Reference System(AHRS) in the complex and dynamic conditions for small-UAV, An intelligent Singular Value Decomposition Cubature Kalman Filter(SVDCKF) combined with the Variable Adaptive Methods(VAM) is proposed in this paper. Considering the nonlinearity of quaternion AHRS model and non-positive definite of the state covariance matrix, the SVDCKF algorithm is presented with both the SVD and CKF in order to better obtain the filter accuracy and reliability. Additionally, there are the different changes of the values in the accelerometer measurement resulting from the complex flying conditions. Thus, the VAM is designed to deal with three-axis values of the acceleration and tune intelligently the measurement noise matrix Ra. Moreover, the heading measurement from the three-axis values of the magnetometer is calculated according to the whether to use the three-axis values of the acceleration in the special situations. The simulation and experiment results demonstrate that the proposed filter algorithm has the more excellent attitude solution accuracy and robustness than both the Complementary Filter(CF) and the Error State Kalman Filter(ESKF).

Yue Yang, Ryan Martin, Howard Bondell

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte Carlo, but these can be expensive when the data set is large and/or the model is complex, so more efficient variational approximations have recently received considerable attention. The traditional variational methods, that seek to minimize the Kullback--Leibler divergence between the posterior and a relatively simple parametric family, provide accurate and efficient estimation of the posterior mean, but often does not capture other moments, and have limitations in terms of the models to which they can be applied. Here we propose the construction of variational approximations based on minimizing the Fisher divergence, and develop an efficient computational algorithm that can be applied to a wide range of models without conjugacy or potentially unrealistic mean-field assumptions. We demonstrate the superior performance of the proposed method for the benchmark case of logistic regression.