Adaptive Kalman Filter And Its Applications In Airborne Vector Gravimetry

This study focuses on the adaptive Kalman filter algorithm based on Autocovariance Least-Squares (ALS) noise covariance estimation and introdces its applications in airborne vector gravimetry. The main contents and achievements are:(1) The basic conceptions of Kalman filter algorithm is introduced systematically, including the observability, controllability and stability characteristics. From the point of parameter estimation, the formulas of Kalman filter under linear least variance are derived; aiming at the continunity of most physical models in real data processing, the continuous Kalman formula and its discretization strategies are given in the study.(2) The ALS noise covariance estimation methods for linear invariant and linear variant Kalman filter systems and the linear invariant ALS noise covariance estimation method for first kind of correlated noise are introduced.(3) The conventional white noise covariance estimation method is extended to cope with two kinds of correlated noises. The linear invariant ALS noise covariance estimation method for second kind of correlated noise and the linear variant ALS noise covariance estimation method for the two kinds of correlated noise are given respectively. The noise covariance estimation method is also extended to colored noise and the corresponding noise covariance estimation methods for colored state noise, colored observation noise and both of them are proposed. Numerical simulated results show that all the above-mentioned methods can estimate the unknown noise covariances with high accuracy.(4) The multi-rate Kalman filter is an effective method for data fusion of low sampling displacement and high sampling acceleration, but its effectiveness is strongly affected by the prior noise covariance parameters. A new adaptive multi-rate Kalman filter is proposed to estimate the unknown noise covariance parameters. The validity of the proposed method is demonstrated by a numerical example and an earthquake engineering test from the Large High-Performance Outdoor Shake Table.(5) The positive definite and stability of the estimated noise covariance should be guaranteed when adopting ALS. An improved ALS method is given to guarantee the stability of noise covariance estimates by imposing constraint conditions and adopting iterative calculation strategy. Results show that the propsed algorithm can improve the stability of the least square solution to some extent and guarantee the positive definiteness of noise covariance estimates.(6) Considering the noise covariance matrices are usually diagonal matrices, a nonlinear ALS method is proposed to ensure the positive definiteness of the estimated noise covariance matrices. In order to make sure the diagonal elements are positive, the square roots of the diagonal elements in the noise covariance matrix are determined by the homotopy algorithm. Simulation tests show that the nonlinear ALS method can effectively ensure the positive definiteness of the estimated diagonal noise covariance matrix.(7) Although the ALS with semidefinite programming can ensure the positive definiteness of the noise covariance estimates, it is limited significantly by the threshold parameters. Therefore, an ALS with regularized semidefinite programming is presented, in which the selected parameters are more reasonable. The method of variance component estimation (VCE) is applied to estimate the regularization parameters and iterative quasi-Newton method is used to calculate the threshold parameters. Simulation results show that this algorithm can guarantee the positive definiteness of noise covariance matrices and improve the accuracy of the positive semidefinite least square method.(8) An adaptive Kalman filter algorithm based on the constant acceleration model to determine the acceleration of carriers in airborne vector gravimetry data processing is proposed. And the correctness and validity of this algorithm are verified by numerical experiments.(9) The adaptive initial alignment methods based on the navigation frame is used to overcome the effect of unknown measurement noise covariance on the initial alignment of SINS. In order to eliminate the effects on initial alignment process caused by the prior noise covariance and initial attitude angle, an iterative strategy is adopted. This algorithm can simultaneously estimate the noise covariance and correcte the attitude angle. Numerical tests show that this method can effectively overcome the effects of unknown measurement noise covariance and initial attitude angle on the initial alignment process, and improve the the accuracy of initial alignment(10) The data processing flow of the airborne vector gravimetry based on the inertial coordinate system is introduced. An adaptive method for GNSS/SINS data fusion in inertial coordinate system is proposed, in which an iterative calculation strategy is adopted. This algorithm can simultaneously estimate the noise covariance and correcte the attitude angle. The simulation results show that this algorithm has good convergence and can effectively overcome the effects of prior information on GNSS/SINS data fusion and meanwhile improve the accuracy of data fusion.