基于自协方差最小二乘的组合自适应抗差Kalman滤波方法研究

Kalman filter is a linear recursive minimum variance estimation method, which has been widely used in the field of dynamic measurement data processing. However, in the practical application, the accuracy and reliability of Kalman filter are difficult to be guaranteed due to the influence of dynamic model disturbance, gross error and the unknown noise statistics information, which greatly limits the applicability of Kalman filter method. In this paper, the Autocovariance Least Squares (ALS) algorithm, which has greatly performance in noise covariance estimation, is combined with the adaptive robust filter method to construct a new adaptive robust ALS method. The numerical algorithm of the ALS method is developed to ensure the positive definite and accurate of the noise estimates. The adaptive Kalman filter method based on the correlated noise theory is extended. The anticipated goal of this project will not only enrich and perfect the existing adaptive Kalman filter theory and method, but also provide theoretical support and application guarantee for dynamic data processing in navigation, geodesy and aerospace, and have important scientific significance and application value.

Kalman滤波技术在动态大地测量数据处理领域中有着广泛的应用。然而受限于系统模型异常、粗差观测以及噪声统计信息缺失等因素，Kalman滤波的精度和可靠性难以得到保证。自协方差最小二乘法（ALS）虽然具有较高的噪声协方差估计精度，但无法抵制动态模型异常和粗差观测的影响，而基于自适应因子的滤波方法虽然可靠性高，但精度次优。为了实现两类自适应算法的优势互补，本项目将ALS算法和基于自适应因子的滤波方法相结合，构造一种新的组合自适应抗差Kalman滤波算法；将基于白噪声理论的自适应算法拓展到相关噪声，提出相关噪声的组合自适应抗差Kalman滤波算法；并提出正则的抗差半正定最小二乘算法，保证噪声协方差估值的正定性和准确性。预期研究成果不仅能丰富和完善现有的自适应Kalman滤波理论和方法，还将为导航、大地测量及航天航空等领域中的动态数据处理提供理论支持和应用保证，具有重要的科学意义和应用价值。

Kalman滤波技术在动态大地测量数据处理领域中有着广泛的应用。然而受限于系统模型异常、粗差观测以及噪声统计信息缺失等因素，Kalman滤波的精度和可靠性难以得到保证。自协方差最小二乘法虽然具有较高的噪声协方差估计精度，但无法抵制动态模型异常和粗差观测的影响，而基于自适应因子的滤波方法虽然可靠性高，但精度次优。本项目以构造一种高精度、高可靠性的组合自适应抗差Kalman滤波方法为目标，围绕自适应抗差Kalman滤波及平滑方法和噪声协方差估计方法展开研究。重点研究了系统模型异常、粗差观测和未知噪声的隔离与处理方法，构造基于M估计和卡方检验的组合自适Kalman滤波方法；研究了数据后处理的滤波平滑方法，并提出了一种改进的自适应正反向Kalman滤波平滑算法；将基于白噪声理论的自适应滤波方法拓展到有色噪声领域，重点研究多步相关噪声的Kalman滤波算法；并将上述成果应用到导航定位和大地测量相关数据处理中。相关研究成果不仅能丰富和完善现有的自适应Kalman滤波理论和方法，也将为导航定位、大地测量及航天航空等领域中的动态数据处理提供理论支持和应用保证，具有重要的科学意义和应用价值。