基于有色噪声的改进卡尔曼滤波方法

Improved Kalman filtering method for MIMU with colored noises

为了解决实际工程中微机械惯性测量单元加速度计数据存在有色噪声导致计算的姿态角波动异常的问题,提出一种基于有色噪声的改进卡尔曼滤波方法。通过对有色噪声的特点进行分析,建立了针对有色噪声的状态预测协方差公式、卡尔曼滤波增益公式、系统状态与动态有色噪声的协方差公式、测量值与观测有色噪声的协方差公式,推导出处理有色噪声的卡尔曼滤波公式。仿真试验表明,改进的卡尔曼滤波方法能有效解决有色噪声导致的姿态角波动异常问题,证明了基于白噪声的卡尔曼滤波是基于有色噪声卡尔曼滤波的特例。

In practical engineering system, there usually exist colored noises in the accelerometer data of Micro-Electro-Mechanical Inertial Measurement Unit（MIMU）, which may induce the problem of incorrect attitude angle when processed by traditional Kalman filtering. To solve this problem, an improved Kalman filtering is proposed. Based on the characteristics of colored noises and its influences on the navigation alignment results, the Kalman filtering equations for processing the colored noises are derived, including： 1） the covariance equation of state prediction; 2） the gain equation, the covariance equation between the status of system and the colored noises of system; and 3） the covariance equation between the value of measurement and the colored noises of measurement. Simulations results show that the improved method can effectively solve the problem of incorrect attitude angle, and the Kalman filtering based on white noises is only the special case of the Kalman filtering based on colored noises.