基于卡尔曼滤波的信息融合算法优化研究

通过比较采用联邦卡尔曼滤波的状态向量融合和量测信息融合,得出量测信息融合优于状态向量融合,因为只有当卡尔曼滤波一致时状态向量融合才有效.采用基于最小均方差估计的观测值加权融合法融合了多传感器数据,保持了观测向量的维数.这种方法具有高效性.为了提高该算法的速度和精度,对系统的量测空间进行了等价变换,而等价系统的状态空间却没有改变.给出了等价变换前后的系统误差方差阵和状态估计均一致性的证明.把矩阵分析中的L-D分解算法运用到该算法中以避免计算矩阵的逆,从而改善了算法的稳定性和精度.举例验证了所设计算法的这些优点,给出了采用联邦卡尔曼滤波和所优化滤波算法的状态估计和误差的仿真结果,并依次进行了分析.经过这种优化,算法的精度和速度得到很大提高,已经应用到实际工程中.

Optimizing algorithm of data fusion based on Kalman filter

By comparing the state-vector fusion using Federal Kalman filter with the measurement fusion, it was concluded that the measurement fusion was preferable to state-vector fusion since the state-vector fusion is only effective when the Kalman filters are consistent. The fused measurement information by weighted observation was proved high efficiency, which combines the multi-sensor data based on minimum-mean-square-error estimates and keeps the observation vector dimension unchanged. In order to improve the speed and precision of this algorithm, an equivalent transformation was taken for the system's measurement-space at the same state space. The system's error-covariance matrix and the state estimation before and after transformation were proved conformity. The L-D factorization was also applied into Kalman filter to avoid computing the inverse of matrix, so its stability and precision is improved. One example was given to prove these. Also presented are simulation results on state estimation and error using Federal Kalman filter and the proposed method, followed by the analysis of each method. The algorithm has been already used in project due to its improvement in precision and speed.