多传感器测量中的方差估计

On the Estimation of Variances for Multi-Sensor Measurement

在多传感器加权融合算法中 ,各传感器的权值仅由传感器的测量方差决定。假设各传感器噪声为平稳过程且相互独立 ,本文提出了待测状态未知且时变情况下 ,多传感器测量方差的估计算法 ,并讨论了估计方差的统计特性 ,证明了估计的无偏性。针对工程中环境噪声的变化 ,进一步提出了加窗方差估计方法 ,并给出了窗口宽度和估计精度的关系 ,使算法能有效地跟踪环境噪声的变化。该算法无需设置依赖于环境的初始值 ,并给出了递推公式 ,使其可用于对多传感器测量方差的实时自适应估计。

In weighted fusion algorithm for multi sensor, the weights are only determined by sensor variances. Assuming that the noises are stationary and independent each other and considering that the state is unknown and time variant, an algorithm of variance estimation for multi sensors is proposed and the unbiased estimation by discussing the statistical property of estimated variance is proved. In order to suit to the change of the environmental noise, a windowing variance estimation method is presented which can follow the change of the environmental noise effectively, and the relationship between the sample size and the precision of estimation is also proposed. The algorithm is independent of initial values and can be described as a recurrence formula, which makes the algorithm be capable of being used in real time adaptive estimation. Numerical examples are given to show the usefulness of the approach.