不等精度数据融合的最优权值与参数估计方法

The Method of Optimal Weight and Parameter Estimation of Unequal-precision Data Fusion

摘要:

对测量数据进行融合处理是提高数据处理精度的一个十分有效的方法。本文使用引入加权因子的方法，对不等精度测量数据融合处理的最优加权与参数估计的问题进行了研究。对于线性回归模型，从理论上证明了，最优融合权值由数据的精度唯一确定，这与经典的Gauss-Markov定理是一致的；对于非线性回归模型，在理论上获得了最优融合权值的计算方法，给出了实际数据融合处理的最优权值与参数估计算法，并且证明了非线性模型的不等精度数据融合的最优权值，不但与数据本身精度相关联，而且与模型的结构、模型的导数相关联，则在此时经典Gauss-Markov定理不再成立。通过算例进行对比验证，证明了所提方法的有效性。

Abstract:

Abstract: Data fusion is one effective method to improve the precision of data processing. The weight and parameter estimation of unequal-precision data fusion was studied. For the linear model, the optimal weight is only determined by the precisions of measured data, which is consistent with the classic Gauss - Markov theorem. For nonlinear model, the optimal weight and algorithm of the multi-structure unequal-precision nonlinear regression model are established according to the curvature representation of the estimation mean square error. Numerical simulation results show that the weight of the nonlinear model has great influence on the precision of parameter estimation. The optimal weight is related to both the statistical feature of data and the model structures, such as the model curvature, sampling number, etc. In this case, the weight (only related to the precision of measured data) obtained based on the Gauss-Markov theorem for the linear model is no longer optimal. The proposed method was verified by examples, and its effectiveness was proved.