一种应用于外场实验数据处理的非概率参数估计方法

A Non-Statistical Approach of Parameter Estimation for Field Data Processing

参数估计是数据处理的一个重要方面。概率参数估计方法需要已知数据样本的分布规律,但在外场实验中由于客观环境的复杂多变,得到的数据样本其分布规律往往是未知或有多种可能性存在。如果采用概率参数估计方法必须对样本分布模型进行假设,这样会引进新的误差使参数估计的结果可靠性降低。本文结合灰色理论和泛函的相关概念提出了一种非概率参数估计方法。该方法从样本空间的拓扑关系和样本点之间的距离关系考虑问题,定义了灰色距离测度、灰色关联熵等概念;利用灰色距离测度的性质和最大灰色关联熵准则,可以在数据样本分布未知的情况下给出参数估计结果;通过与概率参数估计方法的比较,得到两种参数估计在一定条件下是等价的。最后通过举例说明该方法具有实际意义,可以在实际的工程实践中应用。

Parameter estimation is one important part of data processing. Traditional statistical parameter estimation approach needs to know the distribution regularity of samples. But in filed test, the sample distribution regularity usually can＇t be known or has many likelihoods due to complex external environments. The traditional statistical approach will give an assumptive model about the sam- ple distribution for parameter estimation. The assumption usually takes new error to the parameter estimation value, and make the relia- bility of the parameter estimation approach lower. This paper proposes a new non-statistical parameter estimation approach based on grey theory and norm, from the view of the topology of the sample space and the distances between samples. The definitions of grey distance measure and grey relation entropy are given. The properties of grey distance measure are discussed. Through the properties of the grey distance measure and the maximum entropy rule, the parameter estimation results and the confidence degrees can be got by the new ap- proach, without knowing the sample distribution under certain conditions. Finally, the simulation results show that this approach is feasible.