EM算法在p范混合模型参数估计中的应用

针对多种分布形式混合的观测数据，建立了p范混合模型，考虑到模型中混合数属于不完全数据，引入期望最大化(expectation-maximum, EM)算法，对该混合模型的参数进行估计，详细推导了p范混合模型参数估计的迭代公式，并给出了相应的迭代步骤。采用混合高斯分布数据、拉普拉斯分布与高斯分布混合数据及实测GPS观测值残差数据，验证了公式的正确性和适应性。算例结果表明，与单一概率分布相比，p范混合模型能够准确反映数据分布的实际情况，同时利用EM算法估计的模型参数具有较高的精度。

Application of EM Algorithm in Parameter Estimation of p-Norm Mixture Model

  Objectives  Aiming at the mixed observation data of multiple distribution forms, a expectation-maximum (EM) combined p-norm distributed model(EM_p) is established.  Methods  Considering that the mixed number in the mixture model belongs to incomplete data, the EM algorithm is introduced to estimate the parameters of the mixture model and the p-model mixture model parameters are derived in detail. The estimated iteration formula and the corresponding iteration steps are given.The mixture Gaussian distribution data, Laplace distribution and Gaussian distribution mixture data, and the residual data of measured global positioning system(GPS) observations are used to verify the correctness and adaptability of the formula in this paper.  Results and Conclusions  The results of the calculation examples show that, compared with the single probability distribution, the p-norm mixture model can accurately reflect the actual situation of the data distribution, and the model parameters estimated by the EM algorithm have higher accuracy.