Effect And Resolution Of Parameter Estimation For Linear Mixed Model EM Algorithm

In the field of signal processing,the division of mixed signals has important significance for audio recognition,signal denoising and spectrum detection,and parameter estimation is one of the key problems in mixed signals.The EM algorithm which is widely used in practice provides an extremely effective solution for parameter estimation in the case of missing data.In order to distinguish two similar signals,this dissertation proposes the concept of parameter resolution which provides a metric for measuring the ability of the algorithm.At the same time,it provides a new effective index for evaluating the accuracy of algorithm parameter estimation.This dissertation made the following contributions:1.Constructing the theory of parameter estimation for linear hybrid model EM algorithm.The most important part of the EM algorithm is to find the iterative formula of the maximum likelihood function expression and the implicit variable.According to the existing scientific research results,the construction and derivation of iterative formula of the three-component(multi-component)hybrid model lack strict probability expression and mathematical argumentation.Therefore,based on the parameter estimation of the two-component hybrid model EM algorithm under incomplete data,the three-component hybrid model is improved.This construction method and derivation process can be extended to any finite mixed model,which provides a good theoretical framework for the construction of linear hybrid model EM algorithm parameter estimation.2.Aiming at the problem that the termination condition of the algorithm affects the effect of its parameter estimation,the method of the infinite norm is proposed as the termination condition without loss of precision,which can achieve convergence faster than other norms.Based on the theory of parameter of linear mixed model EM algorithm,this dissertation further considers the impact analysis of time cost and error accuracy under different termination conditions,it even takes the same type and cross type distribution.Experiments show that compared with other termination conditions,the infinite norm has the advantage of fast calculation speed and strong generalization ability.3.For the finite-type linear combination model,there is no algorithm theoretical guidance about whether each cluster needs to be susdivided continuously during signal division,and it is difficult to quantify the termination condition of signal division.This dissertation combines the Fisher discriminant criterion to give a formal definition of the parameter resolution of the non-distance division method similar to the EM algorithm,and the termination condition of the quantized signal division.Numerical simulation shows that the accuracy of the parameter resolution is higher with the model parameters increases.The local resolution is consistent with the overall resolution.In addition,it is derived that the separate region corresponding to the EM algorithm parameter estimation satisfies a linear relationship with the parameter resolution,and the scale factor graphs with different confidence levels are obtained.The proposed resolution of the parameters provides a metric for distinguish whether the algorithm can separate the adjacent signals,and it also provides a new quantitative indicator for the measurement accuracy estimation of such algorithm.