PARAMETER ESTIMATION FOR COMPLICATED NOISE ENVIRONMENT
DOI:
https://doi.org/10.34185/1562-9945-6-125-2019-02Keywords:
generalized maximum likelihood, cost function, robust estimationAbstract
For a complicated noise environment the use of M-estimator faces a problem of choosing a cost function yielding the best solution. To solve this problem it is proposed to use a superset of cost functions. The superset capabilities provide constructing a parameter estimation method for complicated noise environment. It consists in tuning the generalized maximum likelihood estimation to the current noise environment by setting values of three free superset parameters related to the scale, the tail heaviness and the form of noise distribution, as well as to the anomaly values that presence in data. In general case, this method requires to solve the optimization problem with a non-unimodal objective function, and it can be mostly implemented by using the zero-order optimization methods. However, if the noise environment has known statistics, the proposed method leads to the optimal estimation. If the noise environment is complicated or does not have a complete statistics, the proposed method leads to the more effective estimates comparing to those of mean, median, myriad and meridian estimators. Numerical simulations confirmed the method performance.
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