A Case Study for Outlier Detection Efficiency Based on M estimations of Different Weight Functions and Models

Abstract

The effects of the model and weight function on outlier detection are evaluated by the simulated optical and radar observations. The iterative reweighted M-estimation based on different iterative reweighted functions is used for the outlier detection test. Three typical models of the optical and radar tracking data are compared for their effect on the outlier test. The simulated results show that different weight functions have small difference on the outlier detection efficiency and a good modeling selection for the same dataset is an key factor for a best outlier detection procedure. Introduction To date many approaches have been deeply developed to identify the outliers more accurately. There are two different strategies to mitigate the presence of outliers[1][2]. The first is to identify outliers using outlier tests, and then reject the observation exceeding the critical value for the desired significance level based on the statistic test. If multiple outliers exist then the single outlier test is applied iteratively with the strategy of removing the largest observation first until all the outliers have been removed. The second method is to use robust methods that without removing any observations but down weight suspect observations. When multiple outliers exist, the first method often failed because of the separation. Separability refers to the ability to distinguish or separate outliers from the other normal observations. The poorly separated observations adversely affect the solution of the system by manifesting a high risk of incorrectly flagging a 'good' observation as an outlier or vice versa. In the methods of the second kind, the M-estimation, which is implemented by the iterative reweighted least square, is popular for its simplicity. Different weight functions have been defined for the M-estimation method; if this is the case then which proper weight function should be used for the outlier detection of the given problem? Ideally, the method chosen should be capable of handling multiple outliers. The method should also be resilient to the effects of incorrect exclusion where only some of the outliers are identified and wrong exclusion where a correct observation is identified. If neither incorrect exclusion nor wrong exclusion occurs then it is a correct exclusion as all of the outliers and only the outliers have been excluded. As a result of this, it is the intention of the study to compare the abilities of the outlier test to correctly exclude outliers in three typical models of the optical and radar measurements. The comparison is based on miss rate and false alarm rate. The model effect to outlier detection is also considered in the comparison. Methodology Three typical models are considered in the research. All of the models use the same set or subset of the dataset. Different models are used to evaluate for the model effect in the outlier detection. Single Epoch Model. The first model is called single epoch model which uses multiple synchronized observations from different measure devices. The system measurement equation is