The application of multi-scale wavelet transform in elimination of outliers

The technology of outliers elimination is widely used in many fields, such as environmental monitoring and assessment, space remote sensing, image processing and so on. Kalman filtering algorithm, which is a common method of elimination of outliers, needs harsh conditions and is hard to achieve. After analyzing the Kalman filtering algorithm, according to the basic principles of wavelet transform, in this paper, it presents a new outliers elimination algorithm, which combines Kalman filtering algorithm with wavelet transform. Firstly, the signal is discomposed to different scales with wavelet transform. Secondly, it is filtered using Kalman filter algorithm in different scales. Finally, the filtering signal in different scales is reconstructed with wavelet reconstruction algorithm. Meantime, due to the complexity of Kalman filtering algorithm, in this paper, an easier filtering algorithm is presented. Theory analysis and simulation result prove, this two algorithms can get better elimination result and filtering accuracy than Kalman filtering algorithm.