Quaternion and least mean kurtosis criterion-based multi-dimensional time series prediction method

Abstract

The invention discloses a quaternion and least mean kurtosis criterion-based multi-dimensional time series prediction method through combining an advantage of a quaternion in the aspect of multi-dimensional signal processing and a characteristic of a least mean kurtosis criterion in the aspect of non-Gaussian signal processing. The method is suitable for more common non-Gaussian system or signal processes in reality, has properties of satisfying rapid convergence and being low in steady-state error at the same time, is capable of solving the problems that robustness is not caused to non-Gaussian signals under a least mean square criterion and the multi-dimensional signal calculation is too complicated and the prediction error is too large under the least mean kurtosis criterion, and has relatively important research significance and extensive engineering application value.

Description

【Technical field】 [0001] The invention belongs to method research in the field of signal processing, and relates to a multi-dimensional time series prediction method based on quaternion and minimum average kurtosis criterion. 【Background technique】 [0002] With the continuous development and progress of the subject of signal processing, adaptive signal processing has become an important branch of the subject of signal and information processing, and adaptive filtering theory and technology are an important part of adaptive signal processing. The adaptive filter can follow the change of the external signal in real time to adjust the adaptive coefficient through adaptive learning without prior knowledge, and finally obtain the optimal filtering effect. Therefore, it is used in control, communication, radar, Areas such as earthquake monitoring and cognition are gaining more and more applications. Currently, there are four basic applications of adaptive filtering techniques, i...

AI Technical Summary

Problems solved by technology

However, the multidimensional time series forecasting method based on the minimum mean square error criterion is ideal only when the underlying system is linear and Gaussian, and most of the systems or information processes faced in practical applications are non-Gaussian. Therefore, When dealing with multi-dimensional non-Gaussian time series, the prediction effect of the QLMS method is not satisfactory, and it has the disadvantages of slow convergence speed and low steady-state accuracy.

Images