The ARX Model Based On L_p(p<=1) Norm

Brain science is the research hotspots and frontier science in the 21 st century, which took attention by many countries, and become the critical project to seize the strategic commanding heights. EEG is generated by collecting cerebral cortex or scalp of spontaneous, rhythmic movement of electrophysiological signals, by using the electrode cap, and it is produced by a large number of cortical neurons postsynaptic potentials and is the external manifestations of the brain neural activity. EEG has a high time resolution, and you can record the brain information processing in milliseconds. So, EEG become one of the most commonly used means and method in the brain research. However, under normal circumstances, EEG will inevitably introduced outliers noise, for example EoG artifact, and those noise can seriously interfere the analysis and processing of EEG. When we use the ARX model of system identification to estimate EEG, the traditional method which based on the least-squares has a certain smoothness, but it will be doubling the energy of outliers noise, which can not eliminate the interference. Therefore, in order to solve this problem, this paper proposes a ARX model based on L_p(p≤1) norm. We use the L_p(p≤1) norm to constraint the objective function of the ARX model and solve the model parameters by BFGS iterative algorithm. Experimental results show that this method can effectively suppress the noise interference,thus demonstrating its great theoretical and practical significance. The work in the article is mainly as follows:Firstly, propose the ARX model based on L_p(p≤1) norm. For the outliers noise in the EEG, the framework based least squares can not suppress the influence of outliers noise on the signal, so that it make distortions and errors in forecasting and model estimates of the EEG signals, which disturb follow analysis and processing of the EEG signals. Theoretical studies have shown that the algorithm based on L_p(p≤1) norm has obvious advantages than least squares in suppressing outliers noise. The article will be applied to L_p(p≤1) norm on the objective function of ARX model, replacing the original objective function of ARX model based least squares. In the simulation experiment, we regard the parameter error of the ARX model and the prediction error as evalution index, and find the single-input single-output ARX model and multi-input single-output ARX model based on L_p(p≤1) norm have good results in suppressing outliers noise.Secondly, application resarch of Lp-ARX model. EEG has strong randomness and nonstationarity. When EEG suffer EoG artifact or due to electrode shedding can not collect the data, it will make EEG data severely damaged. In the first place, this paper apply Lp-ARX model to estimate EEG data, and recover off the EEG data that electrodes fall off. Second, because of intracranial pressure data acquisition difficult, we often carried out the data by measuring the craniotomy, causing unnecessary harm to patients. So, nondestructive way to get the intracranial pressure data is extremely important. With the current intracranial pressure and arterial pressure data, we use the ARX model to estimate in order to predict future intracranial pressure. The new method of development has a strong inhibitory effect for outliers noise and has a good robustness.