批处理最小二乘法 python

参考：系统辨识与自适应控制MATLAB仿真（修订版） 庞中华 崔红

仿真实例2.5

import numpy as np 
import matplotlib.pyplot as plt 
from mxulie import M_sequences

plt.rcParams['font.sans-serif'] = ['Yahei consolas hybrid']
#plt.rcParams['axes.unicode_minus']=False

if __name__ == '__main__':
	L = 100 #序列长度
	Y = np.zeros(L)
	phi = np.zeros((L,4))
	[M,IM]=M_sequences(L)
	xi = np.sqrt(0.01) * np.random.randn(L,1)
	
	y1 = y2 =0
	u4 = u3 = u2 =u1 =0
	theta = np.array([1.5,-0.7,1,0.5])

	for i in np.arange(L):
		phi[i,:] = ((y1 , y2 ,u3 ,u4))		
		Y[i] = np.dot(theta,phi[i,:]) + xi[i]
		#Y[i] = 1.5*y1 -0.7*y2 + u3 + 0.5*u4 + xi[i]


		y2 = y1
		y1 = Y[i]

		u4 = u3
		u3 = u2
		u2 = u1
		u1 = IM[i]
	
	
	theta1 = np.dot(np.dot(np.linalg.inv(np.dot(phi.T,phi)),phi.T),Y)
	print(theta1)


	plt.subplot(2,1,1)
	plt.title('输入-逆M序列')
	plt.step(np.arange(L),IM)

	plt.subplot(2,1,2)
	plt.title('输出-Y')
	plt.plot(np.arange(L),Y)

	plt.subplots_adjust(hspace = 0.35)
	plt.show()