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_sequencesplt.rcParams['font.sans-serif'] = ['Yahei consolas hybrid']
#plt.rcParams['axes.unicode_minus']=Falseif __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()