递推梯度校正估计

import numpy as np 
import matplotlib.pyplot as plt 


if __name__ == '__main__':
    L = 100 #序列长度
    Y = np.zeros(L)
    phi = np.zeros((L,4))
    u = np.random.randn(L,1)
    xi = np.sqrt(0) * np.random.randn(L,1)
    alpha = 1 #
    c = 0.1  # 修正因子

    
    y1 = y2 =0
    u4 = u3 = u2 =u1 =0
    theta = np.array([1.5,-0.7,1,0.5])
    P = 1e6 * np.eye(4)
    theta1 = np.zeros((L,4))
    theta1_1 = np.zeros(4)

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


        # RGC       
        K = (alpha*phi[i,:])/(c+np.dot(phi[i,:],phi[i,:]))        

        theta1[i,:] = theta1_1 + K*(Y[i]-np.dot(phi[i,:],theta1_1))


        # 数据更新
        theta1_1 = theta1[i,:]
        y2 = y1
        y1 = Y[i]

        u4 = u3
        u3 = u2
        u2 = u1
        u1 = u[i]

    
    plt.subplot(3,1,1)
    plt.title('输入-白噪声')
    plt.step(np.arange(L),u)

    plt.subplot(3,1,2)
    plt.title('输出-Y')
    plt.plot(np.arange(L),Y)

    plt.subplot(3,1,3)
    plt.title('系数Theta')   
    plt.plot(theta1)

    plt.subplots_adjust(hspace = 0.45)
    plt.show()