tools.py 文件源码

def estimate_X_TLS(y,H):
    """ Estimator of x for the Linear Model using Total Least Square (TLS). As compared to the classical Least Squares Estimator, the TLS estimator is more suited when H is not exactly known or contained with noise [GOL80]_.


        .. [GOL80] Golub, Gene H., and Charles F. Van Loan. "An analysis of the total least squares problem." SIAM Journal on Numerical Analysis 17.6 (1980): 883-893.

        """
    N,L=H.shape
    H=np.matrix(H)

    Z=np.hstack([H,y])
    U,S,V=lg.svd(Z)
    V=np.matrix(V)
    V=V.H
    VHY=V[:L,L:];
    VYY=V[L:,L:];
    x= -VHY*lg.inv(VYY);
    return x