In identification of a finite impulse response (FIR) model using noise-corrupted input and output data, the least squares type of estimation schemes such as the ordinary least squares (LS), the corrected least squares (CLS) and the total least squares (TLS) method become often numerically unstable, when the true input signal to the system is strongly correlated. To overcome this ill-conditioned problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate of the FIR model. The asymptotic MSE can be evaluated by considering the third and fourth order cross moments of the input and output measurement noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using the only accessible input-output data without using any true unknown parameters. The effectiveness of the proposed data-based regularization algorithm is demonstrated and compared with the ordinary LS, CLS and TLS estimates through numerical examples.

A non-invasive method is proposed to estimate the location of intracranial vascular disease using several sensors placed on the forehead. The advantage of this method over earlier measurements with a single ocular sensor is the abilty to localize the region of abnormal vascular tissue. A weighted least mean square procedure is applied to estimating the time difference between the sensor outputs using the phase distribution in the cross-spectrum. It is possible to estimate time differences shorter than sampling period. Computer simulation and clinical experiments demonstrate that a distance difference of around 20 times shorter than the wavelength can be obtained.

A new gradient type adaptive algorithm is proposed in this paper. It is formulated based on the least squares criteria while the conventional gradient algorithms are based on the least mean square criteria. The proposed algorithm has two variable parameters and by changing them we can adjust the characteristic of the algorithm from the RLS to the LMS depending on the environment. This capability of adjustment achieves the possibility of providing better solutions. However, not only it provides better solutions than the conventional algorithms under some conditions but also it provides a very interesting theoretical view point. It provides a unified view point of the adaptive algorithms including the conventional ones, i.e., the LMS or the RLS, as limited cases and it enables us to analyze the bounds for those algorithms.