Total least squares filter for robot localization

In the robot navigation problem, noisy sensor data must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter has become a commonly used method to reduce the effect of uncertainty from the sensor data. However, due to the special domain of robot navigation, the Kalman approach is very limited. The use of the total least squares filter has been proposed (Boley and Sutherland 1993, Yang and Lin 1997) which is capable of converging with many fewer readings and achieving greater accuracy than the classical Kalman filter. Here a Krylov subspace method which uses the Lanczos bidiagonalization process is proposed where the singular values of the corresponding bidiagonal matrix can be solved by the combination of split-merge and bisection algorithms. This approach is more computationally attractive to solve the total least squares problems. This filter is very promising for very large data information and from our experiments we can obtain more precise accuracy