Parallel Lanczos bidiagonalization for total least squares filter in robot navigation

In the robot navigation problem, noisy sensor data must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter, which usually is used for prediction and detection of signals in communication and control problems 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 total least squares filter has been proposed (Boley and Sutherland, 1993) which is capable of converging with many fewer readings and achieving greater accuracy than the classical Kalman filter. The main disadvantage of those approaches is that they can not deal with the case where the noise subspace is of dimension higher than one. Here a parallel Krylov subspace method on parallel distributed memory computers which uses the Lanczos bidiagonalization process with updating techniques is proposed which is more computationally attractive to solve the total least squares problems. The parallel algorithm is derived such that all inner products of a single iteration step are independent. Therefore, the cost of global communication which represents the bottleneck of the parallel performance on parallel distributed memory computers can be significantly reduced. This filter is very promising for very large data information and from our very preliminary experiments we can obtain more precise accuracy and better speedup.