Preconditioned Rayleigh Quotient and Modified Conjugate Gradients for Total Least Squares Filter in Robot Navigation

Noisy sensor data measured in a sequence of images must be filtered to obtain the best estimate of the robot position in the robot navigation. The discrete Kalman filter, which usually is used for prediction and detection of signal or image in communication and image 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. We have proposed the use of a Total Least Squares Filter which is solved by Rayleigh quotient and modified conjugate gradients method efficiently. For large and sparse data matrices, the iteration can be extraordinarily accelerated with the aid of a preconditioning matrix. Here we apply the Incomplete Modified Gram-Schmidt (IMGS) preconditioner, a class of incomplete QR preconditioners to our filter because its existence can be guaranteed theoretically. This filter is very promising for very large data information since the camera i..