ABSTRACT
This chapter deals with linear least-squares error approximation. Readers will finally see that this document warns specifically about suboptimal solutions regarding the least-squares problem. If the suboptimal solutions are adopted, applications of x in (1), in any field, would also be suboptimal when specific noise is presented in the system. For example, in multi-sensor fusion and integration fields, geometrical calibrations between sensors’ position and orientation are often required. Many geometrical calibrations rely on linear least-squares solvers. Thus, if any solver yields a suboptimal result (x), even the geometrical calibration can be complete, it would be suboptimal. Further uses of the sensor set would be affected by some certain sensory noise. In this paper, we use an example of the camera and the IMU calibration. Specifically, we will show that when image noise occurs, one must be very careful which his/her choice of the least-square solvers. The goals of this paper are not limited only to finding the best solver for the camera+IMU set of sensors; however, the finding would be beneficial to other types of problems as well.
