Observability analysis of 2D geometric features using the condition number for SLAM applications

Observability analysis is a very powerful tool for discriminating whether a robot can estimate its own state. However, this method cannot investigate how much of the system is observable. This is a major problem from a state estimation perspective because there is too much noise in real environments. Therefore, although the system (or a mobile robot) is observable, it cannot estimate its own state. To address this problem, we propose an observability analysis method that uses the condition number. Mathematically, the condition number of matrix represents a degree of robustness to noise. We utilize this property of the condition number to investigate the degree of observability. In other words, the condition number of the observability matrix demonstrates the feasibility of state estimation and the robustness of its feasibility for estimation.