Observability Metrics for Single-Target Tracking With Bearings-Only Measurements

This work considers the observability problem in bearings-only tracking (BOT). Although the rank criterion has always been used for observability analysis, the evident drawback that it can only give a qualitative result prevents us from exploiting more information from the observability matrix. In reality, we want to know not only if the system is observable but also the degree of the observability. In order to quantitatively describe the system observability, we propose a series of metrics for BOT. Being derived based on the condition number, the novel metrics can reflect the observability degree as well as evaluate the tracking performance. Besides, the metrics can be extended to be used for sensor trajectory optimization and sensor configuration, which are crucial to enhancing the tracking performance.