Which information metric is the best, CRLB, FIM or EMGR for optimal mobile sensing of a diffusing source?

This study first explores the mathematical relationships between three information metrics: the CramerRao Lower Bound (CRLB), the Fisher Information Matrix (FIM) and the empirical observability gramians (EMGR). Then we applied these three metrics respectively in localizing an emission or a diffusing source task by using a mobile sensor. We focus on maximizing the efficiency of the Maximum Likelihood Estimator (MLE) under the constraints imposed by information metrics, aiming to achieve minimal variance in our estimates. The sensor motion is planned to optimize the localization of emission source using two proposed methods: FIM and EMGR, and compared with CRLB. The MLE is dependent on the sensor measurement model, which further depends on the concentration, bias and sensor noise. Furthermore, the concentration of diffusing source at any point in space is obtained from the solution of the diffusion model. To accurately locate the emission source, the mobile sensor’s path is determined by both proposed methods, which leverage estimates from Maximum Likelihood Estimation (MLE). These methods ultimately aim to minimize the time required to reduce the location error to a specified threshold level. We visualize and compare the results between these three methods.