Yes, the insensitivity of utility to parameter estimates could be further explored and quantified to establish more general guidelines for the applicability of the proposed efficient greedy algorithm. This exploration could involve several approaches:
Sensitivity Analysis: Conducting a comprehensive sensitivity analysis across a range of parameter estimates and configurations can help quantify how variations in parameters affect the utility measure. By systematically varying parameters such as position, orientation, and sensor noise levels, researchers can identify thresholds beyond which the utility remains stable.
Statistical Modeling: Developing statistical models that describe the relationship between parameter estimates and utility could provide insights into the conditions under which the utility is insensitive. This could involve regression analysis or machine learning techniques to predict utility based on parameter variations.
Simulation Studies: Extensive simulation studies can be designed to test the algorithm under various scenarios, including different sensor configurations, noise levels, and operational conditions. By analyzing the calibration performance and runtime across these scenarios, researchers can derive empirical guidelines for when the efficient greedy algorithm is most effective.
Theoretical Framework: Establishing a theoretical framework that defines the conditions for utility insensitivity could provide a solid foundation for understanding the algorithm's applicability. This framework could include mathematical proofs or derivations that demonstrate the robustness of utility under specific assumptions about the system dynamics and measurement noise.
Real-World Validation: Finally, validating the findings through real-world experiments can help confirm the theoretical and empirical results. By applying the algorithm in diverse operational environments, researchers can gather data on its performance and refine the guidelines for its use.
By pursuing these avenues, the research community can develop a clearer understanding of the conditions that favor the use of the efficient greedy algorithm, ultimately enhancing its applicability in various calibration scenarios.