Optimal Heterogeneous Mobile Sensing for Parameter Estimation of Distributed Parameter Systems

Abstract

This chapter shows how results from using some well-known methods of optimum experimental design for linear regression models can be applied to the setting of the mobile sensor trajectory design problem for optimal parameter estimation of DPSs in case we wish to simultaneously optimize the number of sensors and their trajectories and to optimally allocate the experimental effort. The latter is understood here as allowing for different measurement accuracies of individual sensors, which are quantified by weights steering the corresponding measurement variances. This leads to a much more general setting that most frequently produces an uneven allocation of experimental effort between different sensors. This remains in contrast to the existing approaches. The corresponding solutions proposed in this chapter can obviously be implemented on a sensor network with heterogeneous mobile nodes. This chapter demonstrates that these solutions can be determined using convex optimization tools commonly employed in optimum experimental design and show how to apply numerical tools of optimal control to determine the optimal solutions. We also introduce the design of moving sensor optimal trajectories, which does not rely on initial estimates of the parameters but instead is based on knowledge of upper and lower bounds of the parameter values. In most research, the issue of initial estimates has been widely disregarded. Here, instead of using stochastic approximation algorithms for the search, we chose to rely on using the sensitivity coefficients in the average sense.