Optimization of radar scanning strategies using an ensemble relative error criterion

We study the determination of optimal radar scanning direction parameters for a network of n radars. Our approach is to seek directions that minimize relative errors between retrieved and model-based predicted wind fields in ensembles of possible wind fields. The underlying estimation model is based on the variational problem to retrieve wind fields from radar data. The considerations here view retrieved wind fields as functions of parameterized scanning strategies. The scanning strategies are formulated in terms of a scanning model that depends, in particular, on tracking parameters. A mathematical formulation is presented as an optimization problem that may be generalized to networks with any number of radar in which existence and approximation results are developed. A numerical study for a network containing two radar is presented illustrating the theory developed.