Grid Size Selection for Nonlinear Least-Squares Optimization in Spectral Estimation and Array Processing

In many spectral estimation and array processing problems, the process
of finding estimates of model parameters often involves the optimisation
of a cost function containing multiple peaks and dips. Such
non-convex problems are hard to solve using traditional optimisation
algorithms developed for convex problems, and computationally intensive
grid searches are therefore often used instead. In this paper,
we establish an analytical connection between the grid size and the
parametrisation of the cost function so that the grid size can be selected
as coarsely as possible to lower the computation time. Additionally,
we show via three common examples how the grid size depends
on parameters such as the number of data points or the number
of sensors in DOA estimation. We also demonstrate that the computation
time can potentially be lowered by several orders of magnitude
by combining a coarse grid search with a local refinement step.