Computationally Efficient Direct Localization of Narrowband Radio Frequency Emitters

Classical (two-step) localization methods typically first estimate some statistic (e.g., angle-of-arrival) from the raw data and only then-based on that statistic-estimate the un-known emitter position. In contrast, direct position determination (DPD) is a one-step approach that estimates the emitter position from the raw data, consequently leading to superior performance (i.e., accuracy) relative to alternative indirect methods. However, the gain in localization accuracy (seemingly) comes with a cost-indirect methods involve simpler computations of the position estimate, while DPD-based methods typically requires a 2- or 3-dimensional grid search, possibly followed by a nonlinear off-grid optimization. The computational burden, thus, constitutes a considerable challenge for practical systems. This particular aspect of DPD is the focus of this work. Specifically, we provide an efficient solution for the single emitter scenario to alleviate the de-manding computational requirements. By resorting to eigenvalue perturbation theory, we derive a gradient-based optimization algorithm that significantly reduces the necessary computation time. Furthermore, under suitable conditions, and given a pre-viously obtained position estimate, our update equation can potentially be used as a tracking algorithm. The algorithm's successful operation is demonstrated via simulation results.