Abstract
Autonomous vehicles need to localize themselves within the environment in order to effectively perform most tasks. In situations where a Global Navigation Satellite System such as the Global Positioning System cannot be used for localization, other methods are required. One self-localization method is to use signals transmitted by beacons at known locations to determine the relative distance and bearing of the vehicle from the beacons. Estimation performance is influenced by the beacon–vehicle geometry and the investigation into the optimal placement of beacons is of interest to maximize the estimation performance. In this article, a new solution to the optimal beacon placement problem for self-localization of a vehicle on a two-dimensional plane using angle-of-arrival measurements is proposed. The inclusion of heading angle in the estimation problem differentiates this work from angle-of-arrival target localization, making the optimization problem more difficult to solve. First, an expression of the determinant of the Fisher information matrix for an arbitrary number of beacons is provided. Then, a procedure for analytically determining the optimal angular separations for the case of three beacons is presented. The use of three beacons is motivated by practical considerations. Numerical simulations are used to demonstrate the optimality of the proposed method.
Highlights
Autonomous vehicles usually require accurate estimation of their position and heading in a global coordinate system to effectively accomplish mission objectives
We present an analytical solution to the optimal beacon placement problem for self-localization of a vehicle on a two-dimensional plane using angle-of-arrival measurements
In the first simulation task, the optimal beacon angular separations calculated analytically were compared with the beacon angular separations calculated using two numerical methods
Summary
Autonomous vehicles usually require accurate estimation of their position and heading in a global coordinate system to effectively accomplish mission objectives. For self-localization, a vehicle uses AoA measurements from multiple transmitters to estimate its position and heading. For the AoA self-localization problem, the objective is to place the beacons to produce an optimal estimate of the two-dimensional (2D) position and heading of a vehicle from the measured beacon bearings (see, e.g., [6,7]). We propose a new solution to the optimal placement of three beacons for self-localization using AoA measurements. Using the minimum number of beacons for self-localization leads to reduced costs, placement logistics, computational complexity, and energy required for communication. We present an analytical solution to the optimal beacon placement problem for self-localization of a vehicle on a two-dimensional plane using angle-of-arrival measurements. A simplified expression for the determinant of the FIM for vehicle self-localization using AoA measurements for an arbitrary number of beacons.
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