Genetic Algorithm Approach to the 3D Node Localization in TDOA Systems

Positioning asynchronous architectures based on time measurements are reaching growing importance in Local Positioning Systems (LPS). These architectures have special relevance in precision applications and indoor/outdoor navigation of automatic vehicles such as Automatic Ground Vehicles (AGVs) and Unmanned Aerial Vehicles (UAVs). The positioning error of these systems is conditioned by the algorithms used in the position calculation, the quality of the time measurements, and the sensor deployment of the signal receivers. Once the algorithms have been defined and the method to compute the time measurements has been selected, the only design criteria of the LPS is the distribution of the sensors in the three-dimensional space. This problem has proved to be NP-hard, and therefore a heuristic solution to the problem is recommended. In this paper, a genetic algorithm with the flexibility to be adapted to different scenarios and ground modelings is proposed. This algorithm is used to determine the best node localization in order to reduce the Cramér-Rao Lower Bound (CRLB) with a heteroscedastic noise consideration in each sensor of an Asynchronous Time Difference of Arrival (A-TDOA) architecture. The methodology proposed allows for the optimization of the 3D sensor deployment of a passive A-TDOA architecture, including ground modeling flexibility and heteroscedastic noise consideration with sequential iterations, and reducing the spatial discretization to achieve better results. Results show that optimization with 15% of elitism and a Tournament 3 selection strategy offers the best maximization for the algorithm.