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.

Time difference of arrival (TDOA) positioning methods have experienced growing importance over the last few years due to their multiple applications in local positioning systems (LPSs). While five sensors are needed to determine an unequivocal three-dimensional position, systems with four nodes present two different solutions that cannot be discarded according to mathematical standards. In this paper, a new methodology to solve the 3D TDOA problems in a sensor network with four beacons is proposed. A confidence interval, which is defined in this paper as a sphere, is defined to use positioning algorithms with four different nodes. It is proven that the separation between solutions in the four-beacon TDOA problem allows the transformation of the problem into an analogous one in which more receivers are implied due to the geometric properties of the intersection of hyperboloids. The achievement of the distance between solutions needs the application of genetic algorithms in order to find an optimized sensor distribution. Results show that positioning algorithms can be used 96.7% of the time with total security in cases where vehicles travel at less than 25 m/s.

High-accuracy positioning is fundamental for modern applications of autonomous agent navigation. The accuracy and stability of predicted locations are key factors for evaluating the suitability of positioning architectures that have to be deployed to real-world cases. Asynchronous TDOA (A-TDOA) methodologies in Local Positioning Systems (LPS) are effective solutions that satisfy the given requirements and reduce temporal uncertainties induced during the synchronization process. In this paper, we propose a technique for the combined characterization of ranging errors -noise, and Non-Line-of-Sight (NLOS) propagation -through the Cramér-Rao Bound (CRB). NLOS propagation effects on signal quality are predicted with a new ray-tracing LOS/NLOS algorithm that provides LOS and NLOS travel distances for communication links in 3D irregular environments. In addition, we propose an algorithm for detecting multipath effects of destructive interference and disability of LOS paths. The proposed techniques are applied to sensor placement optimization in 3D real scenarios. A multi-objective optimization (MOP) process is used based on a Genetic Algorithm (GA) that provides the Pareto Fronts (PFs) for the joined minimization of location uncertainties (CRB) and multipath effects for a variable number of A-TDOA architecture sensors. Results show that the designed procedure can determine, before real implementation, the maximum capacities of the positioning system in terms of accuracy. This allows us to evaluate a trade-off between accuracy and cost of the architecture or support the design of the positioning system under accuracy demands.

The accuracy requirements for sensor network positioning have grown over the last few years due to the high precision demanded in activities related with vehicles and robots. Such systems involve a wide range of specifications which must be met through positioning devices based on time measurement. These systems have been traditionally designed with the synchronization of their sensors in order to compute the position estimation. However, this synchronization introduces an error in the time determination which can be avoided through the centralization of the measurements in a single clock in a coordinate sensor. This can be found in typical architectures such as Asynchronous Time Difference of Arrival (A-TDOA) and Difference-Time Difference of Arrival (D-TDOA) systems. In this paper, a study of the suitability of these new systems based on a Cramér-Rao Lower Bound (CRLB) evaluation was performed for the first time under different 3D real environments for multiple sensor locations. The analysis was carried out through a new heteroscedastic noise variance modelling with a distance-dependent Log-normal path loss propagation model. Results showed that A-TDOA provided less uncertainty in the root mean square error (RMSE) in the positioning, while D-TDOA reduced the standard deviation and increased stability all over the domain.

The emergence of autonomous vehicles with high needs for accuracy in location has hardened the requirements of the positioning systems used for navigation. Local Positioning Systems (LPS) have shown an excellent adaptation to these conditions, thanks to stability and reduction in the levels of positioning uncertainty. The accuracy achieved by methodologies based on temporal measurements depends mainly on the uncertainties in the measurements of these systems. In this aspect, the presence of noise and the existence of temporary instabilities in measurement clocks, depending on the distribution of sensors in the environment, acquire great relevance. In this article, we introduce for the first time in the authors' best knowledge a Cramér-Rao Lower Bound (CRLB) model for the quantification of the global uncertainty in positioning systems caused by both noise and temporary instabilities in the measurement devices. Additionally, this technique is applied to the optimization of sensor distributions for Time of Arrival (TOA), Time Difference of Arrival (TDOA) and Asynchronous TDOA (A-TDOA) architectures using a Genetic Algorithm in a non-uniform 3D environment. Results show that A-TDOA methodology significantly overcomes synchronous architectures in terms of global accuracy and stability when noise and clock errors are considered in time measurements of LPS applications.