Combined Noise and Clock CRLB Error Model for the Optimization of Node Location in Time Positioning Systems

Abstract

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.

Hybrid Memetic Algorithm for the Node Location Problem in Local Positioning Systems

“…Therefore, the time required for finding an optimized node distribution increases with the number of TLE analyzed points and it is dependent on the fitness function defined for the sensor distribution quality. This function will contain in this paper the combined uncertainties of noise in LOS and NLOS environments [ 21 ] and clock errors [ 20 ]. These effects are introduced in the covariance matrix of the FIM of the Asynchronous Time Difference of Arrival (A-TDOA) architecture.…”

“…Localization NLP assumes an optimal sensor distribution for reducing the uncertainties in the determination of the TS location. The main system uncertainties in TBP are the noise degradation of the positioning signal in LOS and NLOS environments [ 21 ], the clock errors in the time measurements which are generated by synchronization of the system devices, drift and truncation errors in the CS clocks [ 20 ] and the geometric deployment of the sensors in space which affects the positioning algorithm performance [ 60 ].…”

“…Even completely asynchronous architectures are recently being proposed [ 18 , 19 ] and are attracting high research interest since they collect all the time measurements in a single clock of a Coordinator Sensor (CS). This allows us to avoid synchronism among the system receivers, consequently reducing the architecture clock errors [ 20 ] but increasing the signal paths and noise errors [ 21 ], since they rely on a receive-and-retransmit strategy of the positioning signals in the Target Sensor (TS), producing longer path signals. In addition, a possible CS malfunction may produce temporal system unavailability [ 22 ] due to the particular architecture dependence on the CS.…”

“…The signal path noise degradation must deal with heteroscedastic noises [ 29 ], since the signal paths notably differ among sensors in LPS. For the characterization of the clock errors, we have recently introduced [ 20 ] a model in which the initial-time offset, clock drift and the instrument truncating error are considered. The minimization of this combined CRLB model enables the optimal performance of any LPS architecture for a defined TS location.…”

“…In our previous research, we have applied GA to the NLP in LPS [ 7 , 20 , 21 , 22 , 30 ]. In these papers, we have observed that the dimensions of the space of solutions which increases with the number of sensors, the resolution of the pre-defined possible space locations for them and the complexity of the fitness function evaluation, significantly affect the stable performance of the GA.…”