Lower bounds of accuracy for enhanced mode-S distributed sensor networks

Abstract

The aim of this study is to analyse the accuracy of passive location systems by using the Cramér-Rao lower bound (CRLB). The study is focused on sensor networks derived from the well-known Multilateration (MLAT) systems, used for aircraft and vehicle surveillance. The measurement used in the standard MLAT configuration is the Time Difference Of Arrival, but it can be improved by using other types of measurement like angle of arrival, round trip delay or time integration. Here, the CRLB is used to model the system accuracy performance using different measurements and related to the target kinematics, to evaluate a possible system evolution. In this frame, the CRLB analysis is useful to define the basic limitations and the advantages of different system architectures as well as to optimise existing architectures by adding new measurement capabilities to some receiving stations. © 2012 The Institution of Engineering and Technology

Localization algorithms for multilateration (MLAT) systems in airport surface surveillance

“…Most of them are based on the maximum likelihood (ML) principle [18] due to the asymptotic consistency and efficiency of the ML estimators (MLE). Concerning the measurement error distributions, Gaussian distributions are generally assumed [6,7,9]. To solve this kind of highly nonlinear models, linear approximations and iterative numerical methods are required.…”

“…The statistical approach algorithms are commonly classified as open-form algorithms. On the other hand, if the statistical hypotheses are satisfied by the measured data, these models provide optimum estimators, i.e., estimators that are in practice unbiased and with covariance matrix very close to its Cramer-Rao Lower Bound (CRLB) [9].…”

“…Moreover, they provide a unique solution and introduce only linear noise terms in the resulting inverse problem. The latter is very important for wide area multilateration (WAM), where the measurement noise due to propagation losses is considerably large [9].…”

“…Thus, the aim of a localization algorithm is to set both the matrix G and the unknown transponder position vector θ and to obtain a numerical value for θ that fits (3), under the additive noise n. It is well known that the position accuracy of MLAT systems depends on three elements, namely (1) the measurements accuracy, (2) the spatial distribution of the stations (also called system geometry) that is quantified by the Dilution of precision (DOP) parameter, and (3) the localization algorithm used to convert the TOA/TDOA measurements space [i.e., the set of measurements in (1)] into the position one, referenced to the Cartesian space (x, y, z) [7][8][9]. It is generally assumed that the MLAT position errors can be modeled by an unbiased Gaussian distribution with a given variance, where the measurements accuracy and the geometrical effects (i.e., as quantified by the DOP) set its minimum variance values [9]. Nevertheless, this limit only represents the best case for the system accuracy that can be achieved with the corresponding measurements and system geometry.…”

“…Several works can be found in the literature regarding the theoretical analysis (i.e., for the analysis of the lower, theoretical bounds of accuracy) of the MLAT systems [7][8][9], but no general work was found, which analyzes the performance of the various localization algorithms.…”