Efficient location strategy for airport surveillance using Mode-S multilateration systems

Abstract

In this paper, the use of regularization methods to solve the location problem in multilateration systems, using Mode-S signals, is studied, evaluated, and developed. The Tikhonov method has been implemented as a first application to solve the classical system of hyperbolic equations in multilateration systems. Some simulations are obtained and the results are compared with those obtained by the well-established Taylor linearization and with the Cramér-Rao lower bound analysis. Significant improvements, for the accuracy, convergence, and the probability of location, are found for the application of the Tikhonov method.

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

“…In this classification, a localization algorithm is an entity that reconstructs the target position, given a set of TDOA measurements. The interested reader may see [7,10,11] and the references therein for some guidelines in MLAT systems, and [12] for an equivalent comparison for Global Positioning System (GPS) geolocation algorithms. However, really (as we describe later), a localization algorithm is composed of a data model, which mathematically relates the unknown and known parameters, by a system of equations, and a numerical method to solve that system of equations.…”

“…However, really (as we describe later), a localization algorithm is composed of a data model, which mathematically relates the unknown and known parameters, by a system of equations, and a numerical method to solve that system of equations. Hence, it is clear that different data models can be used along with different numerical methods (in fact in the recent years some works [11,[13][14][15][16] about this combination have been presented).…”

“…where J is the Jacobian differential matrix of m (θ) (see [7,11] for details), and θ0 is the required previous estimation of the solution, also called starting point. The convergence of the localization algorithms initially depends on the starting point quality, although the numerical method that is used can work with relatively poor accuracy for the starting points [11].…”

“…The convergence of the localization algorithms initially depends on the starting point quality, although the numerical method that is used can work with relatively poor accuracy for the starting points [11].…”

“…The most relevant localization algorithms that uses this kind of data models are those described in [19], which was statistically described and analyzed in [7], and the ones proposed in [11] and [16]. The main difference in these algorithms is that the ones in [7,19] set the problem in the sense of least squares (LS), while the one in [11] set the problem in the sense of Tikhonov regularization, and the one in [16] in the sense of the singular value decomposition (SVD)-based regularization.…”