Solving passive multilateration equations using Bancroft's algorithm

Geyer, Michael; Daskalakis, Anastasios

doi:10.1109/dasc.1998.739825

Cited by 17 publications

(17 citation statements)

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“…For the WAM simulations we use the real system layout and an approach path, with the measurements simulated as an unbiased Gaussian process whose standard deviation is generated as described in [11]. For the LAM simulations, we use real recorded data coming from the MLAT system at Tallinn (Tallinn, Estonia) airport, which have been kindly provided by the company ERA A. S. Moreover, we compare the proposed TDOA-RLE with the closed form algorithms by Schmidt [15], Smith and Abel [16], Friedlander [17], Schau and Robinson [18], Chan and Ho [21], and Geyer and Daskalakis [23], and with the classical open form algorithm by Foy [12]. For all …”

Section: Simulations and Resultsmentioning

confidence: 99%

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Time‐difference‐of‐arrival regularised location estimator for multilateration systems

Mantilla-Gaviria

Leonardi²,

Galati³

et al. 2014

IET Radar, Sonar & Navigation

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A new version of an open form localisation algorithm, called regularised location estimator (RLE), for time difference of arrival (TDOA) multilateration systems is proposed. This algorithm is based on Tikhonov regularisation and on maximumlikelihood estimation. It is aimed to solve the localisation problem for both well-conditioned and ill-conditioned situations. It provides solutions that are statistically and numerically efficient, in contrast to the algorithms in the literature providing solutions that are only efficient in one sense and that do not solve the ill-conditioned situations, which can be found in some operational conditions. A recursive formulation for estimating the regularisation parameter is provided and some mathematical analyses about the proposed estimator are also presented. A comparison with a large number of open and closed form algorithms in the literature is performed with both simulated and real data. The results show that the novel TDOA-RLE provides superior performance even in the case of well-conditioned situations. Â© The Institution of Engineering and Technology 2014

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Section: Simulations and Resultsmentioning

confidence: 99%

“…Moreover, we show the probability of localisation (PoL), which basically describes the percentage of points that has an error smaller than a predefined threshold. For this case, we have used a threshold of 20 m. Since this is a LAM system, the regularisation parameter is estimated by (23). The full [i.e.…”

Section: Tallinn Lam Systemmentioning

confidence: 99%

Time‐difference‐of‐arrival regularised location estimator for multilateration systems

Mantilla-Gaviria

Leonardi²,

Galati³

et al. 2014

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

show abstract

“…To validate this statement, we have simulated the localization algorithms by Schmidt [24], Foy [19], Smith and Abel [20], Friedlander [21], Schau and Robinson [22], Chan and Ho [23], the application of Bancroft by Geyer and Daskalakis [25], and the Wikipedia [26]. All of these algorithms use the least-squares numerical method.…”

Section: Simulation and Resultsmentioning

confidence: 99%

“…Different set of coefficients A, B, C, and D means different localization algorithms. The most relevant algorithms using this data model are the one by Schmidt [24], the one by Geyer and Daskalakis [25], and the one only published in the open license website Wikipedia [26]. Particularly, the Geyer and Daskalakis [25] algorithm is a practical implementation of the Bancroft algorithm [27], which was originally proposed for GPS and that is based on TOA measurements rather than TDOA or range differences.…”

Section: The Algebraic Approach-based Modelsmentioning

confidence: 99%

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

Mantilla-Gaviria

Leonardi

Galati

et al. 2014

SIViP

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We present a general scheme for analyzing the performance of a generic localization algorithm for multilateration (MLAT) systems (or for other distributed sensor, passive localization technology). MLAT systems are used for airport surface surveillance and are based on time difference of arrival measurements of Mode S signals (replies and 1,090 MHz extended squitter, or 1090ES). In the paper, we propose to consider a localization algorithm as composed of two components: a data model and a numerical method, both being properly defined and described. In this way, the performance of the localization algorithm can be related to the proper combination of statistical and numerical performances. We present and review a set of data models and numerical methods that can describe most localization algorithms. We also select a set of existing localization algorithms that can be considered as the most relevant, and we describe them under the proposed classification. We show that the performance of any localization algorithm has two components, i.e., a statistical one and a numerical one. The statistical performance is related to providing unbiased and minimum variance solutions, while the numerical one is related to ensuring the convergence of the solution. Furthermore, we show that a robust localization (i.e., statistically and numer- ically efficient) strategy, for airport surface surveillance, has to be composed of two specific kind of algorithms. Finally, an accuracy analysis, by using real data, is performed for the analyzed algorithms; some general guidelines are drawn and conclusions are provided.

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“…The Bancroft algorithm was initially developed by Bancroft [113] for GPS applications and the corresponding application for MLAT systems was developed by Geyer and Daskalakis [111]. However, we prefer to call it Bancroft algorithm because the second work is a direct application of the Bancroft work.…”

Section: Bancroft Algorithmmentioning

confidence: 99%

New Strategies to Improve Multilateration Systems in the Air Traffic Control

Gaviria¹,

Antonio²

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This thesis is focused on the Mode S Multilateration (MLAT) systems for the Air Traffic Control (ATC) operations, specifically on their layout design and on the process of cooperative targets localization performed by them. It addresses the development of new design and localization strategies. The design strategies are based on the application of metaheuristic optimization techniques, whilst the localization ones are based on the application and combination of regularization methods along with some current localization algorithms.The design strategies are composed of an effective, general procedure to emplace both the standard and enhanced MLAT receiving stations on a surveillance volume, and a set of design strategies to be used with such a proposed procedure. This procedure uses the metaheuristic of Genetic Algorithms (GA), and is intended to obtain useful design parameters that allow optimal system configurations that provide suitable performance levels. Furthermore, the procedure developed in this thesis is able to evaluate and improve previous system designs, as well as possible system enhancements. For this context, we overcome several issues like the lack of a general model that relates the system performance parameters with those ones that can be simulated on a computer, the setting of the design problem as a computer optimization one, the development and application of the numerical tools to analyze and evaluate the MLAT systems performance, the complexity evaluation of the resulting computer optimization problem, and the application and modification of the GA components for solving such a optimization problem. To validate the contributions in this context, some simulations are performed on a real airport scenario.The localization strategies are composed of a set of developed regularized location estimators, a set of developed additional improvements, and the use of some current localization algorithms. These strategies can be used for both surface and wide areas surveillance, and solve some practical problems like the loss of position accuracy when using a small number of stations, or viii Abstract for small areas where the stations are close to each other (e.g., airport surface surveillance), and the mitigation of some errors due to multipath effect. Moreover, the proposed localization strategies are found to be highly statistically and numerically efficient, in contrast to current ones that are efficient in only one sense (i.e., statistically or numerically). For this context, we overcome several issues like the identification and evaluation of the numerical causes of the above mentioned problems, the analysis of the current localization algorithms, the adaptation of the regularization methods theory for solving the localization problem, the development of some numerical additional tools that allows the real time implementation of such proposed algorithms, and the combination of the current algorithms with the proposed ones. To validate the contributions in this context, some simulations wit...

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Solving passive multilateration equations using Bancroft's algorithm

Cited by 17 publications

References 1 publication

Time‐difference‐of‐arrival regularised location estimator for multilateration systems

Time‐difference‐of‐arrival regularised location estimator for multilateration systems

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

New Strategies to Improve Multilateration Systems in the Air Traffic Control

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