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Multilateration

SpringerReference · 2011

Cited by 0

Bayesian Multilateration

Alisson Alencar, César Mattos, João P. P. Gomes et al. · 2021

Multilateration (MLAT) is the de facto standard to localize points of interest (POIs) in navigation and surveillance systems. Despite sensors being inherently noisy, most existing techniques i) are oblivious to noise patterns in sensor measurements; and ii) only provide point estimates of the POI’s location. This often results in unreliable estimates with high variance, i.e., that are highly sensitive to measurement noise. To overcome this caveat, we advocate the use of Bayesian modeling. Using Bayesian statistics, we provide a comprehensive guide to handle uncertainties in MLAT. We provide principled choices for the likelihood function and the prior distributions. Inference within the resulting model follows standard MCMC techniques. Besides coping with unreliable measurements, our framework can also deal with sensors whose location is not completely known, which is an asset in mobile systems. The proposed solution also naturally incorporates multiple measurements per reference point, a common practical situation that is usually not handled directly by other approaches. Comprehensive experiments with both synthetic and real-world data indicate that our Bayesian approach to the MLAT task provides better position estimation and uncertainty quantification when compared to the available alternatives.

Cited by 0Open access

Bayesian Multilateration

Alisson Alencar, César Mattos, João P. P. Gomes et al. · 2021

Multilateration (MLAT) is the de facto standard to localize points of interest (POIs) in navigation and surveillance systems. Despite sensors being inherently noisy, most existing techniques i) are oblivious to noise patterns in sensor measurements; and ii) only provide point estimates of the POI’s location. This often results in unreliable estimates with high variance, i.e., that are highly sensitive to measurement noise. To overcome this caveat, we advocate the use of Bayesian modeling. Using Bayesian statistics, we provide a comprehensive guide to handle uncertainties in MLAT. We provide principled choices for the likelihood function and the prior distributions. Inference within the resulting model follows standard MCMC techniques. Besides coping with unreliable measurements, our framework can also deal with sensors whose location is not completely known, which is an asset in mobile systems. The proposed solution also naturally incorporates multiple measurements per reference point, a common practical situation that is usually not handled directly by other approaches. Comprehensive experiments with both synthetic and real-world data indicate that our Bayesian approach to the MLAT task provides better position estimation and uncertainty quantification when compared to the available alternatives.

Cited by 0Open access

Mobile Multilateration

Scaramuzza, Maurizio, Loeser, Martin, Früh, Daniel et al. · Zürcher Hochschule für Angewandte Wissenschaften digital collection (Zurich University of Applied Sciences) · 2015

Within civil aviation the implementation of Performance Based Navigation (PBN) and Automatic Dependent Surveillance Broadcast (ADS-B) is ongoing on a worldwide level. It is of particular interest to assess the quality of these new applications. For instance, within PBN, the Total System Error (TSE) is a safety relevant parameter, especially for applications in demanding environments such as approach procedures within mountainous areas. One solution, in order to estimate the TSE, would be to equip an airplane with a dedicated reference GPS receiver and derive carrier-phase position solutions. This approach would be feasible for flight trials but it is barely impossible to apply for commercial operations, e.g. for monitoring purposes of a complete traffic situation. The setting is analogous for the quality assessment of ADS-B, where the TSE cannot be derived by the data broadcast, but has to be retrieved on-board through dedicated non-operational equipment. Therefore a solution is envisaged by applying multilateration (MLAT) technology operating at 1090 MHz. This method has the advantage that all airplanes operating under Instrument Flight Rules (IFR) can be tracked through their transponder replies. Based on the envisaged solution the Zurich University of Applied Sciences in Winterthur, Switzerland, has developed a mobile MLAT system for skyguide. The advantage of this system compared to classical MLAT is the fact, that it can be quickly installed and operates autonomously during 48h powered only by a battery. Therefore no specific infrastructure is needed for the operation of the system. Dedicated flight trials with airplanes equipped with Mode-S transponders and ADS-B transmitters have been performed in order to assess the position accuracy of the mobile MLAT. Additionally, independent GNSS receivers were installed on-board these airplanes too which allowed the determination of the airplane positions through carrier-phase solution in order to validate the mobile MLAT accuracy performance. The measured accuracy within the area of interest is in the range of 5 to 10 m (1σ) depending on the geometry of the receivers.

Cited by 0Open access

Multilateration radar

S. Kazel · Proceedings of the IEEE · 1972

An airborne radar concept is described which would achieve high-resolution mapping of terrain, even with wide-beam antennas, by utilizing a narrow pulse-width. Successive high-resolution range rings, superimposed in a suitable storage medium, cause the terrain image to build up as the aircraft flies by.

Cited by 1

Bayesian Multilateration

Alisson S. C. Alencar, César Mattos, João P. P. Gomes et al. · IEEE Signal Processing Letters · 2022

Multilateration (MLAT) is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de facto</i> technique to localize points of interest (POIs) in navigation and surveillance systems. Despite sensors being inherently noisy, most existing techniques i) are oblivious to noise patterns in sensor measurements; and ii) only provide point estimates of the POI. This often results in unreliable estimates with high variance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., that are highly sensitive to measurement noise. To overcome this caveat, we advocate the use of Bayesian modeling. Using Bayesian statistics, we provide a comprehensive guide to handle uncertainties in MLAT, including principled choices for the likelihood function and the prior distributions. Notably, the resulting model is easy to implement and can leverage off-the-shelf Markov Chain Monte Carlo (MCMC) software for inference. Besides coping with unreliable measurements, our framework can also deal with sensors whose location is not completely known, which is an asset in mobile systems. Our solution also naturally incorporates multiple measurements per reference point, a common practical situation that is usually not handled directly by other approaches. Comprehensive experiments with both synthetic and real-world data indicate that our Bayesian approach to the MLAT task provides better position estimation and uncertainty quantification when compared to the available alternatives.

Cited by 4

Absolute multilateration between spheres

Jody Muelaner, W. J. Wadsworth, Maria Azini et al. · Measurement Science and Technology · 2017

Environmental effects typically limit the accuracy of large scale coordinate measurements in applications such as aircraft production and particle accelerator alignment. This paper presents an initial design for a novel measurement technique with analysis and simulation showing that that it could overcome the environmental limitations to provide a step change in large scale coordinate measurement accuracy. Referred to as absolute multilateration between spheres (AMS), it involves using absolute distance interferometry to directly measure the distances between pairs of plain steel spheres. A large portion of each sphere remains accessible as a reference datum, while the laser path can be shielded from environmental disturbances. As a single scale bar this can provide accurate scale information to be used for instrument verification or network measurement scaling. Since spheres can be simultaneously measured from multiple directions, it also allows highly accurate multilateration-based coordinate measurements to act as a large scale datum structure for localized measurements, or to be integrated within assembly tooling, coordinate measurement machines or robotic machinery. Analysis and simulation show that AMS can be self-aligned to achieve a theoretical combined standard uncertainty for the independent uncertainties of an individual 1 m scale bar of approximately 0.49 µm. It is also shown that combined with a 1 µm m−1 standard uncertainty in the central reference system this could result in coordinate standard uncertainty magnitudes of 42 µm over a slender 1 m by 20 m network. This would be a sufficient step change in accuracy to enable next generation aerospace structures with natural laminar flow and part-to-part interchangeability.

Cited by 5Open access

Sidelink ranging and multilateration

Alawieh, Mohammad, Perner, Bastian, Hadaschik, Niels et al. · Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) · 2019

Embodiments provide a transceiver (132 1) for a wireless communication system. The transceiver is configured to communicate with at least one other transceiver (132 2) of the wireless communication system using a sidelink resource pool of the wireless communication system. Further, the transceiver is configured to determine a distance to the other transceiver based on a time between the transmission of a first signal and the reception of a second signal from the other transceiver, and based on the period based on which the resources are allocated to the transceiver

Cited by 0Open access

Multilateration CMM: First steps

Lewis, A, Hughes, B, Wilson, A et al. · UCL Discovery (University College London) · 2003

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Multilateration as an Eigenvalue Problem

Martin Larsson, Malte Larsson · 2025

Multilateration, positioning a receiver using pseudodistances to known senders, is a problem with 5G and GNSS positioning applications. In contrast, trilateration uses direct distances and was reformulated as an eigenvalue problem in a recent work, resulting in a very competitive positioning method. This paper extends that reformulation to a more general class of problems subsuming multilateration and trilateration. The resulting multilateration method is fast, accurate, and numerically stable, outsourcing complex implementation details to existing mature eigensolvers. By allowing for reweightings of the terms, an iteratively reweighted least squares approach is feasible and can be used to improve the proposed algorithm further. Additionally, we demonstrate how partially known receiver positions are handled with experiments using real-world 5G data. The proposed method is evaluated against the state of the art and shown to be among the most accurate while remaining fast.

Cited by 0

Passive Positioning Using Linear Multilateration

Widdison, Eric R · ScholarsArchive (Brigham Young University) · 2023

Passive localization of aircraft in flight using signal time of arrival (TOA) poses some unique challenges. The sensors must be deployed in an approximately coplanar configuration, which produces significant vertical uncertainty in the estimated position. This dissertation examines the traditional algorithms used in passive localization. It presents general forms of linear TOA, time difference of arrival (TDOA), angle of arrival (AOA), and frequency difference of arrival (FDOA) equations from the literature and explains how to apply an intuitive geometric interpretation of these equations. It presents two novel algorithms for passive localization. One uses a one dimensional AOA (1AOA) to improve the vertical estimate. The other employs an a priori estimate to approximate the non-linear localization problem as a linear problem and produce a high quality position estimate. A comprehensive survey of the literature is presented. This dissertation provides a summary and classification of passive localization algorithms from the literature with simple descriptions of how the form of the equations relate to their numerical stability. It presents two novel algorithms for passive localization. The hybrid multilateration and triangulation algorithm improves wide area multilateration by using vertical 1AOA to constrain the vertical position. The multilateration with a priori estimates algorithm provides a linear localization method that utilizes previous location estimates.

Cited by 1

Three-Dimensional Positioning—by Multilateration

William E. Ball · Journal of the Surveying and Mapping Division · 1974

Systems of equations are derived and computational routines are outlined that can be used to determine the geodetic coordinates and elevation of a point by three-dimensional multilateration using slope distances only. The geodetic coordinates and elevation of a point are computed using slope distances (only) that have been measured from three or more points having known geodetic coordinates and elevations to the point of unknown position. By an alternate method, the position of a point is also determined using as few as two slope distances if, in addition, the elevation of the point is known. Least squares methods are employed and precision evaluation estimators are computed.

Cited by 2

Multilateration of Demodulated Radio Signals

Endre Szabó, Dieter Eier · 2025

In commercial Air Traffic Control (ATC), voice communications between pilots and air traffic operators rely primarily on AM-modulated radio signals, mostly within the VHF frequency band. When multiple radio receivers operate at the same frequency but are located in separate places, this setup is known as Radio Coverage. During a pilot's radio transmission, the signal is received by multiple receiver sites at slightly different points in times, depending on the distance of the receiver site to the transmitter. Radio voice communications do not include any information about the location of the transmitter. To determine the location of the transmitter from the radio signals additional UHF/VHF Direction Finders can be used. (Wide Area) Multilateration is a well-known technique to estimate the location of a transmitter using multiple sensors at separate locations which receive the same transmitted signal, but at different points of time. The estimations of these time differences between the received and demodulated audio signals of separate receiver sites can be used to estimate the location of the transmitting aircraft in real-time. Compared to other surveillance applications, such as radar or ADS-B, which allow the precise determination of an aircraft's location, Multilateration of Demodulated Radio Signals shows a reduced accuracy in estimating the location of the transmitter. However, it can serve effectively as a backup mechanism or as a replacement for UHF/VHF Direction Finders. This paper discusses implementations of Multilateration of Radio Signals. The key for suitable implementations is the association of received and demodulated radio signals of different radio sites to a reference time frame. An implementation with digital radio receivers together with its realization is presented and discussed in detail. But for this implementation, which supports an estimation of a transmitter in real-time further investigations of the presented mechanisms will be necessary.

Cited by 1

Multipath Effect in Multilateration Surveillance

Konchenko, Inna, Yanovsky, Felix · Electronic Institutional Repository of the National Aviation University of Ukraine (National Aviation University, Ukraine) · 2017

This paper is dedicated to the investigation of the errors, caused by multipath effect of signal propagation. Multipath effect was modelled and analyzed on the basis of polarization characteristics of received signal.

Cited by 0

LOCALIZATION ALGORITHM FOR MULTILATERATION SYSTEMS

А. А. Монаков · Journal of the Russian Universities Radioelectronics · 2018

At present, multilateration systems are becoming increasingly important in air traffic control. This is due to their significant advantages in compare with secondary surveillance radar complexes. This article solves the problem of synthesizing an algorithm for object location estimation for multilateration system operating in passive mode. The synthesized algorithm is a combination of a procedure, the result of which is a rough estimate of the observed object coordinates, and an iterative algorithm specifying the resulting solution. The rough estimate is the result of solving a linear system of equations. The iterative refinement procedure is based on the linearization of the observational equations and does not require a large number of iterations. The paper provides a comparative statistical analysis of the proposed algorithm and the known Bancroft algorithm. For an objective analysis of two algorithms, the paper derives the Cramer-Rao boundary for the correlation matrix of estimates of the observed object coordinates, which makes it possible to determine the potential accuracy of the solution of the problem. It is shown that both algorithms allow obtaining estimates, the accuracy of which is close to the potentially achievable accuracy of the object location estimate. In contrast to the Bancroft algorithm, the rough estimate of the object location is unambiguous. This virtue reduces the total amount of computations during the algorithm implementation and reduces the probability of anomalous errors.

Cited by 7Open access

Multilateration Software Development (Phase 2)

John D. Weinberg, Myles Harris, Edward J. Knobbe et al. · 1973

Abstract : Historically, vehicle-borne, radio-hybrid navigation system software has too often been designed around preselected navigation hardware on an ad hoc, system-by-system basis. In these developments, little attention has been paid to the inherent physical and functional commonality which underlies much of this superficially quite different software. This report documents the methods, and the very promising results, of the second phase of a software development effort directed at identifying and specifying a standardized, modular, flexible, radio- hybrid navigation system software processor.

Cited by 0

SAR Geolocation Using Range-Only Multilateration

Armin Doerry, Douglas Bickel · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2021

Radar is by its basic nature a ranging instrument . If radar range measurements from multiple directions can be made and a ssembled, then multilateration allows locating a feature common to the set of Synthetic Aperture Ra dar (SAR) images to an accurate 3-D coordinate. The ability to employ effective multilateration algorithms is highly dependent on the geometry of the data collections, and the accuracy with which rela tive range measurements can be made. The problem can be cast as a least-squares exercise , and the concept of Dilution of Precision can describe the accuracy and precision with which a 3-D location can be made. - 4 - Acknowledgements This report is the result of an unf unded Research and Development effort. The authors thank their colleague Tim Bielek fo r his review of this report and appreciated comments.

Cited by 0Open access

Multilateration Localization for Wireless Sensor Networks

Abdelhady Naguib · Indian Journal of Science and Technology · 2020

Objectives/methodology: Localization in wireless sensor networks (WSNs) has long been one of the most interesting areas that researchers continue to study. This study presents the methodology of mathematical model for multilateration localization in WSNs verified by a simulation model using the NS-2 simulator. Findings: The new modules added to NS-2 can be extended to various rangebased localization techniques, which help many researchers in this field. Applications: This work makes a comparative study of atomic and iterative multilateration localization according to different performance metrics. Keywords: Multilateration, Localization, NS-2, Simulation, WSN.

Cited by 12Open access

Bayesian Multilateration for localization and regression

Alisson Sampaio de Carvalho Alencar · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2023

In this work, we present an innovative approach called Bayesian Multilateration (BMLAT), which addresses challenges in localization and regression systems. The conventional Multilateration (MLAT) technique, commonly used for locating points of interest (POIs), often produces unreliable estimates due to sensor noise and provides only point estimates of the POI. BMLAT employs Bayesian modeling to handle uncertainties in MLAT by utilizing likelihood functions and prior distributions. This Bayesian framework is easy to implement and uses available Markov Chain Monte Carlo (MCMC) software for inference. Moreover, BMLAT can accommodate sensors with incomplete location information and multiple measurements per reference point. Extensive experiments with synthetic and real-world data demonstrate that BMLAT provides better position estimation and uncertainty quantification compared to alternative methods. In another domain, the Minimal Learning Machine (MLM) has gained attention for its efficiency in handling complex classification and regression tasks. However, the traditional MLAT approach, when combined with MLM, does not account for the inherent uncertainties in real-world datasets and only produces a point estimate. To address this challenge, Bayesian principles are integrated into MLM to create the Bayesian MLM (BMLM). BMLM offers a probabilistic perspective, providing not only point estimates but also a comprehensive output distribution, capturing uncertainties in the estimation process. The study aims to elucidate the theoretical and practical implications of BMLM, demonstrating its consistency with Gaussian processes through empirical analyses. The incorporation of Bayesian principles enhances the output estimate quality of MLM and provides a deeper understanding of uncertainties. Additionally, we propose the combined application of BMLAT and BMLM for localization and regression tasks, exploring the synergistic potential of these approaches.

Cited by 0Open access

Incentivizing WiFi-Based Multilateration Location Verification

Mingzhe Li, Wei Wang, Jin Zhang et al. · IEEE Internet of Things Journal · 2021

Due to the proliferation of WiFi devices and the high verification precision, researchers have shown interests in WiFi-based multilateration location verification (WMLV), where multiple WiFi APs (also known as verifiers) verify the location information claimed by a prover. However, it is a high expenditure for any single location-based service provider to deploy densely covered WiFi facilities. Incentivizing independent WiFi owners to corporately verify location information is thus a feasible solution to this plight, yet none of the previous research has taken this into consideration. To this point, we design a double auction-based incentive mechanism for WMLV, which motivates the participation of both provers and verifiers. More importantly, we consider practical situations, where the provers have various verification precision requirements, and different number of verifiers are required by different provers. The proposed double auction mechanism achieves desirable economical properties, including <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">truthfulness, individual rationality, computational efficiency, budget balance,</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nonnegative social welfare.</i> The desired properties are validated through both theoretical analysis and extensive simulations.

Cited by 5