Wide Area Multilateration System Research Articles

Comparative analysis of methods for determining the air objects’ coordinates using wide-area multilateration systems

The presented work considers the place and role of wide-area multi-position airspace surveillance in the information support of airspace control and air traffic control systems. Classification of methods for estimating the coordinates of air objects using various primary measurements of the parameters of received signals in multi-position observation is given. A quantitative assessment of the accuracy in determining the air objects’ coordinates by the considered methods is also given. The capabilities of wide-area multi-position surveillance systems increase significantly when using the principles of constructing a secondary surveillance radar as a non-synchronous network, and an aircraft responder as an open single-channel queuing system with servicing the first correctly received request signal. An unauthorized request from an aircraft responder makes it possible to switch from completely passive methods for detecting and determining the coordinates of an air object to active-passive ones, which provide an increase in the accuracy of solving a coordinate task by dozens of times while maintaining the energy secrecy of a wide-area multi-position observation system. It is shown that the use of active and passive methods for constructing wide-area multi-position observation systems makes it possible to implement goniometric, difference-range, goniometer-range, total-range and goniometer-total-range methods for determining the coordinates of an air object. This increases significantly the number of options for estimating the coordinates of an air object. As a result, it allows improving the quality of information support for users by choosing the optimal method for estimating the coordinates of the observed air objects using various primary measurements of the received signals parameters.

Compensation of Positioning Errors Caused by Tropospheric Wave Propagation in Wide-Area Multilateration Systems

Introduction. Wide area multilateration (WAM) systems are the main competitors of secondary surveillance radar (SSR) systems used in air traffic control (ATC). The general principle of WAM operation is based on the assessment of pseudoranges between a signal source (an aircraft airborne transponder) and the ground receivers with precisely known geographical coordinates deployed over the ATC area. The aircraft position is estimated by measuring pseudoranges. A significant factor affecting the accuracy of aircraft positioning is tropospheric refraction, a phenomenon caused by the inhomogeneity of the earth's atmosphere and manifested in a deviation in the direction of the rays along which the signal of an aircraft transponder propagates. Refraction increases the lengths of ray paths, thus increasing the corresponding pseudoranges. As a result, the estimate of the aircraft position receives an additional bias. Altitude estimates produce unreasonably large errors.Aim. To develop a mathematical model for the signals received by a WAM system, which accounts for tropospheric wave propagation, as well as to derive an algorithm for aircraft positioning with compensated tropospheric errors.Materials and methods. Equations for the pseudorange estimation errors caused by wave propagation in a spherically stratified atmosphere were derived using the method of geometrical optics.Results. This paper proposed a mathematical model for pseudorange estimates in WAM systems, which accounts for the bias associated with the phenomenon of tropospheric refraction. An analysis of the proposed model showed that pseudorange errors depend linearly on the distance between the aircraft transponder and the receiver. This conclusion allowed an algorithm for aircraft positioning with compensated tropospheric errors to be developed. The proposed algorithm yields an unbiased estimate of the aircraft position. The standard deviation of altitude estimates increases by 60%, although remaining within the limits permissible for WAM systems.Conclusions. The developed mathematical model of WAM signals, which considers tropospheric propagation errors in pseudorange estimation, as well as the algorithm for aircraft positioning with compensated tropospheric errors, can be used in the development of spatially distributed navigation systems.

Commentary to: TDOA versus ATDOA for wide area multilateration system

The paper (Stefanski and Sadowski, EURASIP J. Wirel. Commun. Netw. 2018, Article 179) introduces a multilateration algorithm for unsynchronized sensor networks. However, a very similar method has been proposed before that is not cited. Furthermore, in the measurement model of Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179), an incorrect covariance matrix (Eq. (11) in Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179)) has been used that leads to inferior results. We summarize the context and explain the measurement methodology proposed in Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179), while referring to the missing citation. Finally, we derive the correct covariance matrix of the measurement error and demonstrate that the covariance matrix proposed in Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179) is incorrect.

Asynchronous WAM with Irregular Pulse Repetition

Radiolocation systems for aviation based on Multi-Lateration (MLAT) typically use a set of synchronised ground sensors to receive radio signals broadcast by onboard transmitters. In most cases, the sensor synchronisation in Wide Area Multi-Lateration Systems (WAM) is provided by Global Navigation Satellite System (GNSS) receivers. However, in the case of synchronisation failure, there is still a possibility to estimate the coordinates of the tracked aircraft by using the measurements of the time of arrival taken by non-synchronised sensors. The article presents the principle of operation and equations for calculating the coordinates of an aircraft in an asynchronous multi-lateration system, together with the results of a computer simulation allowing comparison of the accuracy of position estimation between the asynchronous and the typical, synchronous MLAT. This paper contains also some comments on the required stability of the clock source for the sensors working in an asynchronous MLAT system.

TDOA versus ATDOA for wide area multilateration system

This paper outlines a new method of a location service (LCS) in the asynchronous wireless networks (AWNs) where the nodes (base stations) operate asynchronously in relation to one another. This method, called asynchronous time difference of arrival (ATDOA), enables the calculation of the position of the mobile object (MO) through the measurements taken by a set of non-synchronized fixed nodes and is based on the measurement of the virtual distance difference between the reference nodes and the several MO positions (more than two), as well as on the solution of a nonlinear system of equations. The novelty of the proposed solution is using the measurements taken by at least five ground sensors without time synchronization between them to estimate the position of the tracked MO transmitting four or more sounding signals in random time.The new method significantly simplifies the localization process in real-life AWNs. It can be used on its own or to complement the traditional synchronous method. The paper focuses on the description of the proposed ATDOA method, two algorithms TS-LS (Taylor series least-squares) and GA (genetic algorithm) for solving the nonlinear system of equations, example application of the new method for a three-dimensional space, and presentation of the simulation models and simulation results. An important part of the paper is the comparison of the efficiency between the asynchronous method and the synchronous one for wide area multilateration (WAM) system. In addition, the Cramér-Rao lower bound (CRLB) is derived for this problem as a benchmark. The preliminary measurement results obtained by applying the proposed ATDOA method against the background of the synchronous one are presented at the end of the paper. As it could be expected, the synchronous solution gives better results. The synchronous method allows to locate the aircraft within 15 m in about 80% of the time, while the ATDOA method in 74% of the time for the base stations clocked from the reference clocks with the stability equal to 10−9, and in 58% of the time for the base stations clocked from the reference clocks with the stability equal to 10−8. The new method therefore should not be treated as the improvement of the existing synchronous positioning systems but as a backup solution which allows to keep the LCS systems running even during ground stations synchronization failure.

Analysis of Wide Area Multilateration Localization Accuracy Under Different Stations Layout ond Aircraft Height

Layout of stations and height of aircraft are very important to localization accuracy of wide area multilateration (WAM) system, and the error produced by layout of stations and height of aircraft may influence WAM system’s localization accuracy. To find the approach to reduce the error, this paper firstly calculates relationship between localization accuracy and height error according to hyperbolic algorithm and least square method, and obtains the change law of horizontal dilution of precision (HDOP) and vertical dilution of precision (VDOP) with height. Secondly, the system localization precision of levels of the same height and levels of different aircraft heights after giving consideration to the various circumstances of wide area stations layout are simulated and analyzed. Thirdly, the impact of different station layouts and baseline length of the levels of the same height on localization precision are discussed. Simulation and discussion results show that the aircraft height has a large impact on the WAM system’s localization precision. In particular, the vertical localization precision reduces obviously when the height is low. When the height is unchanged, a proper station layout and baseline length can improve the system’s localization precision.

항행시스템 성능향상을 위한 강인한 필터링 알고리즘

CNS/ATM(communication navigation surveillance / air traffic management)의 감시 분야에서는 ADS-B(automatic dependent surveillance - broadcast) 시스템, MLAT(multilateration) 시스템, WAM(wide area multilateration) 시스템이 구축되고 있다. ADS-B, MLAT, WAM 시스템의 항공기 추적 성능이 기존의 레이더에 비해 매우 우수하지만 여전히 오차를 포함하고 있다. 따라서 본 논문에서는 차세대 항행시스템의 오차를 줄이고 항공기 추적 성능을 높일 수 있는 필터링 알고리즘을 제안하였다. 필터링 알고리즘 중에서 가장 유용하다고 알려진 IMM(interacting multiple model) 필터를 개선한 Robust IMM 필터를 사용하였으며, ADS-B, MLAT, WAM 시스템 등의 차세대 항공기 추적 시스템에 적용하였다. Robust IMM 필터는 항공기 추적성능을 향상시킬 뿐만 아니라 항공기 위치 데이터가 손실되더라도 필터에서 계산한 추정값을 이용하여 지속적인 위치 추적을 가능하게 한다. 필터링 알고리즘을 차세대 항행시스템에 적용했을 때 평균 19.21%의 성능향상이 있었다. Among various fields of the CNS/ATM, the surveillance field which includes ADS-B system, MLAT system, and WAM system is implemented. These next generation systems provide superior performance in tracking aircrafts. However, They still have error. In this paper, filtering algorithm is proposed in order to enhance aircraft tracking performance of ADS-B, MLAT, and WAM systems. The proposed method is a Robust Interacting Multiple Model filter, called Robust IMM filter, that improves IMM filter. The Robust IMM filter can not only improves the aircraft tracking performance but also track aircraft continually using estimates calculated from the filter when data losses occur. The simulation results of the proposed aircraft tracking methods show that the filtering data provides a better performance up to an average of 19.21%.

Asynchronous wide area multilateration system

A new method for a location service in the wide area multilateration (WAM) system is outlined. This method, which is called asynchronous WAM (AWAM), enables calculation of the geographical position of an aircraft without knowledge of relative time differences (RTDs) between measuring ground stations (sensors). The AWAM method is based on the measurement of round trip times (RTTs) between the aircraft and the serving ground station, and the solution of a nonlinear system of equations with ten variables. The elimination of the RTD parameters significantly simplifies the localization process in real-life WAM system. The proposed asynchronous method could be an alternative solution for the synchronous one as a backup method during the system's failure or as an independent method. The paper concentrates on the description of the method, solving the nonlinear system of equations with ten variables and simulation results.

Potential accuracy of object localization with multilateration systems

Multilateration (MLAT) systems and wide area MLAT (WAM) systems are particular cases of multisite (multistatic) radar systems (MSRSs): passive MSRSs (PMSRSs) with known expected signal waveforms. One of the most stringent requirements on an MLAT system is a very high accuracy of target (emitter) localization. In view of this, the potential accuracy of emitter localization (PAEL) based on Cramer–Rao inequality is important. Its dependence on system geometry and time of arrival (TOA) measurement accuracy allows choosing reasonable system geometry and requirements on TOA measurements. PAEL for MLAT and WAM systems with different geometry is considered, including systems proposed for the Marco Polo airport in Venice, Italy. The possibility of velocity determination using PAEL for landing and taking off aircrafts is also discussed. The concept of PAEL permits one to analyze joint measurements of different signal parameters and target coordinates. The effect of additional elevation angle measurements on PAEL in the WAM system for the Marco Polo airport is shown.