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

Abstract

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.