Development and Evaluation of Airborne Multipath Error Bounds for L1-L5

Abstract

Current aviation standards define a multipath error model that is valid after the smoothing filter is assumed to have converged (assuming a 100 s Hatch filter). The draft standards for dual frequency Satellite-based Augmentation Systems further specify an error model when the code has not been smoothed, and it is defined as a multiple of the converged value. In this paper, multipath and noise error bounds are derived as a function of smoothing time assuming a first order model for the code multipath and the receiver noise. These error bounds are evaluated using GPS and Galileo measurements collected in flight. The derived model appears to account well for the error reduction as a function of smoothing time. INTRODUCTION The standards for Satellite-based Augmentation Systems (SBAS) Dual Frequency Multi-constellation (DFMC) are currently being developed. With dual frequency, the residual ionospheric delay error (which is the largest contributor in single frequency) is no longer the dominant term. In particular, multipath and receiver noise is now a much more important term in the error budget. For this reason, and because of the introduction of new signals (L5 and E5a), these term is receiving more attention, and new data suggests that extrapolating L1 models to L5 and L1-L5 combination might not be sufficient [5]. This multipath and antenna group delay error model used in single frequency SBAS has been in place since 2000 [1]. This model is elevation dependent and only applies once the carrier smoothing filter has converged, which is assumed to occur after 360 s of smoothing. The current standards do not specify how the multipath error bound varies with smoothing time before convergence. The draft SBAS DFMC Minimum Operational Standards [2] (developed within EUROCAE) specifies an additional constraint: for unsmoothed code measurements, the standard deviation is ten times higher than the value at convergence. A strict application of this error model between t=0 and t = 360 s would result in very conservative error bounds, because in reality the actual errors decrease steadily as new measurements are added. In particular, it could result in significant performance losses in the presence of cycle slips. This is especially critical for environments with ionospheric scintillation (for example in low latitudes), where we expect a much higher cycle slip rate. And even if the receivers do use a less conservative multipath curve, service providers evaluating coverage would need to assume the minimum requirement, and therefore could be unable to claim availability where there might be. The goal of this paper is twofold: to derive a multipath error model that is valid before convergence, and to evaluate it using GNSS airborne measurements. In the first part, we develop three models: one corresponding to time invariant smoothing, one corresponding to time varying smoothing, and one where we start with a time varying smoothing that switches to time invariant after a set time interval. In the second part, we evaluate the multipath error model using GNSS data collected in flight. MULTIPATH ERROR MODEL AT CONVERGENCE In this paper, we will assume that the error model at convergence is given by the formulas specified in [2], which are based on the ones used in [1]: ( ) ( ) ( ) 4 4 2 2 1 5 & , , 2 2 2 1 5 L L air MP AGVD i noise i L L f f f f    + = + − (1) Where: ( ) 0.13[m] 0.53[m]exp( /10[deg]) MP    = + − (2) We will further assume that the temporal error model can be modeled as: ( ) ( ) ( )( ) ( )( ) 4 4 2 2 1 5 & , , 2 2 2 1 5 L L air MP MP AGVD i noise noise i L L f f k A k A k f f    + = + − (3) Where k is the time step, and AMP are Anoise are functions such that: ( ) ( ) ( ) ( ) 0 100, 360 1, 0 200, 360 1 MP