Code Tracking Errors for Double Delta Discriminators with Narrow Correlator Spacings and Bandlimited Receivers

T.N. Morrissey, K.W. Shallberg, and B. Townsend

Abstract:	This work was motivated by the desire to more fully understand receiver code tracking error performance for both GPS and SBAS signals for receiver designs allowed in both the WAAS and LAAS MOPS. Of particular interest was tracking error for combinations of small receiver bandwidths, narrow correlator spacings and double delta receiver designs since there was concern that these receiver configurations may have tracking performance inconsistent with that specified in the MOPS. The approach for characterizing double delta code tracking error primarily built on the previous work of Fenton, Van Dierendonck and Betz. Previous theory for code tracking error developed by Fenton and Van Dierendonck provided expressions for early minus late receiver designs with narrow correlator spacings, but for relatively large precorrelation bandwidths (essentially infinite bandwidth). This theory was subsequently extended by Betz to the case of finite receiver bandwidths, including the development of closed form expressions of early-minus-late code tracking error for the case of ideal bandpass (brick wall) receiver filter characteristics. The analysis reported in this paper extends the above theories to arbitrary receiver filters and to double delta discriminators by incorporation of a linearized discriminator model characterized by its slope at equilibrium and an effective additive noise variance. The latter parameters are calculated numerically from the User receiver filter attenuation and group delay characteristics, the discriminator type and correlator spacings, the input carrier-to-noise ratio (CNR), and the delay lock loop bandwidth and integration time. This linearized discriminator approach was validated over the parameters of interest by Monte Carlo simulations using nonlinear discriminator characteristics. This paper documents these conclusions and associated assumptions and provides theoretical and laboratory code tracking results for early-minus-late and double delta discriminators for a wide variety of receiver filters and correlator spacings, for both GPS and GEO input signals. It is anticipated that this paper will be of value to those conducting research in SBAS or GBAS arenas since some of the techniques described lend themselves to Evil Waveform analysis and requirements validation.
Published in:	Proceedings of the 2006 National Technical Meeting of The Institute of Navigation January 18 - 20, 2006 Hyatt Regency Hotel Monterey, CA
Pages:	914 - 926
Cite this article:	Morrissey, T.N., Shallberg, K.W., Townsend, B., "Code Tracking Errors for Double Delta Discriminators with Narrow Correlator Spacings and Bandlimited Receivers," Proceedings of the 2006 National Technical Meeting of The Institute of Navigation, Monterey, CA, January 2006, pp. 914-926.
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