Development of a regional model for GPS inter-frequency biases over Egypt using trigonometric and polynomial functions

Errors in GPS receivers arise from multiple sources, including thermal noise, antenna phase center variations, inter-channel and inter-frequency biases, and receiver clock offsets relative to GPS time. A major challenge is estimating inter-frequency biases (IFBs) for stations outside the International GNSS Service (IGS) network, where predefined IFB products are unavailable. This limitation introduces significant uncertainty in bias correction and degrades the accuracy of derived positioning solutions. Reliable estimation of receiver IFBs for non-IGS stations is therefore essential to maintain precise positioning performance. In this work, we introduce the IFB Estimation Using Regional Modeling (IFBERM) framework, which enables single-station estimation and comparative Analysis of satellite and receiver IFBs across various GNSS receiver architectures over Egypt by combining three regional ionospheric models (GTSM, SCHM, and polynomial). The proposed method estimates satellite and receiver Instrumental Frequency Biases (IFBs) using the Generalized Trigonometric Series Model (GTSM) and a polynomial model applied to standalone dual-frequency carrier-smoothed GPS Pseudorange measurements via elevation-weighted least squares. We evaluated model performance across seven tracking stations in Egypt using 2015 GPS data by comparing estimates against the Spherical Cap Harmonic Model (SCHM) and official International GNSS Service (IGS) products. The results indicate that GTSM and SCHM achieve comparable, consistently high temporal stability (average satellite IFB standard deviations of ~0.30 ns and ~ 0.31 ns, respectively). In contrast, the polynomial model exhibits higher, site-dependent variability (averaging ~0.69 ns and reaching up to 3.77 ns at station Said). Following zero-mean constellation datum alignment, both GTSM and SCHM demonstrate strong quantitative agreement with IGS products, achieving Root Mean Square (RMS) errors of ~0.40 ns and Pearson correlation coefficients exceeding 0.996, proving statistically indistinguishable from global IGS baselines ( p > 0.05).