## 1. Introduction

[2] The geomagnetic field **B** is a fundamental parameter in the magnetoionic theory. The dependency of the ionosphere refractive index on the **B** field vector impacts performance of satellite-based communication, navigation, and surveillance systems by causing signal group delays, carrier phase advances, signal distortions and bending, Doppler frequency shifts, and Faraday rotation [*Ratcliffe*, 1959]. In particular, this paper was motivated by the need to characterize the Global Positioning System (GPS) range measurement error due to higher order ionosphere group delay and carrier advances. Satellite navigation signals traversing the ionosphere have range measurement errors that can be represented as follows:

where *I*_{ρ} and *I*_{ϕ} represent the range error associated with a GPS receiver's code and carrier observables respectively. *RX* denotes the receiver, and *SV* the satellite. *n*_{ρ} is the signal group refractive index and is related to the carrier refractive index *n* by the relationship

[3] *Bassiri and Hajj* [1993] expanded the Appleton-Hartree equation into a series of inverse carrier frequency power terms and applied the results to Equations (1), (2), and (3):

where

*e* is electron charge, *m*_{e} is electron mass, ɛ_{0} is the permittivity of free space, θ_{B} is the angle between the signal and the magnetic field, and TEC is total electron content.

[4] The terms involving *q*, *s*, and *r* are functions of , , and in Equations (4) and (5) and are commonly referred to as the first, second, and third order ionosphere error terms. The first order error does not depend on the geomagnetic field and can be eliminated from the range measurements by linearly combining the observables obtained at two different frequencies, available to any dual-frequency GPS receiver [*Klobuchar*, 1996]. The second and third order terms, however, are functions of the geomagnetic field and electron density distributions along the signal propagation path and are collectively referred to as the higher order ionosphere error in GPS measurement error budget.

[5] There are a number of studies on the higher order ionosphere errors in GPS measurements [*Bassiri and Hajj*, 1993; *Brunner and Gu*, 1991; *Datta-Barua et al.*, 2008; *Hoque and Jakowski*, 2008; *Kedar et al.*, 2003; *Morton et al.*, 2009]. These works have assumed a simple dipole field model [*Bassiri and Hajj*, 1993; *Kedar et al.*, 2003], or applied a mean International Geomagnetic Reference Field (IGRF) model value at a certain height to the entire path [*Brunner and Gu*, 1991; *Datta-Barua et al.*, 2008; *Hoque and Jakowski*, 2008] to obtain the bounds of the ionosphere higher order error. *Morton et al.* [2009] computed the IGRF model along signal propagation path to derive the temporal and spatial variations of the error. The question remains: how accurate is the IGRF model in describing the total magnetic field?

[6] *Lowes* [2000] and *Lowes and Olsen* [2004] give in-depth analyses of potential errors in IGRF-type models, and the magnitude of possible variance in the coefficients from a variety of sources. For an engineering application, however, we may be more interested in the worst case difference in real-world measured magnetic field strength versus prediction, due to whatever unmodeled, sporadic, or even unknown effects are operating. These include external and induced fields, ionospheric currents, magnetic storms, short-wavelength fields, and other events not accounted for by the model. Indeed, the creators of geomagnetic main field models go to great lengths to exclude the effects of ionospheric currents and interplanetary fields, which could be important in signal propagation.

[7] The objective of this work is to validate the IGRF model and its secular variation using space-based magnetometer measurements. These measurements are taken by magnetometers on board Low Earth Orbit (200–1000 km altitude) (LEO) satellites from 1991 through 2010. An excess of 70 GB of raw measurement data have been processed to provide magnetic field measurements in the ionosphere under a wide range of conditions, including all Kp levels, times of day, and times of year. The IGRF model is used to generate the **B** field values corresponding to the measurements' location and time. Extensive analysis of the differences between the model and measurement is presented in the paper. Our results show that the IGRF provides remarkable accuracy in predicting the magnetic field values in the ionosphere measured in the time since its release. Accuracy does decline near the end of a generation's 5 year purview.

[8] Section 2 provides a brief summary of the IGRF model and characteristics of the global **B** field distribution as represented by the IGRF model. Section 3 describes the satellite missions, instruments, and data for the magnetic field measurements, and section 4 describes our methods of filtering and processing the data. Section 5 presents the results and analysis of the comparison between the IGRF model and the measurements, and section 6 discusses the results in more detail. Section 7 introduces potential further work, and section 8 concludes the findings of this study.