In the context of space applications, the GPS system is presently a well-established and accepted tracking system. To meet the basic navigation requirements, most satellites in a low Earth orbit are equipped with single-frequency GPS receivers that measure the coarse acquisition code as well as the L1 phase. However, the resulting kinematic navigation solutions exhibit systematic position errors caused by elevation-dependent ionospheric path delays. In this study a simple analytical model is established, which quantitatively relates the position error to the vertical electron content and the mapping function. This model substantiates the empirical evidence of a mean radial offset that increases in proportion to the total electron content above the satellite. It is furthermore shown that the ratio between this offset and the vertical ionospheric path delay depends on the applied elevation mask angle. Representative ratios of 3--5 are obtained for the mapping function of the Lear ionosphere model and elevation cutoff angles of 10¿, 5¿, and 0¿. This analytical result has further been confirmed by signal simulator tests as well as flight data of the CHAMP satellite.