Theoretical evaluation of group delay on pseudorange bias

The phenomenon of pseudorange bias, which is also called S-Curve bias, becomes more obvious with the combined use of multiple satellite systems or navigation satellites with different phases. The different characteristics of the transmitting channel of a navigation satellite result in different distortions of the pseudorange bias in navigation signals; in particular, this issue worsens when the RF channel is not optimized to decrease the pseudorange bias. Therefore, it is interesting to reveal the essential relationship between pseudorange bias and the non-ideal channel and to present an analytic model of the effect of a non-ideal channel on pseudorange bias. Instead of using the numerical method of finding the bias of the zero-crossing point of the discriminator, we provide a theoretical evaluation of the S-Curve bias for the given parameters of channel and signals. Based on the model and presented analyses, we find that second-order group delay plays an important role in the distortion of S-Curve bias and should be avoided in the design of the RF channel for navigation satellites and receivers.