Receiver Noise, ερ and εφ
Receiver noise is directly related to thermal noise, dynamic stress, and so on in the GPS receiver itself. Receiver noise is also an uncorrelated error source.
The effects of receiver noise on carrier phase measurements symbolized by εφ, like multipath, are small when compared to their effects on pseudorange measurements, ερ. Generally speaking, the receiver noise error is about 1% of the wavelength of the signal involved. In other words, in code solutions, the size of the error is related to chip width. For example, the receiver noise error in a C/A code solution can be around 3m which is about an order of magnitude more than it is in a P code solution, about 3cm. And in carrier phase solutions, the receiver noise error contributes millimeters to the overall error.
Receiver noise is inevitable, and it must be considered. It is a relatively small contributor to the GPS error budget, in most cases. It is an uncorrelated error, meaning that both multipath and the receiver noise are not related to the length of the baseline between GPS receivers. They are uncorrelated in that regard.