RTK with GPS L2

I wonder what is the role of L2 signal in an RTK system (since the expensive RTK setups seem to use L1+L2) - how much precision/accuracy will it add to the system?

The more observations you have the better the accuracy and robustness of the solution - generally speaking. So the L2 observations provide this.

However the main benefit of having L2 is to remove ionosphere errors - the signals from the satellite are “slowed” as they pass through the ionosphere. Different locations of the iono will affect the signals more than others depending on scintilation. Having two frequencies simultaneously from the same source (satellite) allow the determination of the iono error as opposed to trying to model it. This allows for longer baselines between rover and base station without losing accuracy and generally a better and more robust solution. You will note a degradation of the Reach (indeed any L1 only solution) over longer baselines (approx >5km) during periods of high solar activity.

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Ok, so the point of having 2 signals (L1 and L2) is that one can compare these signals to determine the error? Wont both signals have the same (unknown) error since they travel exactly the same way? Or will the different frequency cause the errors to be different (and thus allow for some kind of correction even without base station)?

I found some explanation for L2 with RTK here - see the “L1/L2 RTK or RTK Integer” section.