Sect_8.4.2

8.4.2 Some Dual-Frequency Procedures

USING L1 AND L2 OBSERVATIONS

This is the simplest procedure, requiring a minimum of algorithm development. The double-differences (or triple-differences) are formed as discussed earlier, but for the L1 observations independently of the L2 phase observations. The differenced observables are then processed separately either:

to give a single solution in which the L2 observables are merely "extra" observations, strengthening the solution by virtue of an increase in redundancy (but not strengthening the geometry -- this is influenced by the length of observation session not by the "density" of observations),

to give two independent solutions, one an L1 only solution, the other an L2 only solution, the mean of which may be considered the "optimum" solution.

Both of these approaches are tantamount to assuming that between-station differencing eliminates the ionospheric biases. In the case of double-differences, the two types of observables are:

(8.4-1a)

and

(8.4-1b)

The n₁¹_(L2) ambiguities as well as the n₁¹_(L1) ambiguities have to be estimated. It is assumed that d_ion(L1) and d_ion(L2) are negligible and need no longer be considered. This approach suffers from a number of problems:

d_ion(L2) is larger than d_ion(L1) because the L2 frequency is lower than the L1 frequency.
The L2 observations tend to be "noisier" than the L1 observations, especially if the GPS receivers employ some variation of the "codeless" (or squaring) technique to track L2 (section 3.2.3).
Under Anti-Spoofing the L2 wavelength may not be , but half this value, that is 12cm.
d_ion tends to grow with increasing baseline length, as the ionospheric conditions at the two antennas decorrelate.

The first three problems make ambiguity resolution more difficult in L2-only double-difference solutions. The last point is the crunch. Because the ionospheric bias is not adequately handled for interstation distances of the order of 20km or greater, ambiguity resolution is often difficult, or not possible at all. There are better strategies for using dual-frequency observations for baselines longer than about 20km.

Among the other possibilities are to treat the L1 and L2 observations as two separate observation equations (as mentioned earlier), but to introduce a common ionospheric parameter linking the L1 and L2 observations (using eqn (6.4-2)) to be estimated as an epoch parameter in much the same way that clock errors are accounted for when processing undifferenced phase data. More specifically, at each epoch, the ionospheric parameters are estimated as weighted parameters with an apriori sigma _i. When _i --> 0 , the ionospheric bias contaminating L1 and L2 is assumed to have the characteristics of "white noise", and when _i --> , the solution is identical to the L3 ionosphere-free linear combination (BOCK et al , 1986).

Back to Chapter 8 Contents / Next Topic / Previous Topic