Sect_6.4.4

6.4.4 Dual Frequency Relations

"WIDE-LANE" COMBINATION

This is also sometimes referred to as the "L5" combination. Instead of subtracting the L2 observation from the L1 observation in metric units, the phase equations can be differenced ((6.4-3a) & (6.4-3b)):

(6.4-16)

This is known as the "wide-lane" combination because the effective wavelength of the resultant observable is 0.86 metres. The n₅ ambiguity is:

n₅[cycles] = n₁ – n₂

Hence n₅ is an integer, however each cycle has a 0.86m wavelength. Eqn (6.4-16) can be converted to metric units through multiplication with the wavelength ₅:

(6.4-17a)

or in terms of the L1 ionospheric delay (using eqn (6.4-2)):

(6.4-17b)

Hence the L5 ionospheric effect is approximately 1.28 times that affecting L1 observations (1.28 f₁ / f₂). However, the noise on L5 observables is approximately six times (Table in section 6.4.6) that on L1 observables!

It can be shown that eqn (6.4-17) is the same expression for the L5 observable if constructed from the P1 and P2 pseudo-range observations except that there is no ambiguity term, and the sign of the ionospheric delay is reversed :

(6.4-17c)

(Hint: convert eqns (6.4-10) to cycles, difference the expressions and then scale them back to metric units using ₅). The wide-lane pseudo-range is therefore advanced by the ionosphere (range too short), while the wide-lane phase is delayed by the ionosphere (phase-range too long).

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