6.4.7 Dual Frequency Relations

CARRIER PHASE & PSEUDO-RANGE COMBINATIONS

The combination of single or dual-frequency phase and pseudo-range data can be useful for several purposes:

• Cycle ambiguity resolution (sections 8.2, 8.3 and 8.4).
• Cycle slip detection (section 8.4).
• Ionospheric studies.
• Pseudo-range multipath studies.
• Smoothing of pseudo-range data.

To aid the following discussion the pseudo-range and carrier phase observation equations are expressed as follows (see eqns (6.4-3) & (6.4-10), without subscripts and superscripts, and without the explicit inclusion of the tropospheric, orbit and clock error bias terms, but with the addition of the measurement noise terms):

(L1) = – dion(L1) + n(L1) + (1)	(6.4-23a)
P(L1) = + dion(L1) + (P1)	(6.4-23b)
(L2) = – dion(L2) + n(L2) + (2)	(6.4-23c)
P(L2) = + dion(L2) + (P2)	(6.4-23d)

The following comments can be made:

• The differences between the pseudo-range data and the carrier phase data are: (a) the ambiguity terms, (b) the reversal in the sign for the ionospheric delay, and (c) the significantly larger noise term associated with pseudo-range data.
  
• The multipath terms are not included, however, the pseudo-range data is more sensitive to multipath (hence a larger magnitude term) than carrier phase data.
  
• The additive combination of pseudo-range and carrier phase data (made with respect to the same frequency carrier wave) leads to the elimination of the ionospheric delay.
  
• The subtractive combination of pseudo-range and carrier phase data (made with respect to the same frequency carrier wave) leads to the elimination of the geometric range term and hence leads to the highlighting of the ionospheric delay for further study.
  
• The additive combination of L1 pseudo-range and L1 carrier phase data results in the elimination of the ionospheric delay on L1, while the additive combination of L2 pseudo-range and L2 carrier phase data results in the elimination of the ionospheric delay on L2. The subtractive combination of these two L1 and L2 observables results in the elimination of the geometric range term and the elimination of the ionospheric delay.
  
• The subtractive combination of L1 pseudo-range and L2 pseudo-range data results in the elimination of the geometric term and isolates the difference in ionospheric delay between L1 and L2, while the subtractive combination of L1 carrier phase and L2 carrier phase data also results in the elimination of the geometric term and isolates the difference in ionospheric delay between L1 and L2.

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© Chris Rizos, SNAP-UNSW, 1999