Differential GPS - Understanding GPS: Principles and Applications - page 411

ments making up the least-squares residual vector (parity space). The partitioning
of (8.27) is:

T

Rb QDD
u

= (8.28)

float u s

0qDD = (8.29)

s

Solving (8.28) gives the floating baseline solution:

− 1 T

b RQD
float

= (8.30)

u u s

Equation (8.29), while ideally equal to zero, is the least-squares residual vector
and can be exploited to provide the means for resolving the carrier-cycle integer
ambiguities, a discussion of which follows in the next section. The floating baseline
solution is freshly calculated for each epoch and serves as a temporal benchmark
during the ambiguity resolution process while the fixed baseline solution is being
pursued. Once the fixed baseline solution is in hand, the floating solution subse-
quently serves as a cross-check to ensure the continued integrity of the former.
Recall that this is a dynamic process—one end of the baseline is usually in motion
(e.g., airborne)—thus, both the fixed and floating baseline solutions will vary from
epoch to epoch and must be constantly monitored. On the other hand, the carrier-
cycle integer ambiguities, once resolved, remain fixed in the solution since the
receivers dynamically track the change (i.e., growth or contraction) in the number
of carrier cycles between the baseline antennas and the respective SVs used in the
solution for the baseline. This holds true as long as all SVs remain in constant track
by the receivers with no cycle slips occurring.

8.4.1.6 Carrier-Cycle Ambiguity Resolution
Using the complementary Kalman filter to produce the smoothed-code DDs insures
that each of the DD measurements contributes to a solution whose accuracy is
within 1-2m, as previously stated. In terms of integer wavelengths at L1, for exam-
ple, the DDs values are each within about . Intuitively, it would seem possi-

ble to iterate each DD through this range of carrier wavelengths, recalculate the
least squares solution for each iteration, and then examine the residuals. Residuals
“near” to zero, since there is noise in the process, would be identified, and the num-
ber of integer wavelengths added to each of the DDs would be kept as a candidate
integer ambiguity set for the particular trial. This could be done on an
epoch-by-epoch basis, and those sets of integer ambiguities that continued to
remain valid would be marked and tallied. The list would diminish over time, and
eventually one set of integer ambiguities would emerge victorious. The approach
just described would take place in parity space, since we would be adjusting the
DDs measurements (iteratively) and subsequently examining the new set of
least-squares residuals that resulted. To search the uncertainty volume about the
floating baseline solution would be computational inefficiency at its extreme. For
example, an uncertainty of

± 5-10 λ

would require initially that 23 4 least-square solu-
tions be generated each epoch and the residuals for each examined. Even though the
number would diminish over time, the technique would in general remain

± 11 λ