User`s guide

Chapter 3 - Receiver Descriptions
In most surveying systems and instruments, there are more measurements taken than are
required to compute the solution. The excess measurements are redundant. A system can use
redundant measurements in an averaging scheme to compute a blended solution that is more
robust and accurate than using only the minimum number of measurements required. Once a
solution is computed, the measurements can be inspected for blunders. This is the essence of T-
RAIM.
In order to perform precise timing, the GPS receiver position is determined and then the receiver
is put into Position-Hold mode where the receiver no longer solves for position. With the position
known, time is the only remaining unknown. When in this mode, the GPS receiver only requires
one satellite to accurately determine time. If multiple satellites are tracked, then the time solution
is based on an average of the satellite measurements. When the average solution is computed, it
is compared to each individual satellite measurement to screen for blunders. A residual is
computed for each satellite by differencing the solution average and the measurement. If there is
a bad measurement in the set, then the average will be skewed and one of the measurements
will have a large residual. If the magnitude of the residuals exceeds the expected limit, then an
alarm condition exists and the individual residuals are checked. The magnitude of each residual
is compared with the size of the expected measurement error. If the residual does not fall within a
defined confidence level of the measurement accuracy, then it is flagged as a blunder. Once a
blunder is identified, then it is removed from the solution and the solution is recomputed and
checked again for integrity.
A simple analogy can be used to demonstrate the concept of blunder detection and removal: a
table is measured eight times using a tape measure. The measurements are recorded in a
notebook, but one of the measurements is recorded incorrectly. The tape measure has 2 mm
divisions, so the one-sigma (1σ) reading error is about 1 mm. This implies that 95% of the
measurements should be within 2 mm of truth. The measurements and residuals are recorded in
the table on the following page. From the residual list, it is clear that trial six was a blunder. With
the blunder removed, the average and residuals are recomputed. This time, the residuals fall
within the expected measurement accuracy. This is shown in Table 3.4 below.
Table 3.4: Blunder Detection Example
Trial
Measurement
(m)
Residual
(mm)
Status New Residual (mm)
1 9.998 14.5 OK 2
2 10.001 11.5 OK -1
3 9.999 13.5 OK 1
4 10.000 12.5 OK 0
5 10.002 10.5 OK -2
6 10.100 -87.5 removed
7 9.999 13.5 OK 1
8 10.001 11.5 OK -2
Ave 10.0125
10.000
Motorola GPS Products - M12+ User's Guide Revision 6.X 09FEB05
23