Aerospace and Electronic Systems Magazine August 2017 - 17

Watson et al.

Figure 4.

Cumulative distribution of a 3DRSOS positioning error of the forwardfilter GPS solutions with and without INS. Both solutions are processed
using the PPP models in RTGx but with the Broadcast GPS orbit and
clock solutions.

RESULTS AND DISCUSSION
POSITIONING PERFORMANCE

Sensitivity to Orbit and Clock Products
For this sensitivity study, although all filters were run in forward
filter only as a real-time estimator to assess the sensitivity to orbit
and clock product quality, the use of final postprocessed GPS orbit
and clock products were used (i.e., knowing that final orbits and
clocks that are postprocessed could never be used in real time),
in addition to real-time orbits and clocks and the GPS broadcast
ephemeris. This was conducted to assess the impact of the quality of the orbit and clock products with respect to the benefits of
tightly coupled PPP/INS.

Table 2.

Positioning Error Statistics for Two Alaskan Flights
3DRSOS
(cm)

Median

GPSBrdc

128.6

GPS/
INSBrdc

115.6

PPPRT

rms

141.8

71.9

159.0

651.1

114.7

42.05

122.2

369.8

11.3

19.1

27.9

33.8

312.8

PPP/
INSRT

11.2

15.3

17.6

23.3

227.0

PPPFinal

10.9

19.4

28.9

34.7

297.5

PPP/
INSFinal

9.2

13.8

19.5

235.4

AUGUST 2017

Max.

Figure 5.

Cumulative distribution of a 3DRSOS positioning error of the forwardfilter PPP solutions with and without INS. Solutions that use both
GDGPS in real time and JPL's IGS final GPS orbit and clock products
are shown.

The positioning performance when using broadcast orbit and
clock products both with and without INS is depicted in Figure 4,
in which the cumulative distribution function of the residual sum
of squares (RSOS) for forward filter only shows the overall positioning error reduction because of the incorporation of INS. This
also appears in Table 2, where the INS solution is shown to yield
approximately a 30-cm reduction with respect to position mean,
standard deviation, and rms errors.
The sensitivity of the positioning performance when using
real-time and final orbit and clock products is shown in Figure 5,
where there is an approximately 1-m error reduction with respect
to positioning performance obtained using broadcast products.
One of the most notable insights drawn from Table 2 is that the
PPP/INS using real-time products outperforms the PPP filter even
when using final orbit and clock products with respect to rms and
standard deviation errors. This is significant, because it suggests
that INS reduces the latency needed to produce the highest-quality
positioning performance. Furthermore, it is apparent that the GPSonly PPP solutions with real-time and final products are largely
equivalent (i.e., within a centimeter for most metrics) but that there
is an additional 2-3 cm error reduction with respect to metrics reported in Table 2 when comparing the PPP/INS solutions that use
real-time products and final products. This suggests that it is beneficial to use INS even when final orbits are available.

Convergence Improvements with INS
The clearest benefit of tight-INS integration within PPP is the reduction of the solution convergence time. This is depicted with
respect to estimated states in Figures 6-8. Figure 6 shows a substantial benefit of INS integration with respect to positioning during the first half-hour of the real-time PPP solution.
In Figure 6, the tight-INS PPP filter converges to less than 10cm errors within a few minutes, whereas the GPS-only PPP fil-

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Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine August 2017