Aerospace and Electronic Systems Magazine August 2017 - 19

Watson et al.
Table 3.

Positioning Error Statistics with Real-Time Orbit and
Clock Products for Two Alaskan Flights after a 30Min Filter Convergence Period

Figure 8.

Example of troposphere zenith delay estimation error convergence
during the first 15 min of the real-time filter with and without INS
integration. Errors are estimated with respect to VMF grid delay estimation generated by accepting the position solution of the postprocess
ambiguity-fixed PPP reference.

Sensitivity to Troposphere Nominal and Mapping Function
To evaluate the positioning performance with respect to the method
used to model the troposphere, four troposphere modeling approaches were adopted: (1) a low-fidelity approach in which no wet or dry
nominal delay was provided to the filter, (2) a standard approach
in which a scale height was used to model the dry delay and the
wet delay is estimated, and (3) and (4) postprocessing approaches in
which both wet and dry delays are provided based on reference products. In each case, the positioning error sensitivity to the troposphere
nominal and model is summarized in Table 4. From Table 4, a 10-cm
reduction is seen in both standard deviation and rms positioning error because of INS integration regardless of the troposphere nominal
and modeling approach. This suggests that the INS enables better
separation of position estimates from the troposphere delay.

Median

PPPRT
PPP/
INSRT

An important benefit of INS is the availability of an attitude solution that is not present with only GPS. Table 5 shows good agreement of the RTGx/INS attitude solution with respect to the attitude
provided by the NovAtel SPAN system.
From both Table 5 and Figure 9, the heading error is noticeably
larger than the roll and pitch errors. This is expected because of the
nature of the flight. Each data set is composed almost entirely of
long periods of straight and level flight. During these flight conditions, it is well known that IMU yaw biases have issues with
respect to observability [50].

CONCLUSIONS
For airborne geodetic applications that need accurate positioning,
require long-baseline flights, and are flying in locations that are
distant from a dense GNSS ground reference station network, the
PPP processing technique is favorable over RTK or NRTK. However, in real-time applications, it is well known that PPP, when
compared to RTK, is slower to converge to accurate positioning.
This slow convergence property may become an issue in real time

rms

Max.

9.7

11.3

7.6

13.2

43.2

9.2

11.3

6.8

13.6

43.6

Table 4.

Positioning Error Sensitivity to Troposphere Nominal
Model and Mapping Functions
3DRSOS
(cm)

Median

PPPNo

38.4

43.8

31.6

54.0

394.7

35.1

36.4

21.2

42.1

262.4

11.3

19.1

27.9

33.8

312.8

11.2

15.3

17.6

23.3

227.0

10.8

19.5

28.2

34.3

306.4

11.2

16.0

18.0

24.0

254.4

11.2

18.6

28.1

33.7

306.1

11.2

14.6

17.6

22.9

266.5

rms

Max.

Nom., Neill

PPP/
INSNo
Nom, Neill

PPPStatic
Nom., Neill

PPP/
INSStatic
Nom., Neill

PPPGPT2
Nom., GMF

PPP/
INSGPT2

ATTITUDE ESTIMATION

AUGUST 2017

3DRSOS
(cm)

Nom.,GMF

PPPVMF1
Nom., VMF1

PPP/
INSVMF1
Nom., VMF1

NOTE: All filters use real-time orbits and clocks.

Table 5.

Attitude Error Statistics for Two GRAV-D Alaska Flights
|Error|
(deg.)

Median

Max.

0.35

0.33

0.24

1.10

0.09

0.11

0.10

0.95

2.17

3.10

2.70

15.61

NOTE: Errors are calculated with respect to the onboard realtime NovAtel SPAN estimates as a reference.

IEEE A&E SYSTEMS MAGAZINE

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