Aerospace and Electronic Systems Magazine August 2017 - 16

Flight Data Assessment of Tightly Coupled PPP/INS
solutions were iterated by making multiple passes over the data
in which GNSS data outliers were deleted from the final solution
using an iterative windowing approach similar to the approach adopted by Gross et al. [15]. With the iterative approach, once the
position solution between successive data passes agreed to the
centimeter level, the solution was accepted as final. The reference attitude solutions used in the error analysis are the filtered
and smoothed solutions reported by NovAtel SPAN postprocessing software.
For this study, all error comparisons are drawn with respect
to forward-filter solutions, as would be employed for real-time
applications. That is, the need for rapid convergence only applies
to real-time applications, because PPP solution convergence is
not a problem for postprocessing estimators that employ a backward pass through the data with a Kalman smoother. In addition,
throughout this error analysis, the estimation performance evaluation of the PPP filters is only conducted whenever the airplane is
at its science cruise altitude. The primary reason for starting the error comparisons at altitude is because postprocessed PPP reference
solutions are known to have the largest solution uncertainty during
the flight's ascent and decent periods, whenever the tropospheric
delay is rapidly changing and cannot easily be distinguished from
the vertical positioning error. Therefore, by eliminating these periods from the error analysis, and instead using the solutions only
at altitude, where the troposphere delays can be tightly constrained
to an input model, the periods in which the reference solutions are
expected to exhibit their largest uncertainty cannot skew the error analysis. Furthermore, because most airborne geodetic applications are only concerned with positioning accuracy during the

portion of the flight when the scientific instrumentation is active at
altitude, if the solution is lost during this period because of a large
bank, etc., the rapid convergence obtained with INS would help
maintain accuracy.

REAL-TIME PROCESSING STRATEGY
The dual-frequency ionosphere-free pseudorange and carrier-phase
data combinations were used for all filters. The measurement noise
assumed on every pseudorange and carrier-phase dual-frequency
observable was 2.5 m and 2.5 mm, respectively. The filter used
by RTGx is formulated as a generalized SRIF [48]. This formulation allows any modeled parameter to be estimated as a first-order
Gauss-Markov stochastic process (i.e., ranging from white noise
to random walk). Table 1 lists the stochastic models used for each
PPP and INS model parameter for the filters evaluated in this study.
For filter efficiency, we elected to perform system process
noise updates at 1 Hz (i.e., the same rate as the GNSS data).
However, because 1-s update intervals are longer than the 100Hz INS integration intervals, the INS process noise becomes correlated among the navigation states (i.e., off-diagonal terms exist). Fortunately, this correlation can be analytically propagated
[39]. However, in this study, for simplicity, standard uncorrelated
process noise updates were used. To arrive at the values listed in
Table 1, the IMU stochastic model parameters were initially assigned based on the expected range for a navigation grade IMU
provided by [39]. Empirical tuning was used increase them to account for the 1-Hz update interval and optimize the positioning
performance.

Table 1.

Selected Stochastic Model Parameters for PPP and PPP/INS Filters
Parameter

Only with INS

a priori σ

Position

0.5 m

m
5 s

∞

Troposphere wet
zenith delay

0.05 m

m
5e-7 s

∞

Receiver clock

1,000 m

m
1,000 s

Phase biases

3e8 m

m
0 s

∞

Velocity

Yes

2.0 m/s

m
0.28e-3 s

∞

Attitude

Yes

5.0 deg

deg
4e-5 s

∞

Accelerometer
biases

Yes

m
0.05 s2

m
s2
0.263e-4 s

∞

Gyroscope biases

Yes

2.8 deg/s

deg
s
4e-5 s

∞

IEEE A&E SYSTEMS MAGAZINE

Process Noise

Correlation Time

AUGUST 2017

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