Aerospace and Electronic Systems Magazine August 2017 - 12

Flight Data Assessment of Tightly Coupled PPP/INS
operationally used with the GDGPS to generate real-time GNSS
products, and it underlies the navigation software for the ongoing
development of the U.S. Air Force's next-generation GPS operational control segment [38].

ALGORITHM FORMULATION
This section provides an overview of the PPP/INS integration architecture and a detailed discussion of the INS formulation used
within RTGx. The PPP observation models are not covered in this
article, because they were not modified within RTGx for this study.
For a review on the PPP observation models, refer to [11].

INTEGRATION ARCHITECTURE
The integration of INS with GNSS is possible at different levels,
namely, loosely coupled, tightly coupled, or deeply coupled [39].
In a loosely coupled architecture, GNSS and INS are processed
individually and then combined in a Kalman filter at the state estimate level. In a tightly coupled architecture, INS estimates are
used to model individual GNSS observables before combining into
a single centralized estimation filter. These two integration methods have been used extensively for kinematic applications [27],
[28], [40], where it has been shown that estimation performance
is similar for both integration architectures for docile platforms,
but the tightly coupled architecture is known to have an advantage
in more dynamic situations or situations with few GNSS observations. The deeply coupled integration architecture uses the inertial
information within the correlation process of the receiver's baseband processor [41]. This approach has the benefit of better tracking and reacquisition of GNSS signals that are at reduced power
levels [42]. However, deeply coupled integration requires GNSS
receiver modifications and is therefore not applicable for use in
RTGx. As such, the tightly coupled GNSS/INS architecture was
adopted for integration in RTGx.
Schematically, the tightly coupled architecture is shown in
Figure 1, which depicts the estimation of GNSS observables,
within the Kalman filter (in our case, RTGx uses a functionally
equivalent square-root information filter (SRIF)), using the inertial
data and precise ephemeris information. The model predicts error
states using the difference between the INS-predicted GNSS observables and the measured GNSS observables. For the PPP/INS
filters, the estimated state vector is shown in (1) and is composed
of the following:
C

δvi is three INS velocity errors in ECI.

δri is three INS position errors in ECI.

δΨib is three INS attitude errors, where attitude is defined between the Earth-centered inertial (ECI) i and aircraft bodyaxis b frames.

Figure 1.

Tightly coupled GPS/INS integration schematic.
C

δtu is receiver clock bias.

Tw is the wet zenith tropospheric delay estimate.

N1...j are GNSS carrier-phase bias estimates.

 δΨ ib 
 i 
 δv 
 δ ri 
 accel 
 bb 
 b gryo 
b

x=
 δ tu 


 Tw 
 N1 


  
 N 
 j 

(1)

An additional important aspect of tight GNSS/INS depicted is
Figure 1 is the closed-loop nature of the system. In particular, the
estimated IMU sensor biases are fed back to correct the raw IMU
measurements and thus reduce the INS prediction errors. Furthermore, after each GNSS update, the position, velocity, and attitude
estimates determined by the INS are corrected by the estimated error states. For the position and velocity estimates, this is done with
simple subtraction. For the attitude, small-angle approximations
are used to correct the INS estimates:
Cbi = ( I − δΨ ib ) Cˆ bi ,

(2)

where Cˆ bi is the body-to-ECI direction cosine matrix (DCM) populated with the INS estimated attitude.

INS MECHANIZATION

b
a

b is three IMU triaxial accelerometer sensor biases in the
aircraft body axis.
bgb is three IMU triaxial gyroscope sensor biases in the aircraft body axis.

As depicted in Figure 2, the INS mechanization is composed of
three steps: attitude update, velocity update, and position update.
This section summarizes the INS mechanization in the ECI reference frame, which is offered in greater detail in numerous texts
[39], [43]. The ECI INS mechanization was selected for implementation in RTGx, because ECI was already the frame used for as-

IEEE A&E SYSTEMS MAGAZINE

AUGUST 2017

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