1. Dorota A. Grejner-Brzezinska
Integrated GPS/INS System in Support of Direct Geo-referencing
Dorota A. Grejner-Brzezinska
Civil and Environmental Engineering and Geodetic Science
The Ohio State University
470 Hitchcock Hall
Columbus, OH 43210
Tel. (614)
OSU

2. Presentation outline Direct georeferencing concept
GPS/INS integration for positioning and orientation
INS component
GPS component
Primary integration architectures
Summary

3. Georeferencing: the Concept (1)
Sensor orientation, also called image georeferencing, is defined by a transformation between the image coordinates specified in the camera frame and the geodetic (mapping) reference frame.
requires knowledge of the camera interior and exterior orientation parameters (EOP)
interior orientation: principal point coordinates, focal length, and lens geometric distortion are provided by the camera calibration procedure
exterior orientation: spatial coordinates of the perspective center, and three rotation angles known as , , and 

4. Georeferencing: the Concept (2)
Traditional aerial surveying
EOP determined from the aerotriangulation, defining correlation between ground control points and their corresponding image representations
requires scene pre-targeting
high cost
labor intensive

5. Georeferencing: the Concept (3)
Modern aerial surveying
EOP determined directly from integrated sensors such as GPS/INS or GPS antenna array
no scene pre-targeting (no ground control, except for GPS base station)
no aerotriangulation
low cost
allows automation of the data image processing

6. Automation of Aerial Survey
System augmentation by an inertial sensor offers a number of advantages over a stand-alone GPS
immunity to GPS outages
continuous attitude solution
reduced ambiguity search volume/time
high accuracy and stability over time contributed by GPS, enabling a continuous monitoring of inertial sensor errors
Result  direct platform orientation (geo-referencing)

7. A Comparison of Mapping Scenarios
Planning D a t e T i m S c l .
Compilation
and Editing
Distribution
Aerial Photography
Cost
Cartographic
Finishing
Aerotriangulation
Reproduction
Ground Control
Film Processing
A Comparison of Mapping Scenarios
Conventional
Direct Orientation

8. Direct Geo-referencing
Increased interest in the aerial survey and remote sensing community
need to accommodate the new spatial data sensors (LIDAR, SAR, multi/hyperspectral)
cost reduction of aerial mapping
decreased need for control points
maturity and cost-effectiveness of GPS/INS systems
GPS multi-antenna systems for less demanding applications
GPS/INS systems available:
experimental - University of Calgary, Center for Mapping OSU
commercial - Applanix

9. Direct Orientation Airborne System
INS
Position & Attitude
(x, y, z) and (, , )
GPS
Position & Time
(x, y, z)
Imaging
Stereo Digital Images
Digital Elevation Model
Digital Orthophoto
Hypsography Hydrography
Topography

10. Direct Orientation Land-based System

11. For precise spatial positioning

12. Direct Orientation Land-based System
Digital camera
GPS antenna
INS

13. Direct Orientation Airborne System
GPS Antenna
INS PC
Two Base Stations
Camera
GPS Receiver

14. Direct Georeferencing
ZBINS
XBINS XC YC
YBINS ZM XM YM
rM,k
rm,i,j
rM,INS
3D INS coordinates in mapping frame
3D object coordinates in model frame (derived from i,j stereo pair) attached to C-frame
3D coordinates of point k in M-frame
boresight matrix between INS body frame and camera frame C
rotation matrix between INS body frame and mapping frame M, measured by INS
boresight offset components
scaling factor s

15. GPS/INS Integration for Direct Orientation (direct geo-referencing) of the Imaging Component

16. Principles of Inertial Navigation
Principles defined in the i-frame (inertial)
Real time indication of position and velocity of a moving vehicle using sensors that react on the basis of Newton’s laws of motion
these sensors are called Inertial Measurement Units (IMU)
accelerometers
sense linear acceleration in inertial frame
does not sense the presence of a gravitational field
gyroscopes (sense rotational motion)
facilitate the rotation between navigation and INS body frames (in fact rotation with respect to the inertial frame is measured)
Integration with respect to time of the sensed acceleration to obtain velocity, and subsequent integration to obtain position

17. Coordinate Frame Geometry

18. Inertial Navigation System (INS)
Provides self-contained independent means for 3-D positioning
Three gyros and three accelerometers (or less)
Accuracy degrades exponentially with time due to unbounded positioning errors caused by
uncompensated gyro errors
uncompensated accelerometer errors
fast degradation for low cost INS
High update rate (up to 256 Hz)
Mechanical (stabilized platform) systems
sense acceleration in inertial frame coordinatized in navigation frame
Strapdown systems (digital)
sense acceleration in inertial frame coordinatized in body frame

19. INS LN-100 Body Axes -Y -X Z

20. Primary Error Sources
The main sources of errors in an inertial navigation are due to the following factors:
The time rates of change of the velocity errors are driven chiefly by accelerometer errors and gravity anomalies
The attitude error rates are driven primarily by gyroscope errors
Three basic classes of errors
physical component error: deviation of inertial sensors from their design behavior (drifts, bias, scaling factors)
construction errors: errors in overall system construction such as mechanical alignment errors
initial conditions: errors that arise from imperfect determination of the initial position error, initial velocity error, and initial platform misalignment

21. Comparison of GPS and INS Free Navigation Trajectories (Road Test)
0.4
0.8
1.2
1.6
2.0
(Latitude = 39.99°
Longitude = )
1.1
2.2
3.3
4.4
5.5
6.6
7.7
8.8
East Distance (km)
North Distance (Km)
GPS:
INS:
GPS start &
end position
Total Time 1867s
INS end
position

22. Strapdown INS
Strapdown system algorithms are the mathematical definitions of processes, which convert the measured outputs of IMUs that are fixed to the vehicle body axis, into quantities that can be used to control the vehicle (attitude, velocity and positions)
The outputs are angular rates and linear velocities along the orthogonal axes
The measured angular rates are converted into changes in attitude of the vehicle with respect to its initial orientation
The resulting attitude transformation matrix is used to convert the measured velocities from body axes to the reference coordinate system
The major algorithms are:
Start-up
Initialization
Generation of the transformation algorithm
Navigation

23. Strapdown INS Start-up
the operational readiness is determined immediately after the power is turned on, by buit-in stimuli-response go/no go tests
this tests isolate system faults to a single gyro or accelerometer or control electronics
Initialization
as a dead reckoning device, it INS must know the initial conditions of the position and velocity from the external source
direction of the initial velocity vector is determined by the process of alignment
may include self-calibration

24. Initial Alignment
Process of initially locating the sensitive axes of the accelerometers with respect to the reference or navigation coordinate system axes (transformation matrix)
can be autonomous (without recourse to other equipment)
self-leveling: in the stationary mode it is accomplished by initial computation of the direction cosine transformation matrix to force the transformed velocity to have zero components in the horizontal reference directions
gyrocompassing: closed-loop process of locating true North by computing heading as an element of the transformation matrix that has been initially leveled (analogous to torquing the gimbals until the East gyro angular rate measurement is nulled)
can measure total drift rate about the vertical axes by recursive solution (self-calibration)
or slaved (by matching the starpdown system outputs to some external system

25. Strapdown INS Alignment
Coarse Alignment
For stationary system utilizes the gravity and earth rotation vectors as well as accelerometer and gyro outputs to determine the initial estimate of the transformation matrix (no sensor errors assumed)

26. Coarse Self-Alignment Using Analytic Alignment Scheme
Determination of pitch angle q and the roll angle f
where
are the accumulated accelerometer outputs during the
time interval D T
Determination of azimuth angle y

27. Strapdown INS Alignment
Self-Corrective Alignment
because an initial estimate of the transformation matrix is available from the initial (coarse) alignment, the misalignment between the body and navigation frames can be modeled as a small angle rotation
the updating method consists of detecting error angles between these two frames via the processed accelerometer and gyro signals and generating a signal to the transformation computer in order to drive these angles as close to zero as possible
at the same time compensation is provided for the disturbance angular vibration

28. Alignment (Optimal Estimator)
Calculated
Velocity D V ib b D V n D V n ib nb
Body-Mounted
Accelerometers f d t ( ) ò C n
Known
Velocity b _ + _ + _
Gravity
Computation
Known
Position
Quaternion
Computation
for DCM
Euler Angle
Computation
Calculated
Attitude D q b nb D ib b q in b D q
Body-Mounted
Gyroscopes
Earth Rate
Computation _ +
Calculated
Heading _
Misalignment
Correction
Gyro drift
Correction
Misalignment
Estimator
Magnetic
Heading + _

29. Attitude Determination
Euler method
heading,pitch and roll, not suitable for strapdown system because the differential equations for their propagation contain trigonometric terms with singularities
nonlinear differential equations
Direction cosine method (DCM)
differential equations for DCM propagation are linear and very simple
the main disadvantage of DCM is that it has too many elements to be integrated
computational burden
Quaternion method

30. Attitude Determination
Quaternion method
quaternion Q is a quadruple of real numbers, Q = q0+q1i+q2j+q3k that evolve in accordance with a simple differential equation and are only one more in number than the minimum number required
three components define the axis of rotation, the fourth one – the amount of rotation
numerically stable characteristics
can be converted to direction cosines and Euler angles
preferred for strapdown systems
b, n are skew-symmetric matrices containing the rotation rates of the body-fixed frame w.r.t. inertial frame in body-fixed coordinates

31. Rotation Axis of Vector about which System a is Rotated in Order to Coordinate with System bZ

32. Error Sources in Numerical Solution
(critical for updating transformation matrix)
Commutation errors
result from fixed-sequence numerical processing in the strapdown algorithm
can be minimized by increasing the update rate
Integration errors
due to discrete approximate solution of a continuous process
can be minimized by implementing sophisticated algorithms and increasing the update rate
Round-off errors
due to finite resolution of data
can be minimized by using double precision for critical operations
Quantization errors
analog-to-digital conversion of sensor measured outputs
can be minimized by increased storage hardware and mathematical modeling

33. Navigation Equations
A general navigation equation that describes the motion of a point mass over the surface of the earth
f - acceleration due to applied force sensed by accelerometer
g(r) - gravitational acceleration
r – geocentric vector of vehicle position
v(t) – velocity of the vehicle relative to the earth defined in the navigation system
- earth rotation vector
- angular rate of the navigation frame relative to the earth

34. Navigation Equations (cont)
the Earth’s rotation rate; L is the geodetic latitude, and l is the longitude.
- the direction cosine matrix from body-fixed coordinates (b-frame) to navigation coordinates (n-frame)
the superscript “n” means a vector is coordinated in the n-frame

35. Strapdown Inertial Mechanization
Position
Velocity D V ib b D V n D V n
Body-Mounted
Accelerometers n ib nb C b + _
Gravity
Computation
Transformation
Matrix
Computation
Euler Angle
Computation
Attitude D q b nb D q b ib D q b
Earth and
Vehicle Rate
Computation
Body-Mounted
Gyroscopes in _ + D V b =
Delta velocity from accelerometers ib Dq b =
Delta q from gyros (angular rates) ib C n =
Direction cosine matrix from b-frame to n-frame b

36. Why GPS/INS Integration?
GPS and INS have complementary operational characteristics
GPS contributes its white error spectrum, high accuracy and stability over time, enabling a continuous monitoring of inertial sensor errors
Calibrated INS offers high short-term accuracy and high sampling rate
INS is self-contained; no outages
GPS/INS offers a number of advantages over a stand-alone GPS
immunity to GPS outages and reduced ambiguity search volume/time for the closed-loop systems
and more importantly, continuous attitude solution
Implementation of a closed-loop error calibration allows continuous, on-the-fly (OTF) error update bounding INS errors, leading to increased estimation accuracy
Two primary integration modes
Loose coupling
Tight coupling (closed-loop)

37. GPS/INS Integration Limitations High cost of high quality INS
Mission objectives (what INS is needed and what can be afforded)
How complex is the integration scheme required to achieve the emission objectives

38. GPS/INS Integration Loosely coupled mode
Separate filter to process GPS data
IMU measurements are processed by inertial navigation and attitude algorithms to give inertial position, velocity, and attitude solution
An integrated Kalman filter is then applied to combine the GPS and inertial solutions
The main disadvantage: positioning must be performed on the basis of IMU measurements alone when the number of tracked GPS satellites drops below four

39. GPS/INS Integration Tightly coupled mode
A single Kalman filter is designed to process both sets of sensor data: raw GPS observations and IMU measurements
OTF IMU error calibration by a feedback loop
Allows use of GPS measurements from less than four satellites
High accuracy of the inertial system over short periods of time allows correction of undetected cycle slips affecting GPS measurements
Makes it possible to perform a faster and more robust OTF ambiguity resolution
Offers a possibility to support GPS tracking loop by a direct feedback from the integrated filter to maintain tracking during high dynamics
Offers superior performance compared to loosely coupled mode

40. Computation Diagram for Loosely Integrated GPS/INS System
User Interface
Dialog/Menu
Get Data Processing
Control Parameters
Processing
Organizer
Initialization of
the Kalman Filter
INITIAL.DAT
Filtering/Smoothing
Uses differences
between INS
and GPS positions
UDU Kalman
INS Positioning
IMU.DAT
Supporting
Functions
SMOOTHER.DAT
GPS.DAT
INS Error Model
GPS Positioning
CONTROL.DAT

41. Architecture of Tightly Integrated GPS/INS System
IMU
Airborne
Receiver
Ground
Double Differential GPS Computation
IMU Error
Compensation
Strapdown Navigation Computation
OTF
Ambiguity
Resolution
Error DD
Observation
Generation
GPS/INS Kalman Filter
Construct
Model
Parameters
Covariance
Propagation
Optimal Gain
Computation
Update
State
Estimate
Measurement
Residual
Testing
Position &
Velocity
Coordinate
Transform
Quaternion
Euler Angle

42. Summary: Major Components of Integration Algorithm and Filter Design
Choice of coupling mode
Number of states that should be estimated
Whole-value filter states vs error states
How often should the filter be updated
How should the correlated measurements be treated
How to reduce the computational burden by proper exploitation of the sparseness of the dynamics matrix
How can the filter be used to detect the GPS or INS failure
How can filter be made robust against varying error characteristics of INS or GPS

43. Kalman Filter Model A: using Linear INS Error Model
INS Psi-Angle Error Model
v, r, and  are the velocity, position, and attitude error vectors respectively
is the accelerometer error vector
g is the error in the computed gravity vector
 is the gyro drift vector.
subscript b stands for bias
subscript f stands for scaling factor
Example: 24 INS States

44. Kalman Filter Model B: Using Nonlinear State Equation
v, r, and q are the velocity, position, and quaternion (associated with attitude determination) components
subscript b stands for bias
subscript f stands for scaling factor
Example: 25 INS States