State Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions

195 Pages·2016·3.76 MB·English

University of Colorado, Boulder
CU Scholar
Aerospace Engineering Sciences Graduate Theses &
Aerospace Engineering Sciences
Dissertations
Summer 7-23-2014
State Estimation for Autopilot Control of Small
Unmanned Aerial Vehicles in Windy Conditions
David Paul Poorman
University of Colorado Boulder, [email protected]
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Poorman, David Paul, "State Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions" (2014).
Aerospace Engineering Sciences Graduate Theses & Dissertations.Paper 2.
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STATE ESTIMATION FOR AUTOPILOT CONTROL OF
SMALL UNMANNED AERIAL VEHICLES
IN WINDY CONDITIONS

DAVID PAUL POORMAN
B.S., University of Colorado at Boulder, 2010

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirement for the degree of
Master of Science
Department of Aerospace Engineering Sciences
2014
This thesis entitled:
State Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions
written by David Paul Poorman
has been approved for the Department of Aerospace Engineering Sciences

(Dale Lawrence)

(Eric Frew)

Date

The final copy of this thesis has been examined by the signatories, and we
Find that both the content and the form meet acceptable presentation standards
Of scholarly work in the above mentioned discipline.
© 2014 David Poorman

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Abstract
Poorman, David Paul (M.S. Aerospace Engineering Sciences)
State Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions
Thesis directed by Professor Dale A. Lawrence
The use of small unmanned aerial vehicles (UAVs) both in the military and civil realms is growing. This is
largely due to the proliferation of inexpensive sensors and the increase in capability of small computers
that has stemmed from the personal electronic device market. Methods for performing accurate state
estimation for large scale aircraft have been well known and understood for decades, which usually
involve a complex array of expensive high accuracy sensors. Performing accurate state estimation for
small unmanned aircraft is a newer area of study and often involves adapting known state estimation
methods to small UAVs. State estimation for small UAVs can be more difficult than state estimation for
larger UAVs due to small UAVs employing limited sensor suites due to cost, and the fact that small UAVs
are more susceptible to wind than large aircraft. The purpose of this research is to evaluate the ability
of existing methods of state estimation for small UAVs to accurately capture the states of the aircraft
that are necessary for autopilot control of the aircraft in a Dryden wind field. The research begins by
showing which aircraft states are necessary for autopilot control in Dryden wind. Then two state
estimation methods that employ only accelerometer, gyro, and GPS measurements are introduced. The
first method uses assumptions on aircraft motion to directly solve for attitude information and smooth
GPS data, while the second method integrates sensor data to propagate estimates between GPS
measurements and then corrects those estimates with GPS information. The performance of both
methods is analyzed with and without Dryden wind, in straight and level flight, in a coordinated turn,
and in a wings level ascent. It is shown that in zero wind, the first method produces significant steady
state attitude errors in both a coordinated turn and in a wings level ascent. In Dryden wind, it produces
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large noise on the estimates for its attitude states, and has a non-zero mean error that increases when
gyro bias is increased. The second method is shown to not exhibit any steady state error in the tested
scenarios that is inherent to its design. The second method can correct for attitude errors that arise
from both integration error and gyro bias states, but it suffers from lack of attitude error observability.
The attitude errors are shown to be more observable in wind, but increased integration error in wind
outweighs the increase in attitude corrections that such increased observability brings, resulting in
larger attitude errors in wind. Overall, this work highlights many technical deficiencies of both of these
methods of state estimation that could be improved upon in the future to enhance state estimation for
small UAVs in windy conditions.
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This work is dedicated to Grandmary and Grandbob.
Contents
1 Introduction .......................................................................................................................................... 1
2 Nomenclature ....................................................................................................................................... 4
3 Background Information ....................................................................................................................... 7
3.1 Reference Frames ......................................................................................................................... 7
3.2 The Wind Triangle ....................................................................................................................... 10
3.3 The Extended Kalman Filter ........................................................................................................ 11
3.3.1 Measurement Update ......................................................................................................... 13
3.3.2 Time Update ........................................................................................................................ 14
4 Aircraft States Needed for Autopilots ................................................................................................. 17
4.1 Scoping the Estimation Problem ................................................................................................. 17
4.2 Overview of the Autopilot .......................................................................................................... 20
4.3 Simulation Setup ......................................................................................................................... 24
4.3.1 Benchmark 1: Straight and Level Flight............................................................................... 24
4.3.2 Benchmark 2: Coordinated Turn ......................................................................................... 25
4.3.3 Benchmark 3: Wings Level Ascent ...................................................................................... 27
4.3.4 The Dryden Wind Model ..................................................................................................... 28
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4.4 Sensors ........................................................................................................................................ 31
4.5 Demonstration of Autopilot Performance with Limited State Information ............................... 32
4.5.1 Autopilot Performance under Benchmark 1 ....................................................................... 32
4.5.2 Autopilot Performance under Benchmark 2 ....................................................................... 36
4.5.3 Autopilot Performance under Benchmark 3 ....................................................................... 39
4.6 Relative Importance of the Chosen States.................................................................................. 43
4.7 Autopilot Summary ..................................................................................................................... 46
5 Method 1: IMU Attitude, Smoothed GPS, and Pressure Sensors ....................................................... 47
5.1 Description .................................................................................................................................. 47
5.1.1 The Transport Theorem ...................................................................................................... 48
5.1.2 Attitude Determination....................................................................................................... 49
5.1.3 Extended Kalman Filter 1 .................................................................................................... 52
5.1.4 Extended Kalman Filter 2 .................................................................................................... 55
5.1.5 Method 1 Summary ............................................................................................................ 60
5.2 Detailed Simulation Results ........................................................................................................ 62
5.2.1 Zero Wind ............................................................................................................................ 63
5.2.2 Dryden Wind ....................................................................................................................... 80
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5.3 Method 1 Analysis Summary ...................................................................................................... 95
6 Method 2: IMU and GPS Sensor Fusion ............................................................................................. 97
6.1 Description .................................................................................................................................. 97
6.1.1 Direct IMU Numerical Integration ...................................................................................... 97
6.1.2 Sensor Fusion through Kalman Filtering ........................................................................... 100
6.1.3 Method 2 Summary .......................................................................................................... 108
6.2 Detailed Simulation Results ...................................................................................................... 109
6.2.1 IMU Only Solution (No GPS/EKF3 Corrections) ................................................................. 110
6.2.2 Zero Winds ........................................................................................................................ 118
6.2.3 Dryden Wind ..................................................................................................................... 143
6.2.4 Method 2 Analysis Summary ............................................................................................ 169
7 Method Comparison and Future Work ............................................................................................. 171
7.1.1 Direct Attitude Sensing ..................................................................................................... 173
7.1.2 Replace Integration Method in State Estimation Method 2 ............................................. 175
7.1.3 Parallel Estimators ............................................................................................................ 175
8 Conclusion ......................................................................................................................................... 176
9 References ........................................................................................................................................ 179
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