Embed Size (px)
DESCRIPTION
10/31/ Model and Parameters to Drive Simulation Aircraft Motion Aircraft Model Trajectory Input Time Input Turbulence Input Errors GPS Satellite Constellation Processing Mode Antennas Number, Location Errors INS Position, Attitude, Rates Filter Aircraft Position & Attitude Estimate and Uncertainty Transformation to Sensor Position, Attitude, and Uncertainty Errors Sensor Parameters Image Acquisition Parameters Site Model Imaging System Target Coordinates Uncertainty, CE90 Graphic Animation Multi-Image Intersection Synthetic Image Generation Errors Target Tracking Do these simultaneously rather then serially. Image target and Control point.
Citation preview
10/31/01 - 1
Simultaneous Estimation of Aircraft and Target Position
With a Control Point
Professor Dominick AndrisaniPurdue University, School of Aeronautics and
Astronautics1282 Grissom Hall, West Lafayette, IN 47907-1282
[email protected] 765-494-5135
Presented at the The Motion Imagery Geolocation WorkshopSAIC Signal Hill Complex, October 31, 2001
http://bridge.ecn.purdue.edu/~uav
10/31/01 - 2
Purpose:To determine the benefits of simultaneously estimating aircraft position and unknown target position when there is also a control point (target of known location).
This involves coupling the aircraft navigator(INS, GPS, or integrated INS/GPS) and the image-based target position estimator and image data from the unknown target and known control point.
10/31/01 - 3
Model and Parameters to Drive Simulation
Aircraft Motion
Aircraft Model
Trajectory Input
Time Input
Turbulence Input
Errors
GPS
Satellite Constellation
Processing Mode
AntennasNumber, Location
Errors
INS
Position, Attitude, Rates Position, Attitude, Rates
Filter
Aircraft Position & Attitude Estimate and Uncertainty
Transformation to Sensor Position, Attitude, and Uncertainty
Errors
ErrorsSensor Parameters
Image AcquisitionParameters
Site Model
Imaging System
Target CoordinatesUncertainty, CE90
Graphic Animation
Multi-ImageIntersection
Synthetic Image GenerationErrors
Target Tracking
Do these simultaneouslyrather then serially. Image target and Control point.
10/31/01 - 4
Hypothesis:
Given a combined estimator of aircraft position and target position capable of imaging on a unknown target and a known control point.
If a control point enters the field of view of the imagesystem, the accuracy of simultaneous estimation of aircraft position and unknown target position will be significantly improved.
10/31/01 - 5
Technical Approach
Use a linear low-order simulation of a simplified linear aircraft model, Use a simple linear estimator to gain insight into the problem with a minimum of complexity.A control point of known location will enter the field of view of the image processor only during the time from 80-100 seconds.
10/31/01 - 6
0
Linear Simulation: Fly-Over Trajectory
Unknown Target always visible
Initial aircraft position time=0 sec Final aircraft position time=200 sec
-10,000 10,000
Range Meas., R (ft)
Position (ft)
Image Coord. Meas. x (micron)
Position MeasXaircraft (ft) Focal Plane (f=150 mm)
Camera always looks down.
20,000Nominal speed=100 ft/sec
Data every .1 sec., i.e., every 10 ft
Control pointKnown locationVisible only fromtime=80-100 seconds.
10/31/01 - 7
Nominal Measurement noise assumed in the simulation
Aircraft position = 1 feet Image coordinate = 7.5 microns
Range = 1 feet
10/31/01 - 8
State Space Model
State equationx(j+1)=(j,j-1)x(j)+v(j)+w(j)
Measurement equationz(j)=h(x(j))+u(j)
x(o)=x0 (Gaussian initial condition)
wherev(j) is a known inputw(j) is Gaussian white process noiseu(j) is Gaussian white measurement noise
10/31/01 - 9
The Kalman Filter State EstimatorInitialize P(0 | 0) P
0, ˆ x (0 | 0) ˆ x
0
Predict one step
Measurement update
P(j | j 1) ( j, j 1)P( j 1 | j 1)T ( j, j 1) Q(j 1)ˆ x (j | j 1) ( j, j 1) ˆ x (j 1 | j 1) v( j 1)
PZ (j | j 1) H(j)P(j | j 1)HT( j) R(j)K(j) P(j | j 1)HT (j)PZ
1 ( j | j 1)P(j | j) [I K(j)H(j)]P( j | j 1)
˜ z ( j) z( j) h(ˆ x ( j | j 1))ˆ x (j | j) ˆ x ( j | j 1) K(j)˜ z ( j)
10/31/01 - 10
Estimation results for different measurement noises
Measurement Noise (sigma values)units Run1 Run2 Run3 Run4 Run5 Run6
aircraft position feet 100 10 1 0.1 1 1image coord micron 7.5 7.5 7.5 7.5 75 750range feet 1 1 1 1 10 100
Final position estimates (sigma values)units
aircraft position feet 0.78 0.77 0.6 0.099 0.78 0.78target position feet 0.095 0.088 0.03 0.021 0.21 0.22
** **** These runs were greatly effected by the appearance of the known control point during 80-100 seconds.
10/31/01 - 11
0 20 40 60 80 100 120 140 160 180 200-500
0
500R
es(X
L)ft + and - 2sigma bounds
Run #1: SigmaR=100 ft,7.5 micron,1 ft
0 20 40 60 80 100 120 140 160 180 200-50
0
50
Res
(x1)
mro
n
0 20 40 60 80 100 120 140 160 180 200-5
0
5
Res
(R1)
ft
0 20 40 60 80 100 120 140 160 180 200-100
0
100
Res
(x2)
mro
n
0 20 40 60 80 100 120 140 160 180 200-5
0
5
Res
(R2)
ft
time (sec)
Residuals of the Kalman Filter
No measurement here No measurement here
No measurement here No measurement here
10/31/01 - 12
0 20 40 60 80 100 120 140 160 180 200-100
0
100
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Std1(last half)= 0.79861 SigmaTheoryFinal1= 0.77584
Run #1: SigmaR=100 ft,7.5 micron,1 ft
0 20 40 60 80 100 120 140 160 180 200-100
0
100
Act
err(
XP
1)ft
Std2(last half)= 0.00080613 SigmaTheoryFinal2= 0.095274
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Act
err(
XP
2)ft
time (sec)
Std3(last half)= 0 SigmaTheoryFinal3= 0
Estimated state -Actual state
Major impact of control point here
Major impact of control point here
10/31/01 - 13
60 70 80 90 100 110 120-10
0
10
20
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Run #1: SigmaR=100 ft,7.5 micron,1 ft
60 70 80 90 100 110 120-10
0
10
Act
err(
XP
1)ft
60 70 80 90 100 110 120-1
0
1
Act
err(
XP
2)ft
time (sec)
Expanded time scale for Estimated state -Actual state
Major impact of control point here
Major impact of control point here
10/31/01 - 14
0 20 40 60 80 100 120 140 160 180 200-1
0
1
2x 10
4
XL(
ft)
Run #1: SigmaR=100 ft,7.5 micron,1 ft
Solid line is the actual state. Dotted line is the estimated state
0 20 40 60 80 100 120 140 160 180 2004900
5000
5100
5200
XP
1(ft)
0 20 40 60 80 100 120 140 160 180 2005999
6000
6001
XP
2(ft)
time (sec)
Estimated state and actual state time histories
10/31/01 - 15
0 20 40 60 80 100 120 140 160 180 200-10
0
10
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Std1(last half)= 0.79504 SigmaTheoryFinal1= 0.77233
Run #2: SigmaR=10 ft,7.5 micron,1 ft
0 20 40 60 80 100 120 140 160 180 200-10
0
10
Act
err(
XP
1)ft
Std2(last half)= 0.0056979 SigmaTheoryFinal2= 0.088282
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Act
err(
XP
2)ft
time (sec)
Std3(last half)= 0 SigmaTheoryFinal3= 0
Estimated state -Actual state
10/31/01 - 16
60 70 80 90 100 110 120-5
0
5
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Run #2: SigmaR=10 ft,7.5 micron,1 ft
60 70 80 90 100 110 120-1
0
1
Act
err(
XP
1)ft
60 70 80 90 100 110 120-1
0
1
Act
err(
XP
2)ft
time (sec)
Expanded time scale for Estimated state -Actual state
Major impact of control point here
10/31/01 - 17
0 20 40 60 80 100 120 140 160 180 200-4
-2
0
2
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Std1(last half)= 0.60885 SigmaTheoryFinal1= 0.59831
Run #3: SigmaR=1 ft,7.5 micron,1 ft
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Act
err(
XP
1)ft
Std2(last half)= 0.0060581 SigmaTheoryFinal2= 0.030299
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Act
err(
XP
2)ft
time (sec)
Std3(last half)= 0 SigmaTheoryFinal3= 0
Estimated state -Actual state
No impact of control point
Little impact of control point here
10/31/01 - 18
60 70 80 90 100 110 120-4
-2
0
2
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Run #3: SigmaR=1 ft,7.5 micron,1 ft
60 70 80 90 100 110 120-0.2
0
0.2
Act
err(
XP
1)ft
60 70 80 90 100 110 120-1
0
1
Act
err(
XP
2)ft
time (sec)
Expanded time scale for Estimated state -Actual state
Littler impact of control point here
10/31/01 - 19
0 20 40 60 80 100 120 140 160 180 200-5
0
5
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Std1(last half)= 0.78796 SigmaTheoryFinal1= 0.78316
Run #5: SigmaR=1 ft,75 micron,10 ft
0 20 40 60 80 100 120 140 160 180 200-10
0
10
Act
err(
XP
1)ft
Std2(last half)= 0.055301 SigmaTheoryFinal2= 0.21331
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Act
err(
XP
2)ft
time (sec)
Std3(last half)= 0 SigmaTheoryFinal3= 0
Estimated state -Actual state
No impact of control point here
10/31/01 - 20
60 70 80 90 100 110 120-5
0
5
Act
err(
XL)
ft Act Err = Xhat-Xexact. + and - 2sigma theoretical bounds
Run #5: SigmaR=1 ft,75 micron,10 ft
60 70 80 90 100 110 120-1
0
1
Act
err(
XP
1)ft
60 70 80 90 100 110 120-1
0
1
Act
err(
XP
2)ft
time (sec)
Expanded time scale for Estimated state -Actual state
No impact of control point here
10/31/01 - 21
“New Black Box Navigator” with camera #1 on Target #1.
Image-based targetLocator using camera#2 on target #2.
Improvedaircraft position
Improvedtarget position
Two Useful Scenarios
Aircraft and target #1 and #2 data Integrated navigator and image
processorusing one camera to simultaneously or sequentially track two targets.
Aircraft and target #1 data
Improvedtarget position
Target #2 data
10/31/01 - 22
Conclusions
1. When the measurement noise on aircraft position is large (sigmaXL>>1), the sighting of a known control point significantly improves the aircraft position accuracy AND the unknown target position accuracy. This suggests a that flying over control points is tactically useful!
2. In my talk at the last workshop at Purdue we concluded that a dramatic improvement of aircraft position estimation suggests a new type of navigator should be developed. This navigator would integrate INS, GPS, and image processor looking at known or unknown objects on the ground. One or two cameras might be used.
10/31/01 - 23
Related Literature1. B.H. Hafskjold, B. Jalving, P.E. Hagen, K. Grade, Integrated Camera-Based Navigation, Journal of Navigation, Volume 53, No. 2, pp. 237-245.2. Daniel J. Biezad, Integrated Navigation and Guidance Systems, AIAA Education Series, 1999.3. D.H. Titterton and J.L. Weston, Strapdown Inertial Navigation Technology, Peter Peregrinus, Ltd., 1997.4. A. Lawrence, Modern Inertial Technology, Springer, 1998.5. B. Stietler and H. Winter, Gyroscopic Instruments and Their Application to Flight Testing, AGARDograph No. 160, Vol. 15,1982.6. A.K. Brown, High Accuracy Targeting Using a GPS-Aided Inertial Measurement Unit, ION 54th Annual Meeting, June 1998, Denver, CO.
