7/ 24/ Simultaneous Estimation of Aircraft and Target Position Professor Dominick Andrisani Purdue University, School of Aeronautics and Astronautics 1282 Grissom Hall, West Lafayette, IN Presented at the The Motion Imagery Geopositioning Review and Workshop Purdue University, 24/25 July,

7/ 24/ Purpose: To determine the benefits of simultaneously estimating aircraft position and target position. This involves coupling the aircraft navigator (INS, GPS, or integrated INS/GPS) and the image-based target position estimator.

7/ 24/ 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.

7/ 24/ Hypotheses: 1. … aircraft positioning, 2. … target positioning. Simultaneous estimation of aircraft position and target position will improve the accuracy of...

7/ 24/ 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.

7/ 24/ Linear Simulation: Fly-Over Trajectory Stationary Target Initial aircraft position Final aircraft position 0 -10,00010,000 Range Meas., R (ft) Position (ft) Image Coord. Meas. x (micron) Position Meas X aircraft (ft) Focal Plane (f=150 mm) Camera always looks down. 20,000 Nominal speed=100 ft/sec Data every.1 sec., i.e., every 10 ft

7/ 24/ Measurement noise assumed in the simulation  Aircraft position = feet  Image coordinate = 5 microns  Range = 0.5 feet

7/ 24/ State Space Model State equation x(j+1)=  (j,j-1)x(j)+v(j)+w(j) Measurement equation z(j)=h(x(j))+u(j) x(o)=x 0 (Gaussian initial condition) where v(j) is a known input w(j) is Gaussian white process noise u(j) is Gaussian white measurement noise

7/ 24/ The Kalman Filter State Estimator Initialize Predict one step Measurement update

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7/ 24/ Point #1: A simple Kalman filter for aircraft (A/C) positioning-only estimation reduces the A/C position uncertainty from a  of 35 to 5.87 feet.

7/ 24/ Point#2: A combined estimator of A/C position and target position reduces A/C position uncertainty from 35 to feet. Hypothesis #2 is therefore proven.

7/ 24/ Point#3: Improving A/C position accuracy improves aircraft and X-target position accuracy. Obviously!

7/ 24/ Point#4: Combined estimator of A/C and target position does not reduce the target position uncertainty. Hypothesis #2 is not proven directly. However...

7/ 24/ Point#5: With a combined A/C and target estimator, if the target is at a known location, the aircraft position uncertainty is further reduced for 0.51 feet.

7/ 24/ Point # 6: New Black Box Navigator Imagine a “New Black Box Navigator” consisting of an INS, GPS and image-based target tracker all integrated together. This navigator outputs improved aircraft position estimates using camera #1. If this “New Black Box Navigator” was imaging on an unknown target, then it would produce aircraft position accuracy of feet. If this “New Black Box Navigator” was imaging on an known target, then it would produce aircraft position accuracy of 0.51 feet.

7/ 24/ Point # 7: Continued Imagine that the “New Black Box Navigator” feeds this improved aircraft position accuracy to a separate image-based target estimator which uses a second camera tracking a second target. Then, if the first target is at an unknown location, then the second target might be located with an accuracy of ft. Also, if the first target is at an known location, then the second target might be located with an accuracy of ft. This point is speculative at this time. Work continues. Other configurations of estimators and one or two cameras are possible and will be explored in the future.

7/ 24/ “New Black Box Navigator” with camera #1 on Target #1. Image-based target Locator using camera #2 on target #2. Improved aircraft position Improved target position Possible Scenarios Aircraft and target #1 and #2 data Integrated navigator and image processor using one camera to simultaneously or sequentially track two targets. Aircraft and target #1 data Improved target position Target #2 data

7/ 24/ Conclusions 1. The 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. 2. If such a new navigator were developed and used to track an unknown object on the ground, preliminary results suggests that the target position errors might be reduced by a whopping 96%. 4. If such a new navigator were developed and used to track a known object on the ground, preliminary results suggests that the target position errors might be reduced by a whopping 98%.

7/ 24/ Related Literature 1. B.H. Hafskjold, B. Jalving, P.E. Hagen, K. Grade, Integrated Camera-Based Navigation, Journal of Navigation, Volume 53, No. 2, pp Daniel J. Biezad, Integrated Navigation and Guidance Systems, AIAA Education Series, D.H. Titterton and J.L. Weston, Strapdown Inertial Navigation Technology, Peter Peregrinus, Ltd., A. Lawrence, Modern Inertial Technology, Springer, B. Stietler and H. Winter, Gyroscopic Instruments and Their Application to Flight Testing, AGARDograph No. 160, Vol. 15, A.K. Brown, High Accuracy Targeting Using a GPS-Aided Inertial Measurement Unit, ION 54th Annual Meeting, June 1998, Denver, CO.