Sensor Modeling and Sensitivity Analysis for a Next-Generation Time-Space Position Information System
By Mark Smearcheck and Michael Veth, Air Force Institute of Technology
Increasing availability and performance of state-of-the-art navigation sensors motivates the need for a highly accurate reference system commonly referred to as a time-space position information (TSPI) device. The Advanced Navigation Center at the Air Force Institute of Technology is working with the Air Force Flight Test Center to develop a next generation time-space position information (TSPI) system to be used for test and evaluation of modern navigation devices.
TSPI systems such as the GPS Aided Inertial Navigation Reference (GAINR) or Advanced Range Data System (ARDS) accompany navigation sensors during flight testing to collect the precise position, velocity, and attitude. Current GAINR TSPI performance levels include 1.0 m of position uncertainty, 0.1 m/s of velocity uncertainty, and 1.75 mrad of attitude uncertainty. Goal performance levels for next-generation TSPI call for an order of magnitude improvement over current systems.
A more accurate test and evaluation device will likely require fusion of multiple sensors of varying modalities such as GPS, inertial, electro-optical and infrared cameras, laser range sensors, barometric altimeters, ground-based theodolites, and ground-based tracking radar. This research aims to identify an integrated sensing package and the sensing techniques required to achieve the next generation TSPI accuracy.
In order to accomplish this task, a sensitivity analysis is performed that predicts the quality of the navigation solution attainable using various external sensor combinations. The sensitivity analysis requires sensor characterization and modeling in addition to development of a software simulated world (the flight test range) that the sensors are able to observe. Issues also investigated in this research include vision-aiding techniques, optical feature deployment, and testing in GPS-denied scenarios.
Sensors and Simulated World
The Air Force Flight Test Center currently obtains TSPI using the GAINR, which includes a navigation grade inertial measurement unit (IMU) and dual-frequency code-based differential GPS (DGPS). Carrier-phase GPS, if available, could be implemented to increase position accuracy.
When integrated into a highly dynamic platform, such as tactical fighter, a kinematic solution may not always be obtainable due to difficulty resolving integer ambiguities and cycle slips experienced in the receiver’s tracking loops. The sensitivity of both code and carrier-phase differential GPS is included in this research due to the uncertain availability of a kinematic solution.
Scenarios of GPS denial are always an area of concern for the warfighter, and thus GPS-independent test-platforms must be examined. Other positioning sensors, useful in GPS-denied testing, include ground-based theodolites and radars. These devices are installed at surveyed locations on the test range and are used to track the test aircraft. Theodolites are pivoting platforms that may contain various sensors and provide range, azimuth angle, and elevation angle measurements. Radars are also used to provide the same type of measurements, along with an additional velocity measurement (Figure 1).
Onboard optical sensors including high-resolution digital cameras and laser range finders have also been investigated for TSPI use. This research proposes to install surveyed targets on the test range that are easily identifiable through feature extraction and tracking methods such as the scale-invariant feature transform (SIFT).
Cameras are able to observe position and attitude through homogenous pixel location measurements of image features (FIGURE 2).
An objective of this sensitivity analysis is to show the attitude performance achievable through feature tracking of surveyed targets. When image-aiding of an IMU is implemented in a navigation filter, such as the extended Kalman filter (EKF), next generation TSPI level attitude accuracy should be reached.
The other optical sensor investigated, the laser range finder, is used to augment the navigation solution by measuring distance to the surveyed targets detected by the camera.
For the sensitivity analysis a simulated world is generated for the sensors to make observations. The world simulation includes GPS ephemeris, a digital terrain elevation database (DTED), gravity models, natural terrain landmarks/targets, manmade targets, a ground sensor deployment map, simulated flight test profile, and vehicle sensor installation lever-arms.
The goal of the sensitivity analysis is to determine the minimal set of sensors that will meet next generation TSPI performance requirements. Sensor models and world characteristics are used to calculate expected position, velocity, and attitude uncertainty given a particular trajectory, sensor package, and feature set. The aircraft’s state vector, , as a function of the measurement, z, and uncertainty matrix, R, is represented as
where H is the observation matrix. The observation matrix is a Jacobian made up of partial derivates of each sensor’s measurements with respect to position, velocity, and attitude. Example H matrix elements include the partial derivates describing the camera measurements with respect to position and attitude. The partial deviate of the pixel coordinate, zi, of an image feature with respect to position, pn, is
where Tcpix is the camera frame to pixel frame transformation matrix made up of calibration parameters, sc is the line of sight vector from the camera to the target expressed in the camera frame, Cnb and Cbc are direction cosine matrices, and the subscript z denotes the z dimension of the indicated navigation frame. The partial derivative of the pixel coordinate of an image feature with respect to attitude, α, is calculated as
The H matrix’s partial derivatives describing observations from other navigation sensors are derived in our previous
work, “Sensor Modeling and Sensitivity Analysis for a Next Generation Time-Space Position Information (TSPI) System,” Proceedings of the ION International Technical Meeting, 2010. The a posteriori uncertainty of the state or sensitivity, P, at time k is calculated as
where P0 is the initial uncertainty.
Results show the three sigma median uncertainty of position and attitude for various sensor combinations over a common flight profile through the test range (Figure 3).
The sensitivity analysis indicates that the most practical sensor package that meets next-generation TSPI performance is the combination of carrier-phase GPS and a high-resolution camera tracking ten SIFT features per image.
In this example, tracking only two SIFT features per image does not provide the necessary level attitude accuracy, although incorporating inertial measurements is expected to reduce the overall number of features required per image.
In the absence of GPS, theodolites when coupled with a camera can function as a reasonable alternative. It should be noted that since the sensitivity analysis relies on a simulated world the feature tracking performance and target surveying accuracy may change during operational testing.
The next phase of this research is to integrate the sensors with an IMU using an extended Kalman filter. Fusion with a navigation-grade INS is expected to improve position, velocity, and attitude accuracy.
If simulated results are promising, the next phase of the effort will focus on collecting flight test data to validate the simulation and further increase the fidelity of the simulation.
The authors would like to thank the Air Force Flight Test Center for supporting this research.
MARK SMEARCHECK is a research engineer with the Advanced Navigation Technology Center at the Air Force Institute of Technology (AFIT) at Wright Patterson Air Force Base in Dayton, Ohio. He received his B.S. in electrical engineering in 2006 and his M.S. in electrical engineering in 2008, both from Ohio University. His research topics include micro-air vehicles, indoor navigation, image-aided navigation, pseudolites, and test range instrumentation.
LT. COl. MICHAEL VETH is an assistant professor of electrical engineering at AFIT and deputy director of the Advanced Navigation Technology Center. He received his Ph.D. and M.S. in electrical engineering from AFIT and his B.S. in electrical engineering from Purdue University. He is a graduate of Air Force Test Pilot School.