Algorithm for Geodetic Positioning Based on the Angle of Arrival of Aircraft Automatic Dependent Surveillance Broadcasts
Richard Gross and Nicholas Baine, Grand Valley State University
Since their deployment, Global Navigation Satellite Systems (GNSS) have set the standard for geodetic positioning. The highly engineered nature of these systems can produce geodetic position estimates with errors on the order of 10 meters. In addition, various augmentation methods have been developed to further improve the accuracy of GNSS including but not limited to: Wide Area Augmentation System (WAAS), Differential Global Positioning System (DGPS), and Real Time Kinematic (RTK) GNSS. Utilizing these augmentation methods can improve the accuracy of the GNSS position estimate to the centimeter range. Despite the unparalleled accuracy of GNSS systems, the low power of the satellite-based Radio Frequency (RF) signals required to formulate the geodetic position estimate leave GNSS susceptible to a lack of availability and to spoofing. A lack of GNSS availability may be due to natural phenomenon, obstructions in the line of sight to the satellite constellation, or malicious intent. Spoofing, on the other hand, is the intentional introduction of a higher power ‘look-a-like’ GNSS signal that causes the GNSS receiver to report an incorrect position estimate. It has been widely theorized that spoofing can be used to ‘take control’ of a GNSS guided vehicle; therefore, significant research has been performed to detect spoofing attempts.
This paper develops a lower-resolution geolocation system for airborne vehicles that can serve as a redundant navigation system for use during locally limited GNSS availability and can be used to validate on-board satellite navigation systems to detect local spoofing attempts. The proposed system will utilize the proliferation of Automatic Dependent Surveillance – Broadcast (ADS-B) equipped aircraft as airborne navigation aids in a radio frequency angle-of-arrival (AOA) based geodetic positioning algorithm.
ADS-B is a modern technology that has been designed to enhance air traffic control’s situational awareness of aircraft operations by providing a three-dimensional depiction of each ADS-B equipped aircraft’s intended flight path . To accomplish this, each ADS-B equipped aircraft periodically transmits its identification, position, altitude, and velocity information to an ADS-B ground station for processing and display on an air traffic controller’s console . Suitably equipped aircraft may also receive these transmissions directly, allowing them to utilize the information to maintain adequate aircraft separation in uncontrolled airspace . The Federal Aviation Administration (FAA) has mandated that all aircraft operating within certain airspace segments over the United States be ADS-B compliant by January 1, 2020 . According to 2015 data released by the Bureau of Transportation Statistics, there are over 6,800 commercial aircraft and 210,000 general aviation aircraft registered in the United States . A vast majority of these aircraft will be subject to the ADS-B mandate. As such, the large quantity of ADS-B equipped aircraft make them ideal candidates to serve as airborne navigation aids in the proposed navigation system.
The accuracy of ADS-B position reports and the precision of AOA measurements from ADS-B transmissions has been studied thoroughly by Reck et al., in , , , , , and . Reck studied the accuracy of ADS-B position reports by comparing the AOA of the received ADS-B data with the expected AOA computed based on the receiving antenna location and the ADS-B transmission’s position report . Reck concluded that the position information provided by ADS-B transponders is reliable and follows a Rayleigh distribution with a mean error on the order of 250 m . Reck also analyzed various AOA processing techniques to determine the optimal method to accurately determine the AOA of ADS-B transmissions and reported that an AOA RMSE on the order of 0.66° can be achieved across a variety of ranges . Reck’s analysis suggests that ABS-B position information is accurate and that accurate AOA measurements can be determined from ADS-B transmissions.
Similar to Reck’s work, United States Patent 2014/0327581 A1 details a method for utilizing AOA measurements to authenticate ADS-B transmissions . The patent also describes a method to utilize AOA from ground based targets of opportunity to determine a receiver’s position . The primary embodiment of the patent proposes that ADS-B authentication can be achieved by comparing the expected AOA derived from received ADS-B position, and the measured AOA of the received RF signal . Discrepancies between the estimated AOA and the measured AOA would result in an indication of an ADS-B position validation failure. The secondary embodiment describes a means to determine the receiver’s position using AOA information from multiple ground based targets of opportunity that transmit in the aviation frequency band . This secondary embodiment limits the position determination algorithm to the use of ground based targets of opportunity where the absolute position of the transmitter is published . This differs from the proposed navigation system in that the navigation aids in the proposed system are airborne and their position is not fixed or published.
United States Patent 2011/1063908 A1 describes a method for validating the position information being transmitted by an ADS-B capable aircraft using a direction finding antenna to determine the bearing from the receiver to the transmitter . Given the position of the receiver, the bearing to the transmitter, and the distance to the transmitter, the transmitter’s location can be precisely determined and validated against the transmitted position . This disclosure is currently impractical because the proposal theorizes that the distance to the transmitting aircraft can be calculated based on time of flight of the RF signal. This is not currently possible with ADS-B data packets because the time of transmission is not a member of the ADS-B data set. Therefore, an additional distance measuring sensor or method would be required to make this invention feasible.
The navigation algorithm presented in this paper is loosely based on Simultaneous Localization and Mapping (SLAM) in that it will track ADS-B capable aircraft to refine their ADS-B reported position estimates while simultaneously determining the geodetic position and velocity of the host vehicle. Unlike SLAM, where the absolute location – latitude/longitude – of the landmarks is unknown and must be estimated as the vehicle encounters them, the absolute position of the airborne navigation aids is reasonably well-known and periodically reported in the ADS-B data set. Because the absolute position of the navigation aids is known, the resulting host vehicle position will also be an absolute rather than a relative position. Secondarily, the continuous tracking of the airborne navigation aids allows reported ADS-B positions to be validated against the estimated navigation aid position; thereby, concurrently accomplishing ADS-B validation and host vehicle geolocation. Finally, unlike GNSS systems that utilize low power RF signals, ADS-B transmissions are relatively high power, ranging from 70 W to 200 W , making them very difficult to jam or spoof.
To validate the theoretical capability of the navigation algorithm, a software application has been developed to simulate ADS-B capable aircraft that serve as airborne navigation aids for the proposed solution. Given the suitable simulation and separate implementation of the proposed solution, the solution was evaluated by generating position and uncertainty plots to demonstrate the accuracy of the resulting geodetic position. Accuracy, in this context, is a measure of the difference between the estimated host vehicle position and the true host vehicle position generated by the simulation.
A nearly infinite number of test cases could be derived to evaluate the performance of the proposal; however, as an initial assessment of a somewhat novel navigation solution, the bulk of the test cases were configured to evaluate nominal conditions. Nominal conditions are those cases where multiple airborne navigation aids are available, reporting positions with minimal uncertainty, and positioned to provide a favorable geometry. A small set of test cases were considered that present abnormal inputs to the system. Examples of these abnormal conditions include: a minimal number of airborne navigation aids, navigation aids with unreasonable uncertainty, and/or poor navigation aid geometry. An analysis of these results is presented with the focus on evaluating the true position error of the computed position.
In summary, GNSS has been engineered and augmented to accurately provide geodetic position estimates. However, the low power RF signals leave GNSS susceptible to loss of availability and spoofing. The proposed solution provides a low-resolution means of determining an airborne vehicle’s geodetic position in the absence of GNSS availability that can be used in a redundant capacity in a locally GNSS denied or spoofed environment.
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