Automatic positioning of UAVS to optimize TDOA geolocation ...

AUTOMATIC POSITIONING OF UAVS TO OPTIMIZE TDOA GEOLOCATION PERFORMANCE Don R. Van Rheeden, Brad C. Brown, Jeremy C. Price, Ben A. Abbott, Greg C. Willden Southwest Research Institute@,P.O. Drawer 28510, San Antonio, Texas 78228-0510 Kumar Chhokra,Jason Scott, Theodore Bapty, Institutefor SofWare Integrated Systems (ISISJ, Vanderbilt University, Box 1829, Station B, Nashville, TN 37235

Abstract Unmanned Aerial Vehicles (UAVs) have proved extremely useful for a number of important tasks such as surveillance, remote sensing, and geolocation of radio frequency (RF) transmitters. Typically UAVs fly pre-programmed flight paths, or they allow for limited flight path changes via ground station controllers. However, it is difficult for ground station controllers to position UAVs in a manner that optimizes geolocation performance. This paper explores the problem of automatically repositioning UAV assets to optimize geolocation accuracy via Time Difference of Arrival (TDOA) methods. First, we determine the geolocation accuracy that can be achieved for various scenarios and the TDOA timing accuracy needed. Second, we describe an algorithm to determine the quality of each TDOA measurement. Signal data corrupted by propagation effects and co-channel interference is used to validate the approach. Third, a path-planning algorithm for repositioning the UAVs to optimize geolocation accuracy is presented. Finally, some results using field test data are presented.

Introduction UAV applications range from surveillance to weapons platforms. The size and flight characteristics of the UAV platforms vary greatly. Some UAVs resemble fixed wing aircraft, while others resemble hovercrafts and parafoils. Most UAVs are relatively small, and have fairly severe payload weight and power restrictions. This disadvantage is countered by the ability of the UAV to loiter in hostile areas that are inaccessible to conventional aircraft. This is especially useful for signal collection applications where the aircraft may need to remain on station for hours to collect the desired information.

In the past, most UAVs have flown preprogrammed flight paths, or have allowed for limited flight path changes via ground station controllers. However, ground station controllers are not ideally suited for positioning UAVs to optimize geolocation performance. Coordination and optimization of when and where various aircraft in a fleet of small UAVs should move involves balancing a set of conflicting constraints. Movement of a UAV increases its risk of detection and consumes its finite power source. Yet, moving allows for a possibly better vantage point with respect to signal strength. Increased signal strength alone does not directly improve geoIocation accuracy. Rather, a signal devoid of multi-path propagation combined with a physical deployment around the object of interest increases the accuracy of the geolocation estimate. This paper explores the problem of automatically repositioning UAV assets to optimize Time Difference of Arrival geolocation accuracy.

TDOA Geolocation Using UAVs UAVs provide a unique platform for performing TDOA-based geolocation. The mobility of the UAV platform allows each UAV in a geolocation network to reposition to locations that provide more and more accurate geolocation fixes. During this project, algorithms were developed to determine where the UAVs should be positioned for each successive TDOA measurement. This involves computing a TDOA geolocation for the current location, making an estimate of the enor in this measurement based on previous measurements, previous geometries, the current measurement, and current geometry, and then determining where to move each sensor to improve the geolocation estimate.

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It was expected that the coordinated set of paths chosen for the UAVs could include waypoints that further refine geolocation accuracy. In the likely chance that the actual scenario involves a cluttered environment, multipath propagation can prove to be a significant factor in degrading geolocation accuracy. Champagne, et al. [l] provide a method for measuring the performance loss in such scenarios. A variation of this methodology has been used in a feedback fashion to provide direction and refinement with respect to the path planning cost function. As is detailed in many places (including [l]) the contribution of specific sensors in a TDOA network may be evaluated based on a chi-squared metric associated with various pairs used to estimate TDOA. In this manner, “lesser contributing nodes” may be chosen for candidate moves. Although geolocation accuracy can vary rapidly with respect to small changes in location, the typical case depends most heavily on significant location changes. Experience shows that two primary factors that influence TDOA geolocation accuracy are geometry considexations and multipath propagation. For geometry considerations, which dominate accuracy considerations in reasonably ‘clean site’ applications, large-scale movements need to be made before significant changes in the TDOA location accuracy are observed. This relationship is not strongly frequency-dependent and the distance moved in relation to the wavelength of the signal being located is not very important. What is important is to significantly change the distance and/or angle between the sensors and the signal of interest. In the case of multipath propagation, large changes in TDOA accuracy may be observed as a sensor is moved less than the signal wavelength. In this case, wave interference patterns, and not geometry considerations, determine TDOA estimation accuracy. Multipath severely degrades TDOA geolocation accuracy. Sensors that are in the presence of multipath should be moved to new locations that present degradation due to multipath. If possible, the new location should be one that has a clear line-of-sight path to the transmitter.

Simulating TDOA Geolocation Accuracy To determine how to move the UAVs based on expected TDOA accuracy, a scenario was programmed into a TDOA geolocation accuracy simulation. This simulation is based on results by Foy [2] who used a Taylor series approach to derive expressions for geolocation accuracy. This simulation only shows geomeq effects. It does not simulate geolocation errors caused by multipath propagation.

In the simulated scenario, numerical simulation was used to generate a sequence of UAV movements that perform what has been called the “tightening the noose” scenario. In this case, three UAVs are sent out to evaluate a five-by-five kilometer region. Three UAVs initially spread out into an equilateral triangle and begin “sweeping” an area. When they discover an emitter of interest, they call in seven more UAVs and then proceed to tighten up the error until a geolocation accuracy of 20 meters has been achieved. While tightening, the UAVs attempt to minimize the amount of motion. Figure 1 presents a sequence of pictures showing the motion steps. Figure 1 plots the UAV locations, and the different shades represent a geolocation Circular Error Radius (CER) in meters. Some observations conceming this scenario include: Efficient “sweeping” may be accomplished with only a few UAVs. Preplanned generic shapes, such as the equilateral triangle and the two columns formed once ten UAVs arrive, provide large expected coverage areas, hut may be bad choices once the noose begins to tighten. A large amount of motion is required to close on the target after the ten UAVs are called in. It is possible to move only a few of the contributing UAVs small distances to improve geolocation accuracy. At the end of the scenario, moving only four of the UAVs lowers the CER from 50 meters to 20 meters.

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detect these conditions, then it can search for a new location that experiences fewer propagation path issues. While evaluation of S N R is relatively simple, multipath is often intertwined with the S N R evaluation and obscures the true values of both. A core concept of this research (that is, moving UAVs to better locations) requires the multipath evaluation of a current location to be valid. Therefore, we developed techniques to evaluate the presence of multipath, and to differentiate these conditions from low S N R conditions. Multipath affects TDOA estimation of narrowband signals primarily through the cross correlation function. If the signal is shadowed, then significant attenuation can occur. Attenuation of a signal at one or more TDOA receivers will reduce the cross correlation peak. If strong reflections are present, then the cross correlation function will widen compared to the signal autocorrelation function. To better understand why this occurs, consider the following multipath channel model.

In the presence of multipath propagation, we will assume two noisy signals sensed by two spatially separated receivers. For simplicity, we'll assume that one receiver senses a direct line-ofsight signal uncorrupted by multipath, and the second receiver senses a signal that travels along N distinct propagation paths.

Figure 1. UAV Geolocation Accuracy Simulation

TDOA in Multipath and Low SNR While the type of geometry considerations shown above are a crucial consideration for UAV repositioning, multipath and low signal-to-noiseratio (SNR)propagation conditions can seriously degrade time difference of arrival estimation performance [3]. If a moving TDOA sensor can

where s(t) is the transmitted signal of interest, n,(r) and nt(t) are additive noise signals, a.is the signal attenuation along propagation path n,and D. is the relative time delay of the signal along propagation path n. TDOA is estimated by finding the time delay corresponding to the peak of the cross correlation function

where E [ . ] is the expected value operator. In the presence of multipath, the estimated time difference of arrival L? will be corrupted by multipath. To see why this is, substitute (1) into (2). Assuming the noise signals are mutually uncorrelated with the signal of interest, this substitution gives

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If we assume the noise terms are zero mean and uncorrelated, then the noise cross correlation function, R,, (r),is zero and (3) can be expressed

If the signal-to-noise ratio is high, then the signal autocorrelation function at zero lag will be large relative to the receiver noise variances, and we can write

as

"4

where €4 represents the convolution operator. Equation (4) shows that the cross correlation function consists of a linear superposition of attenuated and shifted versions of the signal autocorrelation function. The degree to which multipath propagation affects the TDOA estimate depends on the attenuation factors a,,, and the width of the autocorrelation function. For a narrowband signal, the autocorrelationfunction is wider than the multipath time delays. Equation (4) suggests a way to identify a multipath propagation condition. Consider the attenuation factors a.. If an object shadows a sensor, then most, if not all, attenuation factors will be small. A potential way to detect this condition is through a correlation coefficient estimate computed using the cross correlation function value at the estimated time delay.

If the signal autocorrelationfimction is wide relative to the multipath time delays which is true for narrowband signals, then at the estimated time delay 6 ,equation (4) can be approximated as "SI

Using this approximation we can write

If the sum of the attenuation factors are large relative to the noise-to-signal-variance-squared ratio, then

(9) If the attenuation is so severe that the received signal at sensor number two is dominated by noise, then R, (0)