Jammer Hunting with a UAV

May 4, 2015  - By

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A fully autonomous, unmanned aerial vehicle (UAV)-based system for locating GPS jammers, currently under development, seeks to localize a jammer to within 30 meters in less than 15 minutes in an area comparable to that of an airport. Ultimately, the design team targets the ability to locate multiple, simultaneous jammers, and navigate in intermittent GPS and GPS-denied environments using a combination of GPS and alternate navigation aids. The system should be inexpensive and built from commercially available or open-source parts and software.

By James Spicer, Adrien Perkins, Louis Dressel, Mark James, Yu-Hsuan Chen, Sherman Lo , David S. De Lorenzo and Per Enge, Stanford University

The aviation community worries about GPS jamming. Recently, it struggled to find so-called personal privacy devices on Newark’s Liberty International Airport and traveling the nearby New Jersey Turnpike.

A number of unintentional jamming incidents took a long time to resolve. The disruption from an intentional, malicious jamming attack could be far worse. Airport authorities should be prepared to locate and shut down a coordinated attack by numerous jammers capable of disrupting the GPS service over an entire airport.

The closure of a major airport for the many hours or days it would take to locate even a couple of backpack-sized transmitters would be not only be highly disruptive in flights delayed or diverted, it would negatively impact the confidence of the flying public.

Any system in place to mitigate this threat must be inexpensive enough to be deployed at least at the nation’s major commercial airports, autonomous enough to be operable with limited training and certification, and rapid and accurate enough that a jammer can be routinely apprehended by ground-based law enforcement. It must be able to navigate successfully in GPS-denied environments using alternative position, navigation and timing (APNT), and have the range and capacity to search an airport-sized area as well as the approach corridor leading to runway touchdown.

This article describes such a system and device presently in research and development: the Jammer Acquisition with GPS Exploration & Reconnaissance (JAGER).

Vehicle Design and Operation

The JAGER UAV is a based on a commercially available, multi-rotor airframe modified to suit the mission specifications. The 1.2-meter diameter octocopter has a maximum takeoff weight of 11 kilograms (24.2 pounds), a top speed of 20 meters/second (m/s, 45 mph), and can fly unloaded for up to 30 minutes.

We have replaced the battery tray with our own carbon fiber design that allows us to carry 16 Ah of lithium polymer batteries for a maximum power draw of 4 kW. This extra capacity means that even with a 5-kilo experimental payload, the present craft can remain aloft for up to 15 minutes without recharging.

The payload plates are also custom-made from carbon fiber, and it is to these that the UAV’s experimental payloads are mounted (see FIGURES 1 and 2). One payload plate is flown at a time, and is secured on top of the airframe with a quick-release mechanism. This modularity allows for individual experiments to be mounted to their own payload plate and ground-tested before being secured to the UAV. Different experiments can be switched out rapidly for efficient use of battery capacity and flight time.

Figure 1. (A) Diagram of the payload plate showing regularly spaced mounting holes. (B) Plate with APNT experiment mounted. (C) Payload plate / experiment assembly secured atop JAGER UAV.

Figure 1. (A) Diagram of the payload plate showing regularly spaced mounting holes. (B) Plate with APNT experiment mounted. (C) Payload plate / experiment assembly secured atop JAGER UAV.

Figure 2. Image of the vehicle showing the battery tray slung beneath the central body, the APNT experiment and payload plate secured on top, and the jammer-hunting antenna mounted at the front.

Figure 2. Image of the vehicle showing the battery tray slung beneath the central body, the APNT experiment and payload plate secured on top, and the jammer-hunting antenna mounted at the front.

The plate itself also offers flexibility for component mounting. Regularly spaced, threaded holes across the plate mean components’ positions can be easily changed to find an optimal configuration. This can be particularly useful for minimizing interference between computers and noise-sensitive components such as antennas and magnetometers.

Software. We modified existing, open-source autopilot software to fly the mission. The craft is fully capable of completing a mission autonomously, but also can be taken over by a human pilot if necessary. A ground station also can be used to send commands to the octocopter, but is primarily used to monitor UAV location, battery life, and jammer belief state.

The autopilot software also has been adapted to communicate with various vehicle payloads. Experiments using APNT equipment, for example, pass their data to the autopilot, which will combine these signals with its own GPS data for accurate navigation in areas where the GPS signal might be intermittent or unreliable. In return, the autopilot can be used to pass data to experiments reliant on altitude, attitude, atmospheric pressure or location information.

The ground station monitors instruments’ data and status in real time. This not only allows for control of airborne experiments, but also straightforward ground testing. Synthetic autopilot data can be fed to an experiment to ensure that all systems are performing correctly before they are mounted on the vehicle for flight tests.

APNT Overview

Key to navigating in a GPS-denied environment is the use of signals from APNT networks for location determination. The proposed system should be able to navigate using any or all available APNT signals, and should weight each one according to its strength and reliability in order to formulate the most accurate estimate of both its own and the jammer’s position.

Here we describe the use of the universal access transceiver (UAT) and distance measuring equipment (DME) network for our APNT signals. The UAT signal has been implemented by the Federal Aviation Administration (FAA) in the United States as part of automatic dependent surveillance–broadcast (ADS-B), and is transmitted through a network of terrestrial ground stations.

The ADS-B network was only completed across the contiguous United States in 2014, so it is new compared to established cellphone networks. It is more comprehensive than many other terrestrial systems, so that coverage of most airports is guaranteed. While GPS reception requires an unobstructed view of the sky, UAT reception requires a direct line of sight to a transmitting tower. However, the flatness of terrain surrounding most airports as well as the UAV’s airborne vantage point ensures that UAT signals will probably be visible throughout most jammer-seeking missions.

The APNT equipment used for navigation by the JAGER UAV consists of UAT (978 MHz), DME (982 to 1213 MHz), and GPS (1575.4 MHz) antennas, a multichannel transceiver to combine the two signals, and a computer for data processing (see FIGURE 3). A dedicated lithium-ion battery powers the entire APNT payload. The current system does incorporate GPS to estimate the time offset, but future iterations of the system will derive time from sources other than GNSS so that true GPS-denied navigation is possible.

Figure 3. Schematic of the APNT configuration on board the JAGER UAV.  Resulting location information is passed to the autopilot for navigation.

Figure 3. Schematic of the APNT configuration on board the JAGER UAV. Resulting location information is passed to the autopilot for navigation.

The UAT antenna receives multiple signals from visible ADS-B ground station transmitters. The transceiver combines these with a GPS timestamp, and the data is passed to the APNT computer for analysis. Based on knowledge of the absolute locations of the ADS-B antennas, the range of the vehicle from each antenna can be calculated, which in turn can be used to trilaterate the vehicle’s absolute position. This position is then passed to the autopilot for the UAV’s navigation, while the status of the equipment and signal strength are passed down to the ground for monitoring in real-time.

The necessity of using GPS signals as an accurate timing system is a current limitation, as navigation in GPS-denied conditions is clearly not possible while we are using GPS as a clock. As mentioned eariler, future designs will derive time from non-GNSS sources, such as chip-scale atomic clocks or the terrestrial ranging signals.

Carrying an onboard computer allows for real-time processing of the terrestrial alternative navigation signals.  However, there are a few limitations to the use of these signals. First, the vertical position is difficult to calculate due to the geometry of terrestrial signals as well as the sparsity of visible station at low elevation. This is solved by using a baro-altimeter. Second, DME signals do not provide a pseudoranging function. Current work sponsored by the FAA is developing a DME pseudoranging capability. As the technology matures, we will improve the hardware and algorithm that can be integrated into future JAGER designs, resulting in lower weight and power overhead for the APNT payload.

Tracking Overview

GPS jammers do little more than emit signals in the GPS frequency range. Because the signals from GPS satellites are so weak by the time they reach the Earth, ground-based jammers do not have to be especially powerful to overwhelm GPS in their immediate vicinity. A jammer is no more than a ground-based radio-frequency source radiating within the GPS spectrum.

The JAGER system will autonomously locate the nearest beacon emitting electromagnetic signals at the target frequency: the GPS frequency in this scenario. Testing such a system is difficult due to the illegality of jamming the GPS signal within the United States. We instead test the system using a powerful Wi-Fi beacon as a proxy for the overpowering jammer. Excepting the target frequency, the procedure to locate the jammer is identical to the GPS case.

To receive the jamming signal, the front of the craft carries an antenna optimized to receive signals of the target wavelength; the current antenna has a 60° cone of maximum sensitivity. It is angled downward 30° from the horizontal, so that the craft can receive all signals from the horizon to 30° from vertical. This gives the UAV visibility over most of the space in front and underneath it. Like the other payload equipment on the vehicle, the antenna is secured with a fast-release mechanism so that it can be easily swapped out if necessary. For Wi-Fi tracking, we use a Yagi antenna with 60° beamwidth and 9 dBi gain. In upcoming trials, we will test different antenna configurations (such as dual antennas, small antenna arrays, and directional antennas augmented with omni-directional antennas) to determine benefits of these different layouts.

Signals from the antenna are passed into a module that converts the Wi-Fi data to serial, then from serial to USB. A single-board Linux computer with a quad-core processor then analyzes the signal data (see FIGURE 4). The hardware used to locate the jammer weighs 160 grams, so has negligible impact on the vehicle’s flight time or range.

Figure 4. Schematic of the tracking system on board the JAGER UAV. The resulting believed location of the target is passed to the autopilot.

Figure 4. Schematic of the tracking system on board the JAGER UAV. The resulting believed location of the target is passed to the autopilot.

To find the jammer’s location, the UAV performs a controlled yaw spin while recording the strength of the jamming signal. On the basis of the signal landscape surrounding the vehicle, the computer estimates the jammer’s location and sends a message to the autopilot instructing the craft to fly in that direction (or, more accurately, in a direction that optimally improves the ability of JAGER to find the jammer quickly). In return, the autopilot updates the tracking computer and ground station as to the vehicle’s position.

After moving a certain distance towards the jammer’s believed location, the craft repeats the spinning maneuver and starts the process again. Although rotating only the antenna might increase the speed of the operation, the energy required to carry the necessary antenna-rotation mechanisms for the duration of a flight is more than that needed to spin the entire craft.

The tracking algorithm is not as straightforward as gradient ascent or homing, and the vehicle will not always fly in the direction of greatest signal strength. The operational area is uneven, and may include buildings, towers, or airplanes, resulting in a complicated RF environment. Signals are scattered, diffracted and reflected, meaning that an algorithm that simply follows the strongest signal will not always converge on the actual jammer location.

To decide the optimal path from the vehicle’s present location to the jammer’s believed position, the tracking algorithm makes use of partially observable Markov decision processes (POMDPs). POMDPs model decision processes where the underlying state of the system (that is, the location of the jammer) is never completely known, and maintain a probability distribution over the set of all possible states.

The entire deployment area (an airport and its environs, for example) is split up into a square grid. For every possible combination of jammer and vehicle grid square locations, the signal strength and direction that would result is calculated offline prior to deployment and stored in a database on the tracking computer.

During the mission, the UAV records its own position and the sensed jamming signal’s strength and direction. The jammer location that would correspond to this result is retrieved from the database, as well as a measure of the strength of this belief state.

Once the craft has a belief as to the location of the jammer, it moves to a new location in the jammer’s believed direction before taking another measurement of signal strength. The new location and new measurement are combined, and the updated corresponding jammer location is retrieved from the database. This process is repeated until the vehicle believes itself to be right above the jammer, at which point a photograph is taken, the ground station is notified, and the hunting mission is complete.

Having found the jammer, the system can be programmed to execute a wide range of operations. These include reporting coordinates and a live image of the believed jammer location back to the ground station, hovering above and tracking the jammer if it begins to move, landing at the jammer site, or returning to base.

We calculate and store the POMDP decisions in advance of the flight. This strategy has some advantages. First, it allows for almost instantaneous decision-making. This is because the algorithm’s decisions are based solely on the vehicle’s current location and sensory observations and not on any previous states (a defining characteristic of a Markov decision process). The craft needs only to observe its current state in order to look up its next move in the database. This enables rapid tracking in flight.

A second advantage is that safety checks can be pre-programmed into the database in advance of deployment. While JAGER is programmed to move towards the grid square believed to contain the jammer, it can also be programmed to avoid or take special precautions when moving towards or in the vicinity of certain squares in the grid (also called geo-fencing). In an airport situation, for example, the vehicle would avoid moving into the square containing a control tower or ground-based antenna, or would fly at a minimum altitude over buildings and taxiways to avoid collisions.

Finally, the integration between the autopilot and the tracking software can provide other important safeguards: in the proof-of-concept system, any navigation decision taken by the software can be relayed to the ground for human verification before the UAV begins to move. This supervised mode of operation lends itself to a seamless migration path to fully autonomous operation (always overseen by a human operator).

However, one disadvantage of calculating and storing decisions in advance is the storage space needed on the vehicle. Because the result of every possible combination of vehicle and jammer locations within the grid is calculated, the size of the database grows quickly with increasing numbers of possible positions (and states). The larger the grid or the greater the required accuracy, the more space is needed to store the database. With current algorithms, the database needed to locate a jammer to within 30 meters in an area the size of an airport requires 15 gigabytes of storage space, resulting in longer lookup times during flight.

We are considering several strategies to mitigate this disadvantage, including better compression, more effective search algorithms, and uploading from a ground server only the parts of the database that correspond to the vehicle’s current operational area. Another strategy is to use an adaptive mesh that changes in resolution depending on the jammer’s belief state: at low certainty the database resolution is low, but increases in the appropriate area as the jammer’s location becomes more certain.

Another disadvantage of pre-solving the decision-making process is that the system must be reconfigured for every site in which it is deployed. The specifications of the tracking algorithm will change depending on the requirements of the operating area. The grid size, shape and absolute location must change to suit the area being protected. The resolution of the grid depends on the required accuracy of the tracking system, and restricted or prohibited locations must suit the terrain, buildings and geological features of the deployment space. For example, a lead JAGER vehicle could be adapted and tested to suit a particular airport, and then the bespoke algorithm and database uploaded to backup vehicles in that airport’s fleet.

APNT Performance

During the Joint Interagency Field Experimentation (JIFX) event at Camp Roberts, California, in November 2014, we tested the APNT system by deploying the vehicle with GPS, UAT and DME antennas simultaneously recording data. GPS receivers on the ground were used to collect reference measurements to estimate the time of transmission of the signals from the APNT sites. All signals were recorded at an altitude of 275 meters above ground level (600 meters above sea level), at four different points roughly 800 meters apart, and the data analyzed for comparison. As expected, the UAT broadcast was noisier than the GPS signal. However, it was possible to calculate a range from the UAT data that was accurate to within 16.6 meters of the GPS reference position, well within the 30 meters error bound specified in the project specification (see FIGURE 5).

Figure 5. UAT range deviates from GPS derived range-estimate by an average of only 16.6 meters throughout the duration of the test flight.

Figure 5. UAT range deviates from GPS derived range-estimate by an average of only 16.6 meters throughout the duration of the test flight.

While UAV navigation using APNT was done offline in post-processing for these tests, with planned algorithm improvements and hardware acceleration the UAT signal can be used to get real-time position information nearly as accurate as that from GPS. Thus the JAGER UAV can be navigated with comparable reliability in both GPS and GPS-denied environments.

Terrestrial APNT signals will be received at a wide range of power levels. This effect is not observed with the GPS network, as the different satellite signals are broadcast from such a great distance that any differences in received signal strength are relatively small by the time they reach Earth. For terrestrial networks, signals from transmitters close to the receiver can be many times stronger than those further away, which can result in two issues: 1) interference where one signal overwhelms another, and 2) inability to process a signal if the receiver does not have adequate dynamic range to capture strong and weak signals clearly.

This problem was observed in our tests, as we were receiving two signals: one 13.7 kilometers (DME) and the other 43.5 kilometers (ADS-B UAT) from our test site. Calculating accurate ranging estimates from the two required determining a gain setting that had dynamic range adequate for receiving both signals clearly.

Vehicle Performance

During experimental testing, the vehicle itself also underwent rigorous assessment of its performance under different conditions. Due to the delicate and often expensive nature of the payloads and experiments made possible by the JAGER platform, it is essential that the vehicle perform as expected, and that there are multiple procedures in place to protect the payloads in case of vehicle failure.

Because the open-source autopilot had never been used with such a large vehicle, we first ground-tested the craft’s flight control and stability. The vehicle was tethered and constrained to move in only one axis, and ropes were used to control its roll. While altering autopilot variables controlling roll and pitch feedback loops, we measured the vehicle’s response to impulsive disturbances and the time taken for it to right itself when upset. In this way we could tune the control gains and verify that the vehicle would be exceptionally stable during flight in even the most challenging atmospheric conditions. While we preferred to fly in the early morning hours to exploit clear air and lower winds, we did perform tests with momentary gusts of up to 7 m/s during envelope expansion flights.

We tested the vehicle with two accelerometers on board to measure how the rotors’ vibrations affected the rest of the craft. One accelerometer was attached to the airframe itself, while the other was secured to the payload plate. A comparison of the acceleration data recorded by the two instruments revealed that the payload plate experienced significantly less vibration than the airframe during flight, and both measurements remained well within the tolerances advised by the airframe manufacturer.

Two crucial flight modes also were tested before payloads were flown on the vehicle. Both altitude-control mode and position-control mode were tested to ensure that they could precisely constrain respectively the vehicle’s altitude and absolute position in a range of atmospheric conditions. Results showed that in altitude control mode, the vehicle’s z-coordinate was held constant to within ± 0.5 meters. In position control mode, its x- and y-coordinates remained within ± 1.0 meters (or a single vehicle length).

The success of the JAGER tracking mission also depends on accurate position measurements from the UAV. Operators must be confident in the vehicle’s position, so that ground forces can easily apprehend the located jammer, and also so that there is confidence in the success of safety protocols including geo-fencing, no-fly zones and minimum flight altitudes.

In addition to the geo-fencing and flight precautions taken by the tracking algorithm, the JAGER UAV has several other safety procedures executed automatically by the autopilot. A non-catastrophic error in the flight systems or payload is transmitted to the ground station for human troubleshooting, and commands can be sent to the vehicle as to how to proceed.

Finally, should we continue operations and allow its batteries to get sufficiently low, the vehicle will automatically return to launch site for landing and battery replacement. A catastrophic failure such as the loss of a motor will result in an immediate controlled landing. The craft can also be commanded from the ground station to land or return to launch, and can be taken over by a human pilot at any time.

Other tests verified that the vehicle has the range and endurance to be successful when deployed in an airport setting. When fully loaded with APNT and tracking payloads, the UAV exhibited a top speed of 10 m/s, enough to cover the length of an A380-capable runway in less than 5 minutes. A 20-minute flight endurance means that even including hovering during jamming signal observations by the tracking antenna, the JAGER system can hunt easily and effectively throughout an airport-sized area. Furthermore, we continue to explore techniques to improve dash capability, including reducing the weight of the APNT payload, and we anticipate describing results of these efforts in future reports.

Electromagnetic Interference

Because of the payload tray’s small area (0.5 m2), electromagnetic interference (EMI) between APNT components was a significant issue during testing. The GPS and UAT receivers are extremely sensitive to interference from other sources emitting in the frequency ranges to which they are tuned. The APNT computer, by contrast, is composed of various processors, clocks, drives and power boards that emit powerful electromagnetic noise at a wide range of frequencies as a byproduct of their normal operation.

The size and mass of the APNT computer board meant that it had to be mounted in the center of the payload tray to avoid unbalancing the UAV. That left a maximum 7 centimeters of space around the computer on which to mount the two antennas (see FIGURE 6). With no shielding, the EMI from the computer proved powerful enough to completely overwhelm the GPS, UAT and DME network signals, making navigation and position estimation using any network impossible.

Figure 6. Diagram showing the APNT experimental payload, and the proximity of the EMI-radiating CPU to numerous antennas.

Figure 6. Diagram showing the APNT experimental payload, and the proximity of the EMI-radiating CPU to numerous antennas.

The EMI problem was solved in three ways. Masts were used to raise the receiving antennas to a height of 19 centimeters above the payload tray, the maximum height at which a mast collapse wouldn’t cause catastrophic rotor and vehicle failure.

The antennas also were moved around the edge of the payload tray so as to be furthest from the system components radiating at their particular frequency. Two devices that proved particularly problematic were the solid-state hard drive in the CPU and the telemetry radio antenna, which radiated EMI that interfered with the GPS and UAT frequencies respectively. This was solved by moving the telemetry antenna to the underside of the craft, and the GPS antenna to the far side of the payload plate from the hard drive. The flexible design of the payload plate described earlier ensured that the relocation and testing of components was a straightforward process.

Shielding, however, proved to be the most important factor in eliminating EMI. Custom-made copper shields were added to the two masts to shield the antennas from the computer below them while still allowing an unobstructed view of the sky (see PHOTO). We tested numerous shielding iterations, including wire meshes and aluminum and lead foils; however; all were ineffective due to the strength and wide range of EMI wavelengths emitted. Finally, the computer itself was covered in a 2-millimeter layer of copper and 1-millimeter steel sheet. This combination struck the best balance between effectiveness and weight: aluminum was light but proved ineffective at shielding, while lead was very effective at EMI shielding but was too heavy for the UAV to carry.

The APNT payload prior to installation of the DME antenna. The copper shielding on the CPU and antennas can be clearly seen.

The APNT payload prior to installation of the DME antenna. The copper shielding on the CPU and antennas can be clearly seen.

Conclusions

The development of the JAGER system contributes to U.S. preparation for a GPS jamming attack on civil aviation. While the first iteration described here is a significant improvement on previous jammer-hunting systems, future iterations of the JAGER UAV will be able to successfully navigate in a GPS-denied environment using alternative navigation signals including UAT and DME, and broadcast an accurate estimate of their position down to the ground.

The use of an octocopter flight system gives speed, maneuverability and sensory perception that far exceed any ground-based tracking effort. A fully loaded top speed of 10 m/s and almost instantaneous direction changes allow for efficient hunting over an airport-sized area and the location of a GPS jammer to within 30 meters, within a 20-minute flight endurance.

As the JAGER system can be entirely assembled from commercially available or open-source components and operates entirely autonomously, the system provides a low-cost, readily obtainable solution to the problem of GPS jamming. This means that it can be deployed quickly and is operable without extensive prior training.

The integration of autopilot, APNT navigation and tracking systems also allows for comprehensive monitoring and control of the UAV from the ground. Telemetry and data links to the ground station provide real-time updates as to the craft’s position, the jammer’s believed location and the status of all systems and instruments running on the vehicle. Safety protocols implemented in the software ensure that there is no risk of collision with site buildings, vehicles or personnel.

JAGER’s modular design gives operators extensive flexibility in situations that are capable of being successfully resolved by the system. The switching of equipment and software to allow the UAV to use GPS navigation to hunt a UAT or DME jammer, for example, could be effected in a matter of seconds.

The JAGER system also provides a reliable test platform for any experiment that requires airborne operation. The exceptional stability of the airframe combined with extended flight time, high top speeds and pinpoint positioning lends the system to a wide variety of applications beyond jammer tracking, including network monitoring, atmospheric experiments and biological research.

Manufacturers

The JAGER UAV airframe is a S1000 octocopter by DJI Innovations, Shenzhen, China; the flight batteries are a 8000 mAh model by Hextronik, Dongguan, China; the autopilot hardware and GPS antenna is a Pixhawk by 3D Robotics, Inc., San Diego, California; the autopilot software is based on PX4 by Pixhawk.org. The JAGER navigation GPS is made by u-blox, and the receiver for the APNT clock is made by Trimble. The UAT hardware includes an ASR-2300 multichannel transceiver by Loctronix Corporation, Woodinville, Washington; the tracking hardware comprises a 2.4 GHz Yagi antenna from L-com, North Andover, Massachusetts; an RN-XV Wi-Fi module by Roving Networks, Chandler, Arizona; and an Odroid-U3 computer by Hardkernel Co., Gyeonggi, South Korea.


James Spicer is pursuing concurrent bachelor’s and master’s degrees in aeronautics and astronautics at Stanford University.

Adrien Perkins is a Ph.D. candidate in aeronautics and astronautics at the Stanford University GPS Laboratory. He received his undergraduate degree in mechanical aerospace engineering at Rutgers University.

Louis Dressel is a graduate student at Stanford University. He received his undergraduate degree in aerospace engineering from Georgia Tech, with a minor in computer science.

Mark James is a master’s student in aeronautics and astronautics at Stanford University.

Yu-Hsuan Chen is a research associate at the Stanford GPS Laboratory. He received his Ph.D. in electrical engineering from National Cheng Kung University, Taiwan.

Sherman Lo is a senior research engineer at the Stanford GPS Laboratory.

David S. De Lorenzo is a principal research engineer at Polaris Wireless and a consulting research associate to the Stanford GPS Laboratory.

Per Enge is a professor of aeronautics and astronautics at Stanford University, where he is the Vance D. and Arlene C. Coffman Professor in the School of Engineering. He directs the Stanford GPS Laboratory.

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