Simultaneous Localization of Multiple Jammers and Receivers Using Probability Hypothesis Density
Sriramya Bhamidipati and Grace Xingxin Gao, University of Illinois at Urbana-Champaign
The Global Positioning System (GPS) is indispensable for critical infrastructures, such as transportation, communication systems, finance and power grids. However, due to low signal power, the civil GPS signals are vulnerable to jamming attacks. A jammer broadcasts high power signals in the GPS frequency band and causes the receiver to lose track of the satellites. The availability of these low-cost jammers in the commercial market increases the potential threats incurred during critical operations. A few notable jamming incidents occurred near Newark airport  and in United Kingdom , where the GPS-based navigation systems malfunctioned for a significant period. Therefore, it is critical to locate the jammers accurately to ensure prompt neutralization of these malicious devices. In addition, to facilitate robust operation of critical infrastructure, we need jamming-resilient techniques to estimate their position.
We propose a novel algorithm to simultaneously localize an unknown number of active jammers and a network of vehicles (experiencing the effects of jamming) using graph theory and Probabilistic Hypothesis Density (PHD) recursion. Under jamming, the noise power of the GPS signal increases and the overall signal-to-noise ratio of the GPS satellite channel decreases. In our framework, we consider an unknown number of stationary jammers (M) placed at unknown locations and transmitting at the same power. We exploit the motion of N moving vehicles with unknown position coordinates and the difference in the received noise power of their GPS signals to constrain our graphical framework.
Considering the motion of vehicles to be uncorrelated, we formulate a cooperative bipartite graphical framework to simultaneously localize the jammers and vehicles in a sequential manner. We designate one of the vehicle as master and the others as slaves. For each vehicle, we design the graphical architecture as follows: the first layer of variable nodes common to all the vehicles represents the unknown location coordinates of stationary jammers (M). The nodes in the second layer depicts the sequential time series of the vehicle’s unknown location constrained by its motion model. We propose a fully connected framework, where the edges connect the nodes of the first layer to the next. These edges represent weights that indicate the increase in GPS noise power due to the respective jammer. The aggregate of these weights at each of the nodes in the second layer are constrained by the received GPS noise power of the vehicle at that instant. Based on the above architecture, we use graph theory and PHD recursion for simultaneous localization of jammers and vehicles as follows:
1. Once jamming is detected, we initialize our algorithm with a guess estimate of the position of a single jammer (M=1) and the positions of N moving vehicles.
2. We apply PHD recursion to compute the maximum peak in posterior intensity (first order statistical moment) and thereby jointly estimate the number of jammers and the relative distance between each vehicle-jammer pair. We incorporate this as an additional constraint while optimizing our graphical model.
3. Based on the current estimate of the number of jammers, we formulate a cost function that minimizes the squared difference in the received GPS noise power and the total expected jamming power across the network of receivers summed from the start of time till the current time instant.
4. We optimize our graphical model using Levenberg-Marquardt algorithm and thereby estimate the location of all vehicles and jammer positions with respect to the master-designated receiver.
5. The steps 2-4 are iteratively repeated to converge to the accurate number of jammers as well as the position of the vehicles and jammers until jamming lasts.
Our experimental setup consists of a network of independent moving vehicles each equipped with a GPS receiver and spread out in a 10-15-mile radius. We perform statistical analysis to estimate the bounds on the number of vehicles required to obtain accurate convergence with respect to the number of jammers and the transmit power. We validate the accuracy of our jamming-resilient algorithm for different cases of unknown jammers and their varying transmit power as compared to dead reckoning which drifts over time. For jamming transmit power levels where the traditional scalar tracking fails, we demonstrate that our novel algorithm both detects the correct number of jammers and accurately estimates the jammer and vehicle locations.
 Strunsky, Steve, Newark Star-Ledger, N.J. Man Fined 32k for Illegal GPS Device that Disrupted Newark Airport System, 8 August 2013
 Vallance, Chris, 21 February 2012, Sentinel Project Reveals UK GPS Jammer Use, BBC News