From the time that John W. Tukey started to do serious work in statistics, he was interested in problems and techniques of data analysis. Some people know him best for exploratory data analysis, which he pioneered, but he also made key contributions in analysis of variance, in regression and through a wide range of applications.This paper reviews illustrative contributions in these areas.

John W. Tukey and data analysis

Factor graph optimization (FGO) recently has attracted attention as an alternative to the extended Kalman filter (EKF) for GNSS-INS integration. This study evaluates both loosely and tightly coupled integrations of GNSS code pseudorange and INS measurements for real-time positioning, using both conventional EKF and FGO with a dataset collected in an urban canyon in Hong Kong. The FGO strength is analyzed by degenerating the FGO-based estimator into an “EKF-like estimator.” In addition, the effects of window size on FGO performance are evaluated by considering both the GNSS pseudorange error models and environmental conditions. We conclude that the conventional FGO outperforms the EKF because of the following two factors: (1) FGO uses multiple iterations during the estimation to achieve a robust estimation; and (2) FGO better explores the time correlation between the measurements and states, based on a batch of historical data, when the measurements do not follow the Gaussian noise assumption.

Factor graph optimization for GNSS/INS integration: A comparison with the extended Kalman filter

Synchrophasor technology opens a new window for power system observability. Phasor measurement units (PMUs) are able to provide synchronized and accurate data such as frequency, voltage and current phasors, vibration, and temperature for power systems. Thus, the utilization of PMUs has become quite important in the fast monitoring, protection, and even the control of new and complicated distribution systems. However, data quality and communication are the main concerns for synchrophasor applications. This study presents a comprehensive survey on wide-area monitoring systems (WAMSs), PMUs, data quality, and communication requirements for the main applications of PMUs in a modern and smart distribution system with a variety of energy resources and loads. In addition, the main challenges for PMU applications as well as opportunities for the future use of this intelligent device in distribution systems will be presented in this paper.

A Comprehensive Survey on Phasor Measurement Unit Applications in Distribution Systems

The concept of user-level integrity monitoring has been successfully applied to air transport navigation systems mainly focusing on the errors associated with space (satellite system) data processing chain. However, little research effort has been devoted to the study of land vehicle navigation system integrity monitoring. The primary difference is that one needs to consider the errors associated with a spatial map, and the map-matching process when monitoring the integrity of a land vehicle navigation system. To date research has focused on either the integrity of raw positioning information obtained from a satellite system or the integrity of the map-matching process and digital map errors. Here, for the first time all these errors are considered together, and additionally, road network complexity is also taken into account. Therefore, the main contribution of this paper is to develop user-level integrity monitoring by taking into account all the errors associated with a navigation system simultaneously; and to consider the operational environment (i.e., road complexity) to further improve the performance. The errors associated with a spatial road map are given special attention. Two knowledge-based fuzzy inference systems are developed to measure the integrity scale. The performance of the integrity method is checked using field data collected in Nottingham, UK. The integrity method can give 98.4% valid warnings. This is superior to existing integrity methods for land vehicle navigation, and has the potential to support real-time ITS applications.

Map-Aided Integrity Monitoring of a Land Vehicle Navigation System

This paper establishes a fundamental theory of secure clock synchronization. Accurate clock synchronization is the backbone of systems managing power distribution, financial transactions, telecommunication operations, database services, etc. Some clock synchronization (time transfer) systems, such as the global navigation satellite systems, are based on one-way communication from a master to a slave clock. Others, such as the network transport protocol, and the IEEE 1588 precision time protocol (PTP), involve two-way communication between the master and slave. This paper shows that all one-way time transfer protocols are vulnerable to replay attacks that can potentially compromise timing information. A set of conditions for secure two-way clock synchronization is proposed and proved to be necessary and sufficient. It is shown that IEEE 1588 PTP, although a two-way synchronization protocol, is not compliant with these conditions, and is therefore insecure. Requirements for secure IEEE 1588 PTP are proposed, and a second example protocol is offered to illustrate the range of compliant systems.

Requirements for Secure Clock Synchronization

For robust GPS-vision navigation in urban areas, we propose an Integrity-driven Landmark Attention (ILA) technique via stochastic reachability. Inspired by the cognitive attention in humans, we perform convex optimization to select a subset of landmarks from GPS and vision measurements that maximizes the integrity-driven performance. Given the known measurement error bounds in non-faulty conditions, our ILA follows a unified approach to address multiple measurement faults and works with any off-the-shelf estimator. We analyze measurement deviation to estimate the stochastic reachable set of expected position for each landmark, which is parameterized via probabilistic zonotope (p-Zonotope). We apply set union to formulate a pZonotopic cost that represents the size of position bounds based on landmark inclusion or exclusion. We jointly minimize the p-Zonotopic cost and maximize the number of landmarks via convex relaxation. For an urban dataset, we demonstrate improved localization accuracy and robust predicted system availability for a pre-defined alert limit.

Integrity-Driven Landmark Attention for GPS-Vision Navigation via Stochastic Reachability

Now-a-days, the availability of low-cost jammers in the commercial market is increasing. Due to this, there has been a rising risk of multiple jammers, not just one. However, it is challenging to locate multiple jammers because the traditional way of jammer localization via multilateration only works for one jammer. In addition, during attack the positioning capability of the receivers is compromised due to their inability to track the GPS signals. We propose our Simultaneous Localization of Multiple Jammers and Receivers (SLMR) algorithm by utilizing the signal power received at a network of receivers. Our algorithm not only locates multiple jammers, but also utilizes the jammers as additional navigation signals for positioning the receivers. In particular, we design a non-linear Gaussian Mixture Probability Hypothesis Density Filter over a graphical framework, which is optimized using Levenberg-Marquardt minimizer. Under the presence of multiple simulated jammers, we validate that our proposed SLMR algorithm is able to simultaneously locate multiple jammers and receivers, even though the number of jammers is unknown.

Simultaneous localization of multiple jammers and receivers using probability hypothesis density

Our work highlights the improved robustness of Phasor Measurement Units (PMUs) against meaconing i.e., record and replay attack by incorporating new protective measures to our prior work on Direct Time Estimation (DTE). In this paper, we propose a novel GPS spoofer localization based Multi-Receiver Direct Time Estimation (MRDTE) algorithm by leveraging the geometrical diversity of multiple receivers. DTE performs non-coherent summation across the satellites to evaluate the likelihood of the clock candidates considered from a pre-generated search space.

Firstly, we execute DTE based multiple peak vector correlation to detect the presence of spoofer. Thereafter, we compare the time-delayed similarity in the signal properties across the geographically distributed receivers to distinguish these spoofing signals. Lastly, we perform non-coherent summation across the satellites at individual receiver level and then incorporate a Joint Filter module. This module includes a Particle Filter to estimate the spoofer location and a Kalman Filter to collectively process the maximum likely clock parameters obtained from individual receivers to estimate the precise UTC time.

We validate our algorithm under a complex case of meaconing attack generated by recording the GPS signals in the same place as our multi-receiver setup and later replaying them from a different location with higher power. Our experimental results demonstrate precise localization of the spoofer while simultaneously computing the GPS time to within the accuracy specified by the power community (IEEE C37.118).

GPS spoofer localization for PMUs using multi-receiver direct time estimation

A wide-area time authentication algorithm is proposed to compute the Global Positioning System (GPS) timing that is resilient against spoofing attacks. The considered wide-area network consists of multiple GPS receiving systems, each comprising of the innovative distributed multiple directional antennas (DMDA) setup triggered via a common clock.Based on the communication infrastructure of the grid, the single-difference pseudorange residuals across the antennas are processed using the wide-area belief propagation-based extended Kalman filter (BP-EKF) algorithm in a distributed manner. To detect spoofing, a KL-divergence-based threshold is used to estimate the dissimilarity in the antenna-specific timing errors. Thereafter, the pseudoranges are corrected using the BP estimates of timing error and processed via adaptive EKF to compute the GPS timing, which is given to the phasor measurement units (PMUs). We have demonstrated the successfully detection and mitigation of the external timing attack, by subjecting one receiving system to a simulated meaconing attack that induces a 60 micro second time delay. Thereafter, by analyzing the voltage stability index of a critical node in the simulated grid, we have also validated the compliance of the proposed wide-area BP-EKF estimated timing with the IEEE-C37.118 standards.

Wide-Area GPS Time Monitoring Against Spoofing Using Belief Propagation

For the future Smart Grid, devices called Phasor Measurement Units (PMUs) are being widely deployed to continuously monitor the state of the power grid in real-time. The voltage and current phasor measurements are synchronized across the network using GPS. However, because civilian GPS signals are unencrypted, these receivers are susceptible to being spoofed. In this work, we propose a wide-area spoofing detection algorithm for PMUs using a hybrid communication architecture which overlays NAPSInet, a proposed communication structure for the future Smart Grid. We create conditioned signal snippets which contain the military P(Y) signal, whose precise code sequence is unavailable to civilian users and thus cannot be generated by an attacker. Thus, the encrypted signal establishes a type of signature in the background of all authentic GPS signals, the presence of which can be verified by correlating between conditioned signals from other distant receivers. We further consider the potential for a coordinated spoofing attack against regional collections of cross-check receivers and generate representative snippets for each regional network to verify against other distant sites. Additionally, we use real-world data recorded during a government-sponsored, live-sky spoofing event and demonstrate our algorithm can successfully evaluate the authenticity of a widely dispersed network of receivers.

Sriramya Bhamidipati

Papers

Integrity-Driven Landmark Attention for GPS-Vision Navigation via Stochastic Reachability

Simultaneous localization of multiple jammers and receivers using probability hypothesis density

GPS spoofer localization for PMUs using multi-receiver direct time estimation

Wide-Area GPS Time Monitoring Against Spoofing Using Belief Propagation

Detecting GPS spoofing via a multi-receiver hybrid communication network for power grid timing verification