Multi-Constellation GNSS: New Bounds on DOP and a Related Satellite Selection Process

GPS receivers convert the measured pseudoranges from the visible GPS satellites into an estimate of the position and clock offset of the receiver. For various reasons receivers might only track and process a subset of the visible satellites. It would be desired, of course, to use the best subset. In general selecting the best subset is a combinatorics problem; selecting m objects from a choice of n allows for n m potential subsets. And since the GDOP performance criterion is nonlinear and non-separable, finding the best subset is a brute force procedure; hence, a number of authors have described sub-optimal algorithms for choosing satellites. This paper revisits this problem, especially in the context of multiple GNSS constellations, for the GDOP and PDOP criteria. Included are a discussion of optimum constellations (based upon parallel work of these authors on achievable lower bounds to GDOP and PDOP), musings on how the non-separableness of DOP makes it impossible to rank order the satellites, and a review/discussion of subset selection algorithms. Our long term goal is the development of better selection algorithms for multi-constellation GNSS

APNT for GNSS Spoof Detection

Global Navigation Satellite Systems (GNSS) are well known to be accurate providers of position, navigation, and time (PNT) information across the globe. With capable receivers and well-populated satellite constellations, GNSS users typically believe that the position and time information provided by their GNSS receiver is perfectly accurate. More sophisticated users look beyond accuracy and are also concerned with the integrity of the GNSS information. Advances in electronics technology have enabled the creation of malicious RF interference of GNSS signals. Inexpensive jamming devices overpower or distort the GNSS receivers input so as to completely deny the GNSS user of PNT information. A second threat to GNSS integrity is spoofing, the creation of counterfeit GNSS signals. This type of attack is considered more dangerous than a jamming attack since an erroneous PNT solution is often worse than no solution at all. The detection of spoofing is the subject of this paper. A variety of approaches have been proposed in the literature to recognize spoofing; many of these are based on the RF signal alone, including multi-antenna and multi-receiver methods. Another class of spoof detection algorithm is to compare the GNSS result to data from another, non-GNSS (hence, non-spoofed) sensor. In this paper we imagine that the trusted signal is the output of an Alternative PNT (APNT) receiver. APNT refers to stand alone, non-GNSS systems that are intended to provide PNT information during periods in which GNSS is unavailable The wide recognition of the vulnerabilities of the GPS in the Volpe report spurred the search for APNT systems; examples include the development of eLoran in the U.S. and Europe, general work on signals of opportunity ranging, DME-DME positioning, and, quite recently, R-Mode in Europe (we note that none of these systems is currently operational). The intent is that an integrated receiver, either loosely or tightly coupled, would merge the two systems’ observables to yield the best PNT information possible; in practice, since the APNTs’ solutions are typically of lower accuracy than the GNSS solutions, the combined result is nearly equal to the GNSS-alone solution. The goal of this paper is to show that these APNT solutions should be used at ALL times; as a substitute for GNSS PNT when GNSS is unavailable and as an integrity check (e.g. spoof detector) when GNSS is available. At a cursory level spoof detection using APNT appears simple; just compare the two position outputs to see if they are close. This paper looks deeper, considering the questions: How can we use the time estimates to detect position spoofing? How close is close enough in this context? What is the probability of error in the decision? How do the geometries of both systems impact the test itself and its resulting performance? What happens if the receivers are providing different information

Rethinking Star Selection in Celestial Navigation

In celestial navigation the altitude (elevation) angles to multiple celestial bodies are measured; these measurements are then used to compute the position of the user on the surface of the Earth. Methods described in the literature include the classical “altitude-intercept” algorithm as well as direct and iterative least-squares solutions for over determined situations. While it seems rather obvious that the user should select bright stars scattered across the sky, there appears to be no established results on the level of performance that is achievable based upon the number of stars sighted nor how the “best” set of stars might be selected from those visible. This paper addresses both of these issues by examining the performance of celestial navigation noting its similarity to the performance of GNSS systems; specifically, modern results on GDOP for GNSS are adapted to this classical celestial navigation problem

GNSS Spoof Detection Using Passive Ranging

Advances in electronics technology have enabled the creation of malicious RF interference of GNSS signals. For example jamming completely denies the GNSS user of position, navigation, and time (PNT) information. While a serious concern when we expect PNT at all times, current generation GNSS receivers often warn the user when PNT is unavailable. A second threat to GNSS integrity is spoofing, the creation of counterfeit GNSS signals with the potential to confuse the receiver into providing incorrect PNT information. This type of attack is considered more dangerous than a jamming attack since erroneous PNT is often worse than no solution at all. A variety of approaches have been proposed in the literature to recognize spoofing and can vary widely based upon the assumed capabilities and a priori knowledge of the spoofer. One method is to compare the GNSS result to data from a non-GNSS sensor. At the January 2016 ION ITM these authors developed and analyzed a spoof detection algorithm based upon measurements from an active ranging system (distances, but no heading). This paper expands the class of signals viable for this spoofing detection approach to passive ranging; equivalently, to range measurements which depend upon knowledge of precise time (effectively pseudoranges)

Lower Bounds on DOP

Code phase Global Navigation Satellite System (GNSS) positioning performance is often described by the Geometric or Position Dilution of Precision (GDOP or PDOP), functions of the number of satellites employed in the solution and their geometry. This paper develops lower bounds to both metrics solely as functions of the number of satellites, effectively removing the added complexity caused by their locations in the sky, to allow users to assess how well their receivers are performing with respect to the best possible performance. Such bounds will be useful as receivers sub-select from the plethora of satellites available with multiple GNSS constellations. The bounds are initially developed for one constellation assuming that the satellites are at or above the horizon. Satellite constellations that essentially achieve the bounds are discussed, again with value toward the problem of satellite selection. The bounds are then extended to a non-zero mask angle and to multiple constellations

Using Range Information to Detect Spoofing in Platoons of Vehicles

GNSS are well known to be accurate providers of position information across the globe. Because of high signal availabilities, capable/robust receivers, and well-populated satellite constellations, operators typically believe that the location information provided by their GNSS receiver is correct. More sophisticated users are concerned with the integrity of the derived location information. Attacks on GNSS availability and integrity are known as jamming and spoofing. Jamming involves the transmission of signals that interfere with GNSS reception so that the receiver is unable to provide a position or time solution; various methods to detect jamming, and possibly overcome it, have been considered in the literature. Spoofing is the transmission of counterfeit GNSS signals so as to mislead a GNSS receiver into reporting an inaccurate position or time. If undetected, spoofing might be much more dangerous than a jamming attack. A variety of approaches have been proposed in the literature to recognize spoofing. Of interest here are methods which compare GNSS information to measurements available from other, non-GNSS sensors. Recent ION conferences have included several examinations of combining GNSS and non-GNSS data toward spoof detection. This paper considers the use of range-only information to detect GNSS spoofing of a platoon of vehicles equipped with inter-vehicle communications: a statistical model of the problem is developed in which the spoofer is assumed to have limited geographical impact (i.e. only spoofs a subset, nominally one, of the vehicles in the platoon); under a Neyman-Pearson formulation the (generalized) likelihood ratio test to fuse the GNSS and range measurements is presented; examples are included to demonstrate the resulting performance

The Use of Bearing Measurements for Detecting GNSS Spoofing

GNSS are well known to be accurate providers of position information across the globe. Because of high signal availabilities, robust receivers, and well-populated constellations, operators typically believe that the location information provided by their GNSS receiver is correct. More sophisticated users are concerned with the integrity of the derived location information; for example, employ RAIM algorithms to address possible satellite failure modes. The most common attacks on GNSS availability and integrity are known as jamming and spoofing. Jamming involves the transmission of signals that interfere with GNSS reception so that the receiver is unable to provide a position or time solution. Various methods to detect jamming, and possibly overcome it, have been considered in the literature. Spoofing is the transmission of counterfeit GNSS signals so as to mislead a GNSS receiver into reporting an inaccurate position or time. If undetected, spoofing might be much more dangerous than a jamming attack. A typical maritime concern is a spoofer convincing a tanker traveling up a channel to a harbor that it is off track of the channel. A variety of approaches have been proposed in the literature to recognize spoofing; many of these are based on the RF signal alone as, in some sense, they are the simplest to implement. Of interest here are methods which compare GNSS information to measurements available from other, non-GNSS sensors. Examined examples include IMUs, radars, and ranges/pseudoranges from non-GNSS signals. In all cases the data from these others sensors is compared to the position information from the GNSS receiver to assess its integrity. Triangulation of position from bearing measurements is a well-known localization technique, especially for the mariner. This paper considers the use of bearing information to detect GNSS spoofing in a 2-D environment. A typical marine application is a ship entering a harbor and using an alidade to sight landmarks; for mobile, autonomous vehicles the sensor might be a camera taking a bearing to a nearby vehicle or to a signpost. This paper presents a mathematical formulation of the problem and the sensor data, develops a statistical model of the measurements relative to the GNSS position output, constructs a generalized likelihood ratio test detection algorithm based on the Neyman-Pearson performance criterion (maximizing probability of detection while bounding the probability of false alarm), and examines performance of the test, both through analysis and experimentation. A comparison to using both range and bearing is included to show the utility and limitations of bearing data to spoof detection

Modernized eLoran: The Case for Completely Changing Chains, Rates, and Phase Codes

First deployed in the U.S. in 1957, Loran-C dominated radio-based navigation for many years. In 2000 the FAA began a significant recapitalization of Loran in the U.S.; the 2001 Volpe report on the vulnerability of the GPS reinforced the need for a revamped Loran. What emerged was an enhanced or evolved version, so called eLoran, aiming to achieve, for example, 10- 20 meter absolute positioning accuracy, RNP 0.3 mile required navigation performance, and stratum 1 time. After 10 years of development, in 2010, this U.S. e ffort was halted and the U.S. transmitters were silenced; since that time, eLoran is still being developed in Europe and deployed in Asia. Earlier this year U.S. Government interest in eLoran has again stirred (evidenced by a U.S. Army request for information and a U.S. Dept. of Transportation request for public comment); the rest of these initiated much conversation at the 2015 ION ITM. The prior U.S. (and continuing European) development of eLoran kept many of the 1950\u27s system design choices so as to be compatible with legacy Loran receivers. These include the pulse shape, groups, chains, rates, phase codes, emission delays, etc. Chosen to suit 1950\u27s technology, many of these restrictions are no longer necessary given the advances in transmitter and receiver technology (e.g. software defined radio) over the last half century. It is the opinion of these authors that as Loran, per se, no longer exists in the U.S., any re-emergence of a low frequency radio navigation system need not be held to these performance limiting constraints. In prior work these authors have promoted more significant changes to eLoran to improve system performance; specifically, single-rating all stations, reconquering the chain/rate structure within the continental U.S., and changing the phase codes. The current paper expands on these prior e fforts. Specifically, we propose putting all of the eLoran transmitters on the same repetition period and employing unique phase codes for each transmitter. To effectively choose new phase codes for eLoran, and assess their performance, we rely on the auto- and cross-correlation metrics. These metrics describe how well a receiver can both acquire and track a specific signal when contaminated by multi- path interference, the existence of other signals, and noise. While a perfect auto-correlation function, large at zero lag corresponding to the actual arrival of the signal and zero elsewhere, and a perfect cross- correlation function, zero for all lags, are preferred, it is impossible to find such codes. However, limiting the size of the window for which we require perfect auto- and cross-correlations, such codes can be found. To create such codes for eLoran we adapt results from the CDMA literature on complementary sequences and Large Area Synchronized (LAS) codes. This paper begins with a brief review of the relevant characteristics of Loran-C, including a discussion of the effects of sky wave and cross rate interference. This is followed by a survey of previously published ideas/concepts on how elements of the system could be changed so as to improve performance. Finally, details on the proposed rate/chain/phase code structure are presented. The reader should recognize that these ideas and results are not intended to define what the best eLoran system would be; rather, if eLoran soars again in the U.S., we hope to initiate a dialogue that looks beyond the decisions made in the 1950\u27s

GDOP Bounds for GNSS Augmented with Range Information

Code phase GNSS receivers convert the measured satellite pseudoranges into estimates of the position and clock offset of the receiver, typically via an iterative, linearized least squares method. Since the pseudoranges themselves are noisy, the resulting estimates of position and time are random variables. To describe the accuracy of this solution, it is common to describe it statistically via the error covariance matrix. Rather than considering the individual elements of this covariance matrix, users frequently reduce it to a scalar performance indicator; the most common of these is the Geometric Dilution of Precision (GDOP). It is well known that the GDOP is a function of the satellite geometry; with only a few visible satellites in poor locations, the GDOP can become quite large. However, for a future with multiple, fully occupied GNSS constellations it is expected that receivers would select those satellites to track so as to achieve the best possible performance. Hence, an understanding of both how small the GDOP can be as a function of the number of satellites visible and the characteristics of the constellations that meet that bound are of value. Further, once identified, a receiver could exploit those constellation characteristics in selecting a subset of satellites. Investigating the best possible GNSS satellite constellation with respect to the GDOP is not a new problem. Recently, these authors developed achievable lower bounds to the GDOP as a function of the number of satellites; the bounds were also extended to non-zero mask angle and to multiple GNSS constellations. Further, using actual GPS satellite ephemeris data, it was shown by example that good GDOP performance resulted from constellations similar to the “best constellations resulting from the bounds. This paper examines augmentation of the GNSS pseudoragnes with data from non-GNSS sensors; specifically, ranges. While integration of GNSS and non-GNSS sensors is not novel, the perspective in the paper is how such external sensors impact potential receiver performance (i.e. minimum GDOP) and what role they play in satellite selection. Specifically, tight lower bounds to GDOP when the GNSS is augmented by this additional measurement (barometric altimeter or a DME slant range) are presented; achievability of the bounds is also examined

Learning Communities: A Business School Perspective

This paper discusses the organization and operation of a university learning community program at the University of North Carolina at Greensboro (UNCG). After several years, the program administrator and certain of the faculty and staff reflected on the achievements of the program. The learning community concept is discussed as well as the nature of the learning activities both general and those specific to the business school. The program reported higher levels of student retention and students reported higher involvement in leadership skill development and the UNCG community than students who were not in the learning community program