In this chapter we consider how external aiding data can be used in acquisition, tracking, and positioning. We use aiding from Inertial Navigation Systems (INS). In general any system which provides measurements of vehicle dynamics such as velocity and acceleration can be used. In particular, we can use relatively cheap inertial measurement unit (IMU) sensors, such as MEMS accelerometers and gyros, to provide suitable information in a wide range of applications, including those less technically demanding. However, we base our examples on a rather more demanding INS for an airborne navigation complex. The theory, approach, and algorithms are applicable to low-end consumer applications in general, however, rather than only to aviation and space applications, which would have been the case just a decade ago at the time of writing.

Principles of GNSS and INS integration

The GNSS gives stable navigation solutions as long as the receiver maintains a signal lock on four or more satellites. We discussed in Chapter 1 that information about height allows us to discard one variable and reduce the number of satellites required to three. Furthermore, a stable enough clock (usually not a part of a conventional receiver) allows reduction of this number to two. In the case of aircraft, attitude information is essential. Clock stability in general is not good enough to assume a constant receiver clock error. Therefore, if the number of satellites is reduced to fewer than four due to signal blockage, intentional/unintentional interference, etc., the position and timing solution will be lost. Vulnerability of GNSS radiowave propagation is a critical issue for aviation safety.

In this chapter we consider in detail how one can compensate errors in GNSS observables. GNSS observables can be constructed from code and carrier measurements made on different frequencies in various ways. Some of these observables are less affected by particular errors than others. We also consider how the usage of measurements from other receivers located at known positions allows elimination of some errors (Figure 8.1).

Error budget of GNSS observables

As explained in previous chapters, we can describe GNSS errors in the form of an error budget. The budget consists of the following errors:

• DOP arising from geometrical properties of the satellite constellation (see Chapter 1);

• Satellite-related errors, including satellite clock error, satellite orbit errors, satellite transmitter errors, including biases (see Chapter 3);

• Propagation errors in a dispersive medium due to the ionosphere (see Chapter 4);

• Propagation errors in a non-dispersive medium due to the troposphere (see Chapter 4);

• Receiver-related errors including noise and hardware biases (see Chapter 5);

• Multipath (see Chapter 7).

We have described the errors related to signal propagation in the atmosphere in Chapter 4. Some R&D tasks may require more specific models to be implemented, especially where development of new algorithms is concerned. One example is spatially correlated ionospheric errors. Algorithm development related to a virtual reference station (VRS), network RTK, or ionospheric research may require an ability to generate a spatially correlated ionospheric model. In that case the signal is generated for more than one receiver and ionospheric errors are properly correlated. The specific fluctuations of TEC distribution can be added on top of nominal TEC distribution. These nominal TEC distribution values come from true Klobuchar, NeQuick, or IGS models. The other example is to specify an anomalous ionospheric gradient with parameters in accordance, for example, with WAAS Super Truth data analysis and simulate a moving slope for the ionospheric gradient. For details of the Threat Model of an anomalous ionosphere gradient see [1]. In this case some specific fluctuations or slope can be implemented on top of the regular total electron count (TEC) distribution model.

Though GNSS satellites are just some among many other satellites which are implemented for geophysical measurements, GNSS play a very significant and increasing role in collecting geophysical data. They have become an indispensable tool for many geophysical applications. Apart from this, GNSS satellites have also allowed spread spectrum radiowave technology to mature. This technology can be used on its own for atmosphere probing in other parts of the electromagnetic spectrum than GNSS’s. Together with other atmosphere sensing instruments, GNSS provides information for weather prediction and monitoring climate change. GNSS has also become an essential tool for estimation of the Earth’s rotation parameters. There are also emerging areas of paramount importance, which are yet under development, such as using GNSS signals for earthquake studies. Figure 11.1 depicts the subject of this chapter in relation to other chapters in this book.

Data from global reference networks are routinely used to monitor movement of the Earth’s tectonic plates relative to each other and to an inertial frame. In this task the same type of GNSS observables as described in Chapter 8 are used. Such observables are created using measurements from globally distributed networks of GNSS receivers, supplying various data in raw data formats, mostly in RINEX. The most prominent among such networks is the IGS network. There are also various regional and local networks, which can provide large volumes of geophysical information. Among such networks, for example, is the Geographical Survey Institute (GSI) network in Japan, which consists of more than 1200 high-end geodetic GNSS receivers. The data from these networks include code and carrier phase measurements, Doppler measurements, and signal-to-noise ratio. All measurements are delivered from dual frequency receivers using two frequencies (L1, L2). We consider implementation of data from such networks in Sections 11.1, 11.3, and 11.4.

Preface

This book is about global navigation satellite systems (GNSS), their two main instruments, which are a receiver and a simulator, and their applications. The book is based on an operational off-the-shelf real-time software GNSS receiver and off-the-shelf GNSS signal simulator. The academic versions of these tools are bundled with this book and free for readers to use for study and research.

The GNSS is probably unique in that it combines such a diverse variety of humanity’s technological achievements. In order to understand a system better one needs to look at it from a wider perspective. Therefore we always try to present a theory behind each aspect of GNSS in general, which not only allows a better understanding of GNSS, but may also make it useful for specialists engaged in other fields.

The book structure is schematically presented on Figure P.1. Chapter 1 describes general methods of using GNSS. Chapter 2 looks at GNSS satellites and deals with their orbital mechanics. Chapter 3 discusses GNSS signals and how they are generated in satellites, simulators, and pseudolites. Chapters 4,7,10 describe GNSS signal propagation. Chapter 4 looks at where the GNSS signals are in relation to other electro-magnetic signals and how their specifics affect their propagation. Chapter 7 deals with multipath and Chapter 10 is devoted to the very interesting subject of signal scintillation. Chapters 5 and 6 describe in detail a software GNSS receiver front end and a baseband processor. Chapter 8 treats the subject of creating and improving various GNSS observables. Chapters 9,11,12 discuss how these observables are used in navigation and geophysics applications.

In this book we consider Global Navigation Satellite Systems (GNSS) and their applications in navigation and geophysics. First established and up until today the main system is the American GPS, followed a little bit later by the Russian GLONASS. Both were created for navigational purposes. In this chapter we consider the principles and methods of navigation with GNSS satellites. We also give some main definitions here, which are used throughout the book.

Global and regional satellite navigation systems

Satellite navigation systems can be divided into two main categories: global and regional. There are also local systems, which are based on pseudolites. These systems, though not strictly satellite systems, are also considered in this book, because they may be used in conjunction with GNSS or they may use the same type of signal and the same user equipment as GNSS.

In this chapter we examine how GNSS signals are created. We mostly concentrate our presentation on the signals of currently operating GPS and GLONASS. We also consider the main specific features of future GNSS signals including modernized GPS, modernized GLONASS, and GALILEO. We also describe in this chapter how GNSS signals are generated in simulators and how those signals differ from the signals generated by satellite transmitters and pseudolites. The particular place which this chapter occupies in the book is schematically depicted on Figure 3.1. In this book we describe GNSS using some help from a GNSS signal simulator. GNSS simulation today has become an important and significant part of the GNSS technology, which enjoys a high demand. Further, any presentation is based on models. These models can be mathematical, empirical, or speculative. A simulator-based model provides one with the best combination of those models, being as close to the real system from a receiver point of view as possible.

Spread-spectrum concept and benefits

The spread-spectrum concept lies at the core of all GNSS signals. As described in the previous chapter, GNSS satellites are located on medium Earth orbits (MEO) at a distance of about 20 000 km from the user receiver. Even spaceborne receivers located on low Earth orbit (LEO) spacecraft are almost at the same distance to GNSS satellites as a user on the surface of the Earth. Signal energy decreases inversely as the square of distance between signal source and a receiver. We have already encountered the inverse square law in relation to gravitational forces. The signal power as well as gravitational force follows an inverse square law because energy is equally spread on the spherical surface at the receiver distance. Satellite payload should be minimized in order to make its delivery to an orbit cheaper, and the transmission energy also should be minimized in order for a transmitter to consume less energy. As a result of these constraints, the satellite signal is not very powerful, and when it reaches the Earth it is well below noise level. The GNSS signal power levels are given in Table 3.1 based on GPS ICD for L1/L2/L2C signals [1], GPS L5 ICD [2], GPS L1C ICD [3], GLONASS ICD [4] , GALILEO ICD [5], and QZSS ICD [6].

Foreword

I built my first crystal radio kit when I was 9 years old. I became hooked on radio technology, even at that tender age, and later went on to build other radios as a teenager, including a shortwave receiver from a kit. I learned how radios worked by building them and tinkering with them. I learned much later on that the famous American physicist, Richard Feynman, also had an interest in radios when he was 11 or 12. He would buy broken radios at rummage sales and try to fix them. That’s the way he learned how they worked. As he says in the first chapter of his book Surely You’re Joking Mr. Feynman!–Adventures of a Curious Character, ‘The sets were simple, the circuits were not complicated . . . It wasn’t hard for me to fix a radio by understanding what was going on inside, noticing that something wasn’t working right, and fixing it.’ As we know, Feynman went on to unravel the nature of quantum mechanics amongst other accomplishments. And, all his life, he took great pleasure in finding things out.

My interest in radio and electronics together with a love of physics led me eventually into a teaching and research career in space geodesy and precision navigation. Over the years, I have been involved with a number of mostly radio-based space geodetic techniques. As a Ph.D. student, I worked with very long baseline interferometry (VLBI) and satellite Doppler (the US Navy Navigation Satellite System or Transit) and as a postdoctoral fellow at MIT, I worked with lunar laser ranging data and was introduced to one of the very first civil GPS receivers: the Macrometer™. Upon arriving at the University of New Brunswick’s then Department of Surveying Engineering in 1981, it was back to satellite Doppler. But within a year or two, GPS captured my attention and it has been virtually my sole interest ever since.

In the previous chapter we described how a GNSS signal is generated. In this chapter we consider how a GNSS signal propagates through the atmosphere. Figure 4.1 shows how this chapter is related to the book’s contents.

How a radio signal propagates through the Earth’s atmosphere to a great degree depends on the signal carrier frequency. We consider here a relatively narrow frequency range, which is allocated to various GNSSs. Figure 4.2 shows linear and logarithmic scales for signals with various wavelengths. It is possible to see the GNSS frequency allocation in relation to light, radio, and audio signals only on a logarithmic scale. Radiowaves, GNSS, and visible light are located relatively close to each other on a wavelength scale. This proximity between GNSS signals and light allows us to use most of the mathematical tools we use for optics for GNSS signal propagation.

A GNSS signal is affected by the atmosphere. It causes ray bending, signal delays, and frequency, amplitude and phase fluctuations. In this chapter we consider mostly systematic effects of the atmosphere on GNSS signals. In this respect most of the theory that has been developed to describe the behavior of light in the part of the electromagnetic spectrum visible to humans can be applied to GNSS signals.

The perception–action cycle

We begin this final chapter of the book by reemphasizing the basic ideas that bind the study of cognitive dynamic systems to the human brain, where the networks dealing with perception are collocated with those dealing with action.

For a very succinct statement on the overall function of a cognitive dynamic system made up of actuator and perceptor, we simply say:

Elaborating on perception performed in the perceptor and action performed in the actuator, we may go on to say:

1. (1) Cognitive perception addresses optimal estimation of the state in the perceptor by processing incoming stimuli under indirect control of the actuator.

2. (2) Cognitive control addresses optimal decision-making in the actuator under feedback guidance from the perceptor.

These two closely related functions reinforce each other continually from one cycle of directed information processing to the next. The net result is the perception–action cycle, discussed in detail in Chapter 2. This cyclic directed information flow is a cardinal characteristic of every cognitive dynamic system, be it of a neurobiological or artificial kind. Naturally, the exact details of the perception–action cycle will depend on the application of interest. In any event, a practical benefit of the perception–action cycle is information gain about how the state of the environment is inferred by the system, with the gain increasing from one cycle to the next.

As discussed in Chapter 2, perception of the environment is the first of four defining properties of cognition, putting aside language. To cater for perception in an engineering context, we not only need to sense the environment, but also focus attention on an underlying discriminant of the environment that befits the application of interest. In this chapter, we focus attention on spectrum estimation, which is of particular interest to sensing the environment for cognitive radio. Moreover, with radar relying on the radio spectrum for its operation, spectrum sensing is also of potential interest to cognitive radar.

With spectrum estimation viewed as the discriminant for sensing the environment, there are four related issues that are of practical interest, each in its own way:

1. (1) Power spectrum, where the requirement is to estimate the average power of the incoming signal expressed as a function of frequency.

2. (2) Space–time processing, where the average power of the incoming signal is expressed as a function of frequency and spatial coordinates.

3. (3) Time–frequency analysis, in which the average power of the signal is expressed as a function of both time and frequency.

4. (4) Spectral line components, for which a special test is needed.

Throughout the presentation, the emphasis will be on the use of a finite set of observable data (measurements), which is how it is in practice.

In Section 2.12 we stated that perception in a cognitive dynamic system may be viewed as an ill-posed inverse problem.

With the material presented in the previous four chapters dealing with fundamental aspects of cognitive dynamic systems at our disposal, the stage is now set for our first application: cognitive radar, which was described for the first time by Haykin (2006a).

Radar is a remote-sensing system with numerous well-established applications in surveillance, tracking, and imaging of targets, just to name a few. In this chapter, we have chosen to focus on target tracking as the area of application. The message to take from the chapter is summed up as follows:

This profound statement has many important practical implications, which may be justified in light of what we do know about the echolocation system of a bat. The echolocation system (i.e. sonar) of a bat provides not only information about how far away a target (e.g. flying insect) is from the bat, but also information about the relative velocity of the target, the size of the target, the size of various features of the target, and azimuth and elevation coordinates of the target. The highly complex neural computations needed to extract all this information from target echoes are performed within the “size of a plum.”

The previous two chapters of the book have focused on the basic issue: perception of the environment from two different viewpoints. Specifically, Chapter 3 focused on perception viewed as power-spectrum estimation, which is applicable to applications such as cognitive radio, where spectrum sensing of the radio environment is of paramount importance. In contrast, Chapter 4 focused on Bayesian filtering for state estimation, which is applicable to another class of applications exemplified by cognitive radar, where estimating the parameters of a target in a radar environment is the issue of interest. Although those two chapters address entirely different topics, they also have a common perspective: they both pertain to the perceptor of a cognitive dynamic system, the basic function of which is to account for perception in the perception–action cycle. In this chapter, we move on to the action part of this cycle, which is naturally the responsibility of the actuator of the cognitive dynamic system.

Just as the Bayesian framework provides the general formalism for the perceptor to perceive the environment by estimating the hidden state of the environment, Bellman's dynamic programming provides the general formalism for the actuator to act in the environment through control or decision-making.

Dynamic programming is a technique that deals with situations where decisions are made in stages (i.e. different time steps), with the outcome of each decision being predictable to some extent before the next decision is made.

This quotation is taken from a point-of-view article that appeared in the Proceedings of the Institute of Electrical and Electronics Engineers (Haykin, 2006a). In retrospect, it is perhaps more appropriate to refer to Cognitive Dynamic Systems as an “integrative field” rather than a “discipline.”

By speaking of cognitive dynamic systems as an integrative field, we mean this in the sense that its study integrates many fields that are rooted in neuroscience, cognitive science, computer science, mathematics, physics, and engineering, just to name a few. Clearly, the mixture of fields adopted in the study depends on the application of interest. However, irrespective of the application, the key question is

In this book, we adopt human cognition as the frame of reference. As for applications, the book focuses on cognitive radar and cognitive radio.

In Chapter 1 of his book entitled Cortex and Mind: Unifying Cognition, Fuster (2003) introduces a new term called the cognit, which is used to characterize the cognitive structure of a cortical network; it is defined as follows:

Towards the end of Chapter 1 of the book, Fuster goes on to say:

These two quotes taken from Fuster's book provide us with a cohesive statement on the cortical functions of cognition in the human brain; both are important. In particular, the second quotation highlights the interrelationships between the five processes involved in cognition: perception, memory, attention, language, and intelligence. Just as language plays a distinctive role in the human brain, so it is in a cognitive dynamic system where language provides the means for effective and efficient communication among the different parts of the system. However, language is outside the scope of this book.