of speed and elapsed time to determine the distance traveled. Heading may be determined from celestial observations or by using a magnetic compass. Dead reckoning is generally implemented by plotting lines connecting successive locations on a chart, a practice at least as old as the works of Claudius Ptolemy (∼85–168 CE).
Radio navigation relies on radio‐frequency sources with known locations, suitable receiver technologies, signal structure at the transmitter, and signal availability at the receiver. Radio navigation technology using land‐fixed transmitters has been evolving for about a century. Radio navigation technologies using satellites began soon after the first artificial satellite was launched.
Inertial navigation is much like an automated form of dead reckoning. It relies on knowing your initial position, velocity, and attitude, and thereafter measuring and integrating your accelerations and attitude rates to maintain an estimate of velocity, position, and attitude. Because it is self‐contained and does not rely on external sources, it has the potential for secure and stealthy navigation in military applications. However, the sensor accuracy requirements for these applications can be extremely demanding [2]. Adequate sensor technologies were not developed until the middle of the twentieth century, and early systems tended to be rather expensive.
These modes of navigation can be used in combination, as well. The subject of this book is a combination of the last two modes of navigation: global navigation satellite system (GNSS) as a form of radio navigation combined with inertial navigation. The key integration technology is Kalman filtering, which also played a major role in the development of both navigation modes.
The pace of technological innovation in navigation has been accelerating for decades. Over the last few decades, navigation accuracies improved dramatically and user costs have fallen by orders of magnitude. As a consequence, the number of marketable applications has been growing phenomenally. From the standpoint of navigation technology, we are living in interesting times.
1.2 GNSS Overview
Satellite navigation development began in 1957 with the work of William W. Guier (1926–2011) and George C. Weiffenbach (1921–2003) at the Applied Physics Laboratory of Johns Hopkins University [3], resulting in the US Navy Transit GNSS [4]. Transit became operational in the mid‐1960s, achieving navigational accuracies in the order of 200 m and remained operational until it was superseded by the US Air Force GPS 28 years later. The Transit navigation solution is based on the Doppler history of the received satellite signal as the satellite passed overhead from horizon to horizon – a period of about a quarter of an hour. The US Navy also developed the TIMATION (TIMe/navigATION) in the mid‐1960s to explore the performance of highly accurate space‐based clocks for precise satellite‐based positioning. While Transit and TIMATION were “carrier‐phase” only‐based systems, the US Air Force 621B experimental program validates the use of ranging codes for a global satellite‐based precision navigation system. These programs were instrumental in the concepts and techniques in the development of GPS as well as other satellite‐based GNSS that we know today.
Currently there are several GNSS in various stages of operation and development. This section provides a brief overview of these systems, where a more detailed discussion is given in Chapter 4.
1.2.1 GPS
The GPS is part of a satellite‐based navigation system developed by the US Department of Defense under its NAVSTAR satellite program [5–16].
1.2.1.1 GPS Orbits
The fully populated GPS constellation includes 31 active satellites with additional operational spares, in six operational planes. The satellites are in circular orbits with four or more satellites in each orbital plane. The orbital planes are each inclined at an angle of 55° relative to the equator and are separated from each other by multiples of 60° right ascension. Each satellite is in a medium Earth orbit (MEO), is nongeostationary, and is approximately circular, with radii of 26 560 km, with orbital period of one‐half sidereal day (≈11.967 hours). Four or more GPS satellites will always be visible from any point on the Earth's surface, where the GPS satellites can be used to determine an observer's position, velocity, and time (PVT) anywhere on the Earth's surface 24 h/d.
1.2.1.2 Legacy GPS Signals
Each GPS satellite carries a cesium and/or rubidium atomic clock (i.e. frequency reference oscillator) to provide timing information for the signals transmitted by the satellites. While each satellite carries several internal clock, all navigation signals are generated from one clock. Satellite clock corrections are provided to the users in the signals broadcast by each satellite, with the aid of the GPS Ground Control Segment. The legacy GPS satellite transmits two L‐band spread spectrum navigation signals on – an L1 signal with carrier frequency f1 = 1575.42 MHz and an L2 signal with carrier frequency f2 = 1227.6 MHz. These two frequencies are integral multiples f1 = 154f0 and f2 = 120f0 of a base frequency f0 = 10.23 MHz. The L1 signal from each satellite is binary phase‐shift keying (BPSK) modulated by two pseudorandom noise (PRN) codes in phase quadrature, designated as the C/A‐code and P(Y)‐code. The L2 signal from each satellite is BPSK modulated by only the P(Y)‐code. A brief description of the nature of these PRN codes follows, with greater detail given in Chapter 4.
Compensating for ionosphere propagation delays. The time delay from when a navigation signal is transmitted, to when the signal is received, is used to eventually estimate the distance between the satellite and the user. This signal propagation delay is affected by the atmosphere. As the signals pass through the ionosphere, the delay chances with frequency. This is one motivation for use of two different carrier signals, L1 and L2. Because delay through the ionosphere varies approximately as the inverse square of signal frequency f (delay ∝ f−2), the measurable differential delay between the two carrier frequencies can be used to compensate for the delay in each carrier (see Ref. [16] for details).
Code‐division multiplexing. Knowledge of the PRN codes allows users independent access to multiple GPS satellite signals on the same carrier frequency. The signal transmitted by a particular GPS signal can be selected by generating and matching, or correlating, the PRN code for that particular satellite. All PRN codes are known and are generated or stored in GPS satellite signal receivers. For legacy GPS there are two PRN codes transmitted from each satellite. The first PRN code from each GPS satellite, sometimes referred to as a precision code or P‐code, is a relatively long, fine‐grained code having an associated clock or chip rate of f0 = 10.23 MHz. A second PRN code from each GPS satellite, sometimes referred to as a clear or coarse acquisition code or C/A‐code, is intended to facilitate rapid satellite signal acquisition and handover to the P‐code. It is a relatively short, coarser‐grained code having an associated clock or chip rate of f0 = 1.023 MHz. The C/A‐code for any GPS satellite has a length of 1023 chips or time increments before it repeats. The full P‐code has a length of 259 days, during which each satellite transmits a unique portion of the full P‐code. The portion of P‐code used for a given GPS satellite has a length of precisely one week (seven days) before this code portion repeats. Accepted methods for generating the C/A‐code and P‐code were established by the satellite developer (Satellite Systems Division of Rockwell International Corporation) in 1991 [17].
Navigation signal. The GPS satellite bit stream includes navigational information on the ephemeris of the transmitting GPS satellite and an almanac for all GPS satellites, with parameters providing approximate corrections for ionospheric signal propagation delays suitable for single‐frequency receivers and for an offset time between satellite clock time and true GPS time. The legacy navigational information is transmitted
