From Wikipedia:

Dead Reckoning

On May 21, 1927 Charles Lindbergh landed in Paris, France after a successful non-stop flight from the United States in the single-engined Spirit of St. Louis. As the aircraft was equipped with very basic instruments, Lindbergh used dead reckoning to navigate.

Dead reckoning in the air is similar to dead reckoning on the sea, but slightly more complicated. The density of the air the aircraft moves through affects its performance as well as winds, weight, and power settings.

The basic formula for DR is Distance = Speed x Time. An aircraft flying at 250 knots airspeed for 2 hours has flown 500 nautical miles through the air. The wind triangle is used to calculate the effects of wind on heading and airspeed to obtain a magnetic heading to steer and the speed over the ground (groundspeed). Printed tables, formulae, or an E6B flight computer are used to calculate the effects of air density on aircraft rate of climb, rate of fuel burn, and airspeed.

A course line is drawn on the aeronautical chart along with estimated positions at fixed intervals (say every ½ hour). Visual observations of ground features are used to obtain fixes. By comparing the fix and the estimated position corrections are made to the aircraft's heading and groundspeed.

Dead reckoning is on the curriculum for VFR (visual flight rules - or basic level) pilots worldwide. It is taught regardless of whether the aircraft has navigation aids such as GPS, ADF and VOR and is an ICAO Requirement. Many flying training schools will prevent a student from using electronic aids until they have mastered dead reckoning.

Inertial navigation systems (INSes), which are nearly universal on more advanced aircraft, use dead reckoning internally. The INS provides reliable navigation capability under virtually any conditions, without the need for external navigation references, although it is still prone to slight errors.

Transcontinental Airway System

In 1923, the United States Congress funded a sequential lighted airway along the transcontinental airmail route. The lighted airway was proposed by National Advisory Committee for Aeronautics (NACA), and deployed by the Department of Commerce. It was managed by the Bureau of Standards Aeronautical Branch. The first segment built was between Chicago and Cheyenne, Wyoming. It was situated in the middle of the airmail route to enable aircraft to depart from either coast in the daytime, and reach the lighted airway by nightfall. Lighted emergency airfields were also funded along the route every 15–20 miles.

Construction pace was fast, and pilots wishing to become airmail pilots were first exposed to the harsh wintertime work with the crews building the first segments of the lighting system.

By the end of the year, the public anticipated anchored lighted airways across the Atlantic, Pacific, and to China.

The first nighttime airmail flights started on July 1, 1924. By eliminating the transfer of mail to rail cars at night, the coast to coast delivery time for airmail was reduced by two business days. Eventually, there were 284 beacons in service. With a June 1925 deadline, the 2,665 mile lighted airway was completed from New York to San Francisco. In 1927, the lighted airway was complete between New York City and Salt Lake City, Los Angeles to Las Vegas, Los Angeles to San Francisco, New York to Atlanta, and Chicago to Dallas, 4121 miles in total. In 1933, the Transcontinental Airway System totaled 1500 beacons, and 18000 miles.

The lighted Airway Beacons were a substantial navigation aid in an era prior to the development of radio navigation. Their effectiveness was limited by visibility and weather conditions.Beacon 61B on a modern display tower, originally installed on route CAM-8 near Castle Rock, WA

24 inches (610 mm) diameter rotating beacons were mounted on 53-foot (16 m) high towers, and spaced ten miles apart. The spacing was closer in the mountains, and farther apart in the plains. The beacons were five million candlepower, and rotated six times a minute. "Ford beacons" (named after Ford Car headlights) were also used, placing four separate lights at different angles.Air ports used green beacons and airways used red beacons. The beacons flashed identification numbers in Morse code. The sequence was "WUVHRKDBGM", which prompted the mnemonic "When Undertaking Very Hard Routes Keep Directions By Good Methods".Engineers believed the variations of beacon height along hills and valleys would allow pilots to see beacons both above ground fog, and below cloud layers.

Towers were built of numbered angle iron sections with concrete footings. Some facilities used concrete arrows pointing in the direction of towers. In areas where no connection to a power grid was available, a generator was housed in a small building. Some buildings also served as weather stations. Many arrow markings were removed during World War II, to prevent aiding enemy bombers in navigation, while 19 updated beacons still remain in service in Montana.

ADF

An automatic direction finder (ADF) is a marine or aircraft radio-navigation instrument that automatically and continuously displays the relative bearing from the ship or aircraft to a suitable radio station. ADF receivers are normally tuned to aviation or marine NDBs (Non-Directional Beacon) operating in the LW band between 190 – 535 kHz. Like RDF (Radio Direction Finder) units, most ADF receivers can also receive medium wave (AM) broadcast stations, though as mentioned, these are less reliable for navigational purposes.

The operator tunes the ADF receiver to the correct frequency and verifies the identity of the beacon by listening to the Morse code signal transmitted by the NDB. On marine ADF receivers, the motorized ferrite-bar antenna atop the unit (or remotely mounted on the masthead) would rotate and lock when reaching the null of the desired station. A centerline on the antenna unit moving atop a compass rose indicated in degrees the bearing of the station. On aviation ADFs, the unit automatically moves a compass-like pointer (RMI) to show the direction of the beacon. The pilot may use this pointer to home directly towards the beacon, or may also use the magnetic compass and calculate the direction from the beacon (the radial) at which their aircraft is located.

Unlike the RDF, the ADF operates without direct intervention, and continuously displays the direction of the tuned beacon. Initially, all ADF receivers, both marine and aircraft versions, contained a rotating loop or ferrite loopstick aerial driven by a motor which was controlled by the receiver. Like the RDF, a sense antenna verified the correct direction from its 180-degree opposite.

More modern aviation ADFs contain a small array of fixed aerials and use electronic sensors to deduce the direction using the strength and phase of the signals from each aerial. The electronic sensors listen for the trough that occurs when the antenna is at right angles to the signal, and provide the heading to the station using a direction indicator. In flight, the ADF's RMI or direction indicator will always point to the broadcast station regardless of aircraft heading. Dip error is introduced, however, when the aircraft is in a banked attitude, as the needle dips down in the direction of the turn. This is the result of the loop itself banking with the aircraft and therefore being at a different angle to the beacon. For ease of visualisation, it can be useful to consider a 90° banked turn, with the wings vertical. The bearing of the beacon as seen from the ADF aerial will now be unrelated to the direction of the aircraft to the beacon.

VOR

Very high frequency omni-directional range (VOR) is a type of short-range radio navigation system for aircraft, enabling aircraft with a receiving unit to determine its position and stay on course by receiving radio signals transmitted by a network of fixed ground radio beacons. It uses frequencies in the very high frequency (VHF) band from 108.00 to 117.95 MHz. Developed in the United States beginning in 1937 and deployed by 1946, VOR is the standard air navigational system in the world, used by both commercial and general aviation. In the year 2000 there were about 3,000 VOR stations operating around the world, including 1,033 in the US, reduced to 967 by 2013 (stations are being decommissioned with widespread adoption of GPS).

A VOR ground station uses a phased antenna array to send a highly directional signal that rotates clockwise horizontally (as seen from above) 30 times a second. It also sends a 30 Hz reference signal on a subcarrier timed to be in phase with the directional antenna as the latter passes magnetic north. This reference signal is the same in all directions. The phase difference between the reference signal and the signal amplitude is the bearing from the VOR station to the receiver relative to magnetic north. This line of position is called the VOR "radial". The intersection of radials from two different VOR stations can be used to fix the position of the aircraft, as in earlier radio direction finding (RDF) systems.

VOR stations are fairly short range: the signals are line-of-sight between transmitter and receiver and are useful for up to 200 miles. Each station broadcasts a VHF radio composite signal including the navigation signal, station's identifier and voice, if so equipped. The navigation signal allows the airborne receiving equipment to determine a bearing from the station to the aircraft (direction from the VOR station in relation to Magnetic North). The station's identifier is typically a three-letter string in Morse code. The voice signal, if used, is usually the station name, in-flight recorded advisories, or live flight service broadcasts.

Area Navigation

The continuing growth of aviation increases demands on airspace capacity, making area navigation desirable due to its improved operational efficiency.

RNAV systems evolved in a manner similar to conventional ground-based routes and procedures. A specific RNAV system was identified and its performance was evaluated through a combination of analysis and flight testing. For land-based operations, the initial systems used very high frequency omnidirectional radio range (VOR) and distance measuring equipment (DME) for estimating position; for oceanic operations, inertial navigation systems (INS) were employed. Airspace and obstacle clearance criteria were developed based on the performance of available equipment, and specifications for requirements were based on available capabilities. Such prescriptive requirements resulted in delays to the introduction of new RNAV system capabilities and higher costs for maintaining appropriate certification. To avoid such prescriptive specifications of requirements, an alternative method for defining equipment requirements has been introduced. This enables the specification of performance requirements, independent of available equipment capabilities, and is termed performance-based navigation (PBN). Thus, RNAV is now one of the navigation techniques of PBN; currently the only other is required navigation performance (RNP). RNP systems add on-board performance monitoring and alerting to the navigation capabilities of RNAV. As a result of decisions made in the industry in the 1990s, most modern systems are RNP.

Many RNAV systems, while offering very high accuracy and possessing many of the functions provided by RNP systems, are not able to provide assurance of their performance. Recognising this, and to avoid operators incurring unnecessary expense, where the airspace requirement does not necessitate the use of an RNP system, many new as well as existing navigation requirements will continue to specify RNAV rather than RNP systems. It is therefore expected that RNAV and RNP operations will co-exist for many years.

However, RNP systems provide improvements in the integrity of operation, permitting possibly closer route spacing, and can provide sufficient integrity to allow only the RNP systems to be used for navigation in a specific airspace. The use of RNP systems may therefore offer significant safety, operational and efficiency benefits. While RNAV and RNP applications will co-exist for a number of years, it is expected that there will be a gradual transition to RNP applications as the proportion of aircraft equipped with RNP systems increases and the cost of transition reduces.

INS

Inertial navigation is a self-contained navigation technique in which measurements provided by accelerometers and gyroscopes are used to track the position and orientation of an object relative to a known starting point, orientation and velocity. Inertial measurement units (IMUs) typically contain three orthogonal rate-gyroscopes and three orthogonal accelerometers, measuring angular velocity and linear acceleration respectively. By processing signals from these devices it is possible to track the position and orientation of a device.

Inertial navigation is used in a wide range of applications including the navigation of aircraft, tactical and strategic missiles, spacecraft, submarines and ships. It is also embedded in some mobile phones for purposes of mobile phone location and tracking  Recent advances in the construction of microelectromechanical systems (MEMS) have made it possible to manufacture small and light inertial navigation systems. These advances have widened the range of possible applications to include areas such as human and animal motion capture.

An inertial navigation system includes at least a computer and a platform or module containing accelerometers, gyroscopes, or other motion-sensing devices. The INS is initially provided with its position and velocity from another source (a human operator, a GPS satellite receiver, etc.) accompanied with the initial orientation and thereafter computes its own updated position and velocity by integrating information received from the motion sensors. The advantage of an INS is that it requires no external references in order to determine its position, orientation, or velocity once it has been initialized.

An INS can detect a change in its geographic position (a move east or north, for example), a change in its velocity (speed and direction of movement) and a change in its orientation (rotation about an axis). It does this by measuring the linear acceleration and angular velocity applied to the system. Since it requires no external reference (after initialization), it is immune to jamming and deception.

Inertial navigation systems are used in many different moving objects. However, their cost and complexity place constraints on the environments in which they are practical for use.

Gyroscopes measure the angular velocity of the sensor frame with respect to the inertial reference frame. By using the original orientation of the system in the inertial reference frame as the initial condition and integrating the angular velocity, the system's current orientation is known at all times. This can be thought of as the ability of a blindfolded passenger in a car to feel the car turn left and right or tilt up and down as the car ascends or descends hills. Based on this information alone, the passenger knows what direction the car is facing but not how fast or slow it is moving, or whether it is sliding sideways.

Accelerometers measure the linear acceleration of the moving vehicle in the sensor or body frame, but in directions that can only be measured relative to the moving system (since the accelerometers are fixed to the system and rotate with the system, but are not aware of their own orientation). This can be thought of as the ability of a blindfolded passenger in a car to feel himself pressed back into his seat as the vehicle accelerates forward or pulled forward as it slows down; and feel himself pressed down into his seat as the vehicle accelerates up a hill or rise up out of their seat as the car passes over the crest of a hill and begins to descend. Based on this information alone, he knows how the vehicle is accelerating relative to itself, that is, whether it is accelerating forward, backward, left, right, up (toward the car's ceiling), or down (toward the car's floor) measured relative to the car, but not the direction relative to the Earth, since he did not know what direction the car was facing relative to the Earth when they felt the accelerations.

However, by tracking both the current angular velocity of the system and the current linear acceleration of the system measured relative to the moving system, it is possible to determine the linear acceleration of the system in the inertial reference frame. Performing integration on the inertial accelerations (using the original velocity as the initial conditions) using the correct kinematic equations yields the inertial velocities of the system and integration again (using the original position as the initial condition) yields the inertial position. In our example, if the blindfolded passenger knew how the car was pointed and what its velocity was before he was blindfolded and if he is able to keep track of both how the car has turned and how it has accelerated and decelerated since, then he can accurately know the current orientation, position, and velocity of the car at any time.

Global Positioning System

The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite systems (GNSS) that provides geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. Obstacles such as mountains and buildings block the relatively weak GPS signals.

The GPS does not require the user to transmit any data, and it operates independently of any telephonic or internet reception, though these technologies can enhance the usefulness of the GPS positioning information. The GPS provides critical positioning capabilities to military, civil, and commercial users around the world. The United States government created the system, maintains it, and makes it freely accessible to anyone with a GPS receiver.

The GPS project was started by the U.S. Department of Defense in 1973, with the first prototype spacecraft launched in 1978 and the full constellation of 24 satellites operational in 1993. Originally limited to use by the United States military, civilian use was allowed from the 1980s following an executive order from President Ronald Reagan after the Korean Air Lines Flight 007 incident. Advances in technology and new demands on the existing system have now led to efforts to modernize the GPS and implement the next generation of GPS Block IIIA satellites and Next Generation Operational Control System (OCX). Announcements from Vice President Al Gore and the Clinton Administration in 1998 initiated these changes, which were authorized by the U.S. Congress in 2000.

During the 1990s, GPS quality was degraded by the United States government in a program called "Selective Availability"; this was discontinued on May 1, 2000 by a law signed by President Bill Clinton.

The GPS service is provided by the United States government, which can selectively deny access to the system, as happened to the Indian military in 1999 during the Kargil War, or degrade the service at any time. As a result, several countries have developed or are in the process of setting up other global or regional satellite navigation systems. The Russian Global Navigation Satellite System (GLONASS) was developed contemporaneously with GPS, but suffered from incomplete coverage of the globe until the mid-2000s. GLONASS can be added to GPS devices, making more satellites available and enabling positions to be fixed more quickly and accurately, to within two meters (6.6 ft). China's BeiDou Navigation Satellite System began global services in 2018, and finished its full deployment in 2020. There are also the European Union Galileo positioning system, and India's NavIC. Japan's Quasi-Zenith Satellite System (QZSS) is a GPS satellite-based augmentation system to enhance GPS's accuracy in Asia-Oceania, with satellite navigation independent of GPS scheduled for 2023.

When selective availability was lifted in 2000, GPS had about a five-meter (16 ft) accuracy. GPS receivers that use the L5 band can have much higher accuracy, pinpointing to within 30 centimeters (11.8 in). As of May 2021, 16 GPS satellites are broadcasting L5 signals, and the signals are considered pre-operational, scheduled to reach 24 satellites by approximately 2027.