Navigation

Question 1

Definition of Navigation

Answer 1

Where am I? Where do I want to go?

Navigation deals with moving objects, mostly vehicles, and involves trajectory determination (Where to go?) and guidance (How to go?).

1. To accurately determine position and velocity relative to a known reference.
2. To plan and execute the maneuvers necessary to move between desired locations.

Question 2

Coordinate frames: definitions

Answer 2

• Earth-Centered Inertia (ECI):
To be used as inertial frame for application of Newton‘s laws of motion
• Earth-Centered-Earth-Fixed (ECEF): To describe the position on the earth•WGS84: 𝜆,𝜇,ℎinstead of 𝑥,𝑦,𝑧
• North-East-Down (NED):
To describe the attitude of the aircraft with respect to the earth‘s surface
• Body-Fixed (B):
To describe forces and moments acting on the aircraft
• Aerodynamic (A):
To describe aerodynamic forces and moments
• Kinematic (K):
To describe the aircraft trajectory

Question 3

Definitions: Heading, Bearing, Track, Course

Answer 3

• Heading 𝚿: The angle between the longitudinal 𝑥𝐵-axis of the body fixed frame system and the 𝑥0-axis (North) of the NED system. (The horizontal direction of the airplane’s nose)
• Bearing: The angular direction of a distant point measured in degrees clockwise from a local meridian or other reference. Usually relative bearings are described clockwise from 000°to 360°.
• Track:

1) The path of the aircraft over the earth‘s surface
2) The flight-path azimuth angle 𝜒𝑘between the 𝑥0-axis of NED (North) and the 𝑥𝑘-axis of the kinematic flight-path system.

• Course:The intended direction of flight in the horizontal plane measured in degrees from north.

Question 4

Definitions: Compass North/Heading, Magnetic North/Heading, True North/Heading

Answer 4

• Compass North CN: The direction in which the magnetic needle points to is along the local geomagnetic field lines and is not generally directed to the magnetic north pole.
• Magnetic North MN: The direction of the earth‘s magnetic pole, to which the north-seeking pole of a magnetic needle points when it is free from local magnetic influence.
• True North TN: The direction along the earth‘s surface towards the geographic north pole. The geographic north pole is the intersection between the rotation axis of the earth with it‘s surface.
• Compass Heading CH: The heading measured clockwise from north as indicated by the compass.
• Magnetic Heading MH: The heading angle measured clockwise from magnetic north.
• True Heading TH: The direction in which the nose of the aircraft points during a flight when measured in degrees clockwise from true north.

Question 5

Loxodrome and orthodrome

Answer 5

Loxodromes (spirale zum Nordpol) are curves on the surface of a sphere which always cut the meridian in a constant angle. Their purpose in the early navigation was to move forward in the same heading Ψ from the north pole reference. This was not necessarily the shortest route, but it was easy to travel along a constant angle.

The orthodrome is the shortest connection between the two points 𝑃1(𝜆1,𝜇1) and 𝑃2(𝜆2,𝜇2) on the surface of a sphere. It is the arc of a circle with its center in 0. Thus, the points 𝑃1(𝜆1,𝜇1), 𝑃2(𝜆2,𝜇2) build a spherical triangle together with the north pole 𝑁.

Question 6

Inertial navigation

Answer 6

• Integration of acceleration signals to determine velocity and position in a desired coordinate system.
Required sensors: Accelerometers, gyroscopes

Platform
•Advantages: ▪High accuracy ▪Little computational effort
•Drawbacks: ▪Very cost intensive ▪Fault liability ▪Higher complexity

Strapdown systems
•Advantages: ▪Small, light and cheap ▪No moving parts
•Drawbacks: ▪Increased dynamic range of gyroscopes leads to more scale factor errors and nonlinearities. ▪Relationship between vehicle, navigation and inertial coordinate frames must be computationally calculated

Question 7

Principles of accelerometers

Answer 7

▪An accelerometer consists of at least …
•a proof mass
•a suspension that holds the mass
•a pickoff providing a signal related to the acceleration.

•Pendulous / translational mass displacement / rebalance
−Electrical restraint−Rotational restraint−Elastic restraint
•Resonant element frequency−Vibrating string
−Vibrating beam−Double ended tuning fork

• Open loop: Measure change/displacement due to acceleration
• Closed loop: A disturbance in a position control system. The proof mass ismaintained in a fixed position and the force (or current, power, etc) necessary to maintain that position is measured.

Micro Electro-Mechanical Systems (MEMS)
Piezo-Resistive Accelerometer

Question 8

Alignment: Vertical alignment and north-finding

Answer 8

The Azimut angle can be determined with sufficiently precise measurement data of the Earth rate by gyroscopes. This procedure is referred to as north finding.

vertical alignment ?

Question 9

Schuler oscillation

Answer 9

Initial error: When horizontal position error occurs, due to the curved shape of the earth, the estimated direction of the gravity vector does not fit with its real direction.
Computation: In the strapdown algorithm the gravity vector is not compensated completely and an acceleration component remains. This remaining acceleration component is oppositely directed to the position error.

Explanation of the Schuler oscillation by describing it as a pendulum anchored on the surface of the Earth, with a pendulum length of the Earth radius R

Question 10

Error model of the accelerometers

Answer 10

Error estimation: An error of 0,001g results in a deviation of measured acceleration of Δ𝑎=0,01 𝑚/𝑠^2
After one hour:
Deviation of computed speed: Δ𝑉=Δ𝑎𝑡=36 𝑚/𝑠
Deviation of computed position:Δ𝑠=1/2Δ𝑎𝑡^2=64,8𝑘𝑚

Question 11

Principles of gyroscopes

Answer 11

• Gyroscopes are known as inertial sensors, since they exploit the property of inertia, meaning the resistance to a change in momentum, to sense angular motion. They are important instruments to control and guide an aircraft.
• Gyroscopes are also essential elements of the spatial reference system or the attitude/heading reference system (AHRS) and the inertial navigation system (INS). Their application determines the overall performance and accuracy of these systems and greatly contribute to the system costs.
• Gyroscopes are used as error detectors to sense small rotations on the gimbaled systems relative to the navigation coordinates. In a strapdown system, where the gyroscopes and accelerometers are fixed to the vehicle, they follow the vehicle‘s angular motion.

Question 12

Navigation errors

Answer 12

• Instrumentation Errors: Imperfections of the sensors (e.g. bias, scale factor, nonlinearity, noise)
• Computational Errors: Errors made by digital computer (e.g. quantization, overflow, numeric / integration error)
• Alignment Errors: Sensors cannot be aligned perfectly with their assumed directions
• Environment Errors:Modeling errors of the environment and uncertainties

Question 13

Sources of error for gyroscopes

pro/cons inertial navigation

Answer 13

Advantages:
•Indication of position and velocity are instantaneous and continuous. Being able to achieve high data rates and bandwidths.
•Completely self containing. The measurements are based upon data of acceleration and angular rates within the vehicle. It does not radiate electromagnetic waves and cannot be jammed by an interference signal.
•Navigation information (including azimuth) is receivable at all latitudes (including polar regions), as well as in all weather situations without the need of ground stations
.•The inertial system provides outputs of the position, ground speed, azimuth and vertical. It is the most precise means of measuring azimuth and vertical on a moving vehicle.

Disadvantages:
•Information on position and velocity degrades with timedue to several error sources. This is true for moving or stationary vehicles.
•The costsfor INS equipment is very high (1996: 50,000-120,000 $ for airborne equipment).
•Initial alignment is necessary, especially for moving vehicles and on latitudes greater than 75°.
•The vehicle‘s maneuvers have an impact on the navigation information.

Question 14

NAVSTAR: Frequency bands

Answer 14

L1 = 1,57520 GHz
L2 = 1,227600 GHz
since 2013 the L5 on 1176,45 MHz

Question 15

Pseudorange equation: Possibilities for solving the equation

Answer 15

• There are three unknown receiver antenna coordinates and at least one unknown measurement error, which leads to at least four unknown parameters in the pseudorange equation.
• To solve this linear equation system, there is a need for at least four independent measurements, which leads to at least four pseudorange equations to obtain one single solution.
• The pseudorange equations depend on the receiver coordinates in a nonlinear expression.
• Therefore, a typical method to estimate the solution is linearization, as it is straightforward, converges quickly and allows linear analysis techniques to be applied.
• If more accuracy is required, the linearization can be iterated, with the last result as the new linearization point.
• A typical approach is a single iteration for each measurement period, with the result of one period serving as the linearization point for the next period.

Question 16

Satellite navigation: Sources of error

Answer 16

• Satellite clock bias 𝑐∙∆𝑡𝑆
• Receiver clock bias 𝑐∙Δ𝑡𝑅
• Relativistic clock error
• Ephemeris error 𝐸
• Ionospheric delay 𝑐∙∆𝑡𝐴
• Tropospheric delay 𝑐∙∆𝑡𝐴
• Multipath error 𝑀𝑃
• Receiver noise 𝜂

Question 17

Satellite navigation: Sources of error

Answer 17

• Satellite clock bias 𝑐∙∆𝑡𝑆
• Receiver clock bias 𝑐∙Δ𝑡𝑅 (größter Fehler, weil alle anderen mit hochgenauen Uhren arbeiten)
• Relativistic clock error
• Ephemeris error 𝐸
• Ionospheric delay 𝑐∙∆𝑡𝐴
• Tropospheric delay 𝑐∙∆𝑡𝐴
• Multipath error 𝑀𝑃
• Receiver noise 𝜂

Question 18

DGPSprinciple: Correction of pseudoranges

Answer 18

Concept of DGPS:
•Position determination with the classical GNSS techniques is limited in accuracy, due to several previously described error factors.
•The errors cannot be estimated by a single receiver with unknown position.
•The idea is to implement a reference receiver at a known location, which estimates the local errors and transmits the information to other receivers in the local area.
•With this information, the receivers can improve their position accuracy.

Question 19

DGPS implementations: GBAS, SBAS, WAAS, EGNOS

Answer 19

GBAS
The GPS receiver, the computing center and the broadcast station for transmitting the correction data is centralized in one place.
•The service is in the surrounding area of an airport•
Only few ground stations in the airport area.
•The error message is transmitted via local transceiver at 110MHz
•Local ionospheric disturbances can be detected
•The time to alert is 2 seconds.
SBAS
•Within SBAS, the receiver, the computing center and the transmitter are not stationed together in a single place.
Functional principle:
•Network of monitoring GNSS receiver with exactly known locations
•Raw measurement of each station are sent to the master ground station, which calculates the main system errors and broadcasts them via geostationary satellites to users.
Broadcast errors:
•Detection of unhealthy satellites (within 6 seconds)
•Ionospheric delay
•Ephemeris errors of each satellite
•Clock error of each satellite
•Confidence bounds on the remaining errors
Main risks reduced by SBAS:
•Distortions by changing ionospheric signal delays,e.g. ionosphere anomaly wave front
•Sudden satellite failures
WAAS EDNOS
•The WAAS is an US and EGNOS (European Geostationary Overlay System) a European satellite based correction service especially for air traffic control in order to use GPS also for instrument landing approaches.
•It consists of ground-based reference stations, decentralized computing centers, space-based satellites and SBAS-compatible receivers and on-board flight management systems.
•The correction data set is transmitted within the L1 frequency range. Therefore, the emitting satellite has to identify itself in the signal as an additional GPS satellite, with its own code and ephemeris errors.
•The end user receiver uses the correction data calculated on the track between GPS satellite and ground reference station which consists of the ionospheric error between GPS satellites and reference station, but not the ionospheric error between emitting satellite and the end user receiver.

Question 20

Description and sketch of AM and FM modulations

Answer 20

AM
Variation of the carrier wave’s amplitude to transmit the signal
FM
Variation of the carrier wave’s frequency to transmit the signal

Question 21

Radio navigation: Principle

Answer 21

NDB-non directional beacon
Frequency range 0,190−1,750𝑀𝐻𝑧
NDB: Line of position using the loop antenna, removal ofthe ambiguity using the sense antennas of NDB
Advantages:
+Incomparison to other radio navigation systems, NDBs are in expensive
+Simple system architecture
+NDBs have an omnidirectional range and can be used for bearing from several aircraft
+The accuracy depends mainly on the receiver equipment in the aircraft
Limitations:
-NDB signal information is strongly affected by terrain reflection such as on mountains since the signal is purely transmitted by ground waves.
-Contamination of the ground waves by reflection from the ionosphere cause severe distortions, causing the direction signal to be erroneous.
-In the range of thunderstorms, the ADF receiver picks up the electromagnetic interferences of lightning discharge and the ADF needle is disturbed.
-When the aircraft has a bank angle greater than zero, the needle will show an offset from the true direction
-Shoreline effect refracts or bends radio waves near a shoreline, especially if they are close to parallel of the shore.

Question 22

Radio navigation: Principles of DME,

Answer 22

DME- distance measurung equipment
Frequency range 960–1215 MHz (UHF)
Principle:
•The travel time between the signal sent from the interrogator (onboard transmitter) and the answer of the ground station (transponder = transmitter and responder) is analyzed.
• DME stations are often linked with VOR stations.•
The DME consists of two separate units. The interrogator in the aircraft and the ground beacon transmission station. The interrogator sends pulses in the frequency range from 1025–1150MHz in 126 separate channel grids, spaced 1 MHz apart
Disadvantages
•DME always measures the slant distancefrom the DME station to the receiver in the airplane
•The receiver in the ground station emits a pulsed pair of signals back to the aircraft with a 50 𝜇𝑠time delay after receiving the signal from the aircraft

Question 23

Radio navigation: Principles of VOR,

Answer 23

Very High Frequency (VHF) Omnidirectional Range(VOR)
Frequency range 108,000-117,975MHz (VHF)
•The main information a VOR station delivers is the direction to the ground station (angle 𝜓 between two lines). The first line is attached at the VOR station and ends at the magnetic northpole. The second line is between the VOR station and the position of the aircraft.
•Technically, the phase difference 𝝋 between a reference signal and the rotating main beam of the VOR is being computed.
Advantages DVOR
•Decrease of reflection error (in the order of 10 times), since the antenna array has a larger diameter
•Decrease is even greater if reflection points are situated far away from the line-of-sight between transmitter and receiver, as there are less reflected signals with shifted phase (Multipatherrors)→Increased accuracy in the azimuth error from 6° to less than 1°compared to a conventional VOR
Disadvantages VOR
•Ground station error: Associated with the transmitter, aerial and earth systems and power supply. The magnitude of this error is small, usually below±2°.
•Site effect error: Occur due to topographical features near the groundstation. The combined effect of these several errors at various altitudes must be less than±3°.
•Vertical polarization (Attitude effects): If erroneous vertical polarization effects are present by the radiated beacon, the aircraft can detect those when it is banked in attitude during a turn. Instead of receiving only the horizontally polarized signals, it additionally detects the vertically polarized signals, too. This leads to an incorrect guidance information. Since the vertical component of the beacon is very small, this effect is rarely encountered in practice.
•Airborne equipment error: Attributable to the various components of the VOR equipment in the aircraft. In well designed equipment, the amount of error is usually less than±2°.
•Aggregate/sum error of the VOR: The conventional VOR is not a precision aid. But in practice, there are seldom aggregated errors beyond ±6°.

Question 24

ILS: Principles, positions of the antennas (GS, LOC, marker beacons)

Answer 24

Glideslope (GS)
normalerweise 3°
150Hz und 90Hz,
• The method is called null reference method, since the aircraft detects a null signal of the depth of modulation difference of the Side-Band-Only carrier along the course line.
•The antenna has a height of 10m to 20m. Usually the upper antenna emits the Side-Band-Only(SBO), while the lower antenna, which is positioned at about half of the height, radiates the Carrier and Side band signal(CSB). With this installation, the direct CSB signal forms, along with the reflected CSB signal, a sum pattern, while the direct SBO signal forms with the reflected SBO signal a difference pattern.
•The aircraft receiver: Filters after the detection antenna separate the 150Hz and 90Hz tones, rectify them to the same amplitude and feed them to a microamperemeter. The amperemeter indicates the direction, the pilot or the autopilot has to follow. The measurement principle is the DDM.
•A DDM of 0.175 with a larger 90Hz modulation indicates a full deflection of the needle to the right (-0.175DDM with a larger 150Hz modulation a full deflection to the left). The display of the vertical needle is similarly arranged.
Localizor LOC
fast gleich wie GS nur gedreht für rechts links abweichung
Marker
outer, middle , inner
problem: real estate for these installations, today DME, GNSS services diminishes dependence on markers