Global Positioning System (GPS) Training Reference

The Advantages of Space-Based Transmitters

  • Historical Context:

    • Ground-based radio navigation transmitters have provided reliable coverage for over 50 years.
    • Engineers historically faced a choice between two main transmission frequency ranges:

  • Low Frequency (LF) Transmitters:

    • Mechanism: Utilize very low frequency (VLF) waves that achieve 'wave-form ducting.' Carrier waves reflect off the Earth's ionosphere.
    • Advantages: Broad coverage area; a small number of transmitters can cover a substantial fraction of the globe.
    • Systems: Omega (decommissioned 1997) and LORAN (decommissioned 2015).
    • Disadvantages: Inaccurate navigation results.
      • Information Density: Carrier waves cannot be modulated with much useful information.
      • Refraction Issues: Signals refract off the ionosphere, which has large variations in height and composition.
      • Scale: The Omega system used carrier waves approximately 16 miles long.
      • Error Margin: Errors typically amounted to 4 nautical miles in longitude and latitude (at a 95% confidence interval).

  • High Frequency (HF) Transmitters:

    • Advantages: High-frequency carrier waves provide far more accurate navigation solutions.
    • Disadvantages: These waves 'punch' through the ionosphere rather than reflecting, providing only line-of-sight coverage over a small, localized area.
    • Physical Limitations: A transmitter tower 300 feet high typically offers a circular line-of-sight coverage area of only 40 miles.
    • Infrastructure Requirement: Worldwide coverage would require thousands of ground-based and sea-based transmitters.

  • The Space-Based Solution:

    • High-frequency transmitters are positioned in outer space to overcome terrestrial line-of-sight limits.
    • Waves penetrate the ionosphere from the "top down" to provide global coverage with high accuracy.
    • NAVSTAR GPS Satellites:
      • Altitude: 10,898 nautical miles10,898\,\text{nautical miles}.
      • Visibility: Each satellite has a direct line-of-sight to 42 percent of the Earth's surface.
      • Frequencies: $1575.42\,\text{MHz}$ and $1227.6\,\text{MHz}$.
      • Wavelengths: Approximately $7.5\,\text{inches}$ and $9.6\,\text{inches}$ respectively.

GPS Constellation and Reference Systems

  • Satellite Constellation:

    • Definition: A group of satellites placed in orbit for the same function.
    • NAVSTAR GPS consists of 24 satellites established in six orbital paths.
    • Orbital Properties:
      • Inclination: $55^{\circ}$ relative to the Equator.
      • Inclination Pattern: Alternating left and right inclination.
      • Orbital Period: 11 hours and 58 minutes.
      • Active Status: 21 satellites are always active; 3 serve as 'on-orbit spares' to cover maintenance periods.

  • Ownership and Logistics:

    • Owned and administered by the United States Department of Defense (US DoD).
    • Use of signals is free of charge.
    • Manufacturer: Rockwell International.
    • Size: 17 feet with solar panels extended.
    • Planned Lifespan: 7.5 years.

  • Global Alternatives:

    • GLONASS (Soviet Union/Russia).
    • Galileo (European Union).
    • BeiDou Navigation System (BDS) (China).
    • Navigation with Indian Constellation (NavIC) (India).
    • Quasi-Zenith Satellite System (Japan).

  • The Reference Coordinate System:

    • Standard: World Geodetic System 84 (WGS 84).
    • Coordinate Origin: Located at the Earth's center of mass within $2\,\text{cm}$ accuracy.
    • Datum Point: Intersection of three mutually orthogonal lines:
      1. One line along the polar axis.
      2. One line through the Equator at the Prime ($0^{\circ}$) Meridian.
      3. One line through the Equator at the $90^{\circ}$ Meridian.
    • Application: Australia re-surveyed all aerodrome reference points to align with WGS 84 due to GPS implementation.

GPS Principles of Operation and Trilateration

  • Core Concept: Trilateration:

    • A GPS receiver locates four or more satellites, calculates the distance to each, and deduces its location.

  • Two-Dimensional Example:

    • Point 1: Being $750\,\text{km}$ from Alice Springs places you on a circle.
    • Point 2: Adding $1000\,\text{km}$ from Townsville identifies two intersection points.
    • Point 3: Adding $1250\,\text{km}$ from Broken Hill eliminates one point, leaving the precise location (Mt Isa).

  • Three-Dimensional Trilateration:

    • In 3D space, circles become spheres.
    • Sphere A (e.g., $11,000\,\text{miles}$ radius): You are on the surface of the sphere.
    • Sphere B ($12,000\,\text{miles}$ radius): The intersection of two spheres is a perfect circle.
    • Sphere C ($13,000\,\text{miles}$ radius): The intersection of the circle and the third sphere leaves two points in space.
    • Point Identification: Usually, one of the two final points is ridiculous (e.g., in deep space or moving at impossible velocity). The Earth itself can effectively serve as a fourth sphere to eliminate the invalid point.

Satellite Ranging and Time Keeping

  • The Distance Formula:

    • Position is determined by measuring distance from satellites acting as reference points.
    • Distance=Velocity×Time\text{Distance} = \text{Velocity} \times \text{Time}
    • Velocity: The speed of light/radio waves is approximately 300,000,000 m/s300,000,000\,\text{m/s} (or 186,000 miles per second186,000\,\text{miles per second}).

  • Signal Components:

    • P-code (Precise code): Encrypted signal utilizing two frequencies; reserved for US and allied military forces.
    • C/A-code (Coarse/Acquisition code): Standard signal for civilian applications; uses one frequency and has a specific chip rate (bits per second).
    • Pseudo-random Codes: Complicated digital pulses that look random but repeat every millisecond. This complexity allows for unambiguous signal comparison.

  • Timing Precision:

    • Satellites carry 4 atomic clocks to guarantee accuracy of one nanosecond ($10^{-9}\,\text{s}$).
    • Error Impact: A synchronization error of just $0.000001\,\text{second}$ between the satellite and receiver creates a position error of $300\,\text{metres}$.
    • Receiver Clocks: Much cheaper and less accurate than satellite atomic clocks.
    • The Fourth Satellite Requirement: To fix the offset between the receiver's cheap clock and the satellite's atomic clock, a fourth satellite is necessary. The computer adds/subtracts time equally across signals until they intersect at a single point.

Sources of GPS Error and Dilution of Precision

  • Satellite Position (Ephemeris) Errors:

    • Orbits deviate due to lunar gravity, solar gravity, and solar wind (perturbations).
    • Corrections: Ground stations monitor orbits and uplink correction factors, which the satellite broadcasts to receivers.
    • Equatorial Bulge: Earth's shape causes range errors up to $300\,\text{meters}$ if not corrected.

  • Atmospheric Errors:

    • Ionosphere: Charged particles slow radio signals. Delay is affected by solar flares and sunspots. Military users correct this using dual-frequency (L1 and L2) measurements; civilians use a fixed average correction.
    • Troposphere: Water, dust, and contaminants affect the signal. This is variable and cannot be corrected by software.

  • Multipath Error:

    • Signals reflect off mountains or buildings. The receiver must distinguish between the direct signal and the delayed reflected signal to prevent position errors.

  • Mask Angle:

    • Satellites low on the horizon have signal paths through a greater volume of atmosphere.
    • Typically, any satellite below $7.5^{\circ}$ above the horizon is rejected by the receiver.

  • Geometric Dilution of Precision (GDOP):

    • Position accuracy varies based on relative satellite angles.
    • Fuzzy Circles: Since every measurement has uncertainty (e.g., $\pm 0.001\,\text{mile}$), the intersection point is a box rather than a point.
    • Optimal Geometry: Satellites spread wide across the sky produce a small, square "box." Bunched satellites create a large, elongated uncertainty area.
    • Sophisticated receivers select the four best satellites or use all satellites in view to minimize GDOP.

Augmentation Systems (DGPS, Pseudo-lites, WAAS)

  • Differential GPS (DGPS):

    • Uses precisely located ground transmitters to measure inherent signal errors (atmospheric, ephemeris, etc.).
    • Error correction messages are transmitted to local receivers, allowing for horizontal accuracy of less than one metre.

  • Pseudo-satellites (Pseudo-lites):

    • Ground-based transmitters mimicking L-band GPS signals.
    • Dr. Brad Parkinson's Research: Discovered that a single pseudo-lite could reduce Vertical Dilution of Precision (VDOP) from 12 down to 0.7 near San Francisco airport.
    • Placement: Ideally located $30\,\text{miles}$ south of a runway in the Northern Hemisphere (north in the Southern Hemisphere) to provide optimal viewing geometry without jamming overhead satellites.
    • Integrity Beacon Landing System (IBLS): Uses low-power ground markers ("bubbles") to achieve Category III approach specifications with centimeter-level precision.

  • Wide Area Augmentation System (WAAS):

    • FAA/DOT program for precision flight approaches.
    • Structure: 25 ground reference stations across the US + 2 master stations on either coast.
    • Broadcast: Corrected messages are sent via geostationary satellites.
    • Availability: Currently North America only. Other regions utilize similar Satellite Based Augmentation Systems (SBAS):
      • MSAS: Asia (Japan).
      • EGNOS: Europe.
      • Southern Positioning Augmentation Network: Australasia (operational expected by 2023).

Receiver Autonomous Integrity Monitoring (RAIM)

  • Definitions:

    • Integrity: Ability to provide timely warnings when the system should not be used.
    • Alarm Limit: The allowable radial error for a specific phase of flight.

  • RAIM Functions:

    • Detection: Requires 5 satellites (or 4 plus barometric alt). Can detect a fault exists but cannot identify which satellite is faulty.
    • Isolation: Requires 6 satellites (or 5 plus barometric alt). Can identify, isolate, and ignore the faulty satellite to continue navigating.

  • Least-Squares-Residuals (LSR) Method:

    • Performs a linearized solution of 5 equations with 4 unknowns.
    • Sum of the squares of residuals forms a test statistic.
    • If the test statistic passes a predetermined threshold, an alarm is annunciated.

Airborne GPS Components and Integration

  • Core Configuration:

    1. Antenna: Flat microstrip type with integral pre-amp; mounted on top of the fuselage for line-of-sight access.
    2. Receiver/Processor Unit: Contains the receiver, navigation database, computer assembly, and I/O interface.
    3. Multifunction Control Display Unit (MCDU): User interface for flight plans, data access, and malfunction warnings.
    4. Data Loader: Updates monthly navigation databases (waypoints, VORs, airports).

  • System Inputs:

    • Altitude System: Provides data during periods of reduced satellite coverage.
    • Heading System: Assists with initialization upon application of power.

  • System Outputs:

    • Remote Annunciators: MSG (Amber - message), HLD (Green/White - flight plan suspended), WPT (Green/Amber - approaching waypoint), APR (Green/White - approach mode active/final approach).
    • GPS/NAV Transfer Relay: Controls whether pilot instruments see GPS data or traditional VHF NAV data. Must default to VHF NAV on power failure.
    • ILS Tuned Transfer Relay: Automatically switches to VHF NAV if an ILS frequency is tuned on the NAV control panel.

Technical Details and Maintenance (Trimble 2101 Example)

  • Tracking Loops:

    • Code Tracking Loop: Tracks P and C/A codes to determine signal travel time (pseudorange) via auto-correlation.
    • Carrier Tracking Loop: Tracks doppler shift of the carrier wave to determine the aircraft's velocity components (orthogonal vectors).

  • Kalman Filtering:

    • Mathematical technique for smoothing a sequence of solutions.
    • Provides a Figure of Merit (FOM): FOM 1 = error < $25\,\text{m}$; FOM 9 = error > $5000\,\text{m}$.

  • Installation Specs:

    • Transmission Line Loop: $50\,\text{ohms}$ impedance; Insertion Loss $< 10\,\text{dB}$ at $1.575\,\text{GHz}$; DC Resistance $< 1\,\Omega$.
    • Antenna Power Requirement: Verified values at least $40\,\text{mA}$ and $4\,\text{v}$.
    • VHF Interference: Harmonics from $121.150\,\text{MHz}$, $131.250\,\text{MHz}$, etc., can jam the GPS. Tests involve keying the VHF for 20 seconds to see if satellite tracking drops.

  • Operational Modes:

    • NAV: Primary navigation (destinations, CDI, ground speed).
    • WPT: Access to 8 categories of database info (Airports, SIDs, STARs, etc.).
    • AUX: Sensor status, hardware configuration, and display diagnostics.
    • 3D vs 2D Mode: Automatic switch to 2D (no altitude solution) when only 3 satellites are available; requires manual or encoded altitude input. Flashing GPS light indicates 2D mode.