Lecture 4 Global Navigation Satellite Systems Contents Navigation

Lecture 4. Global Navigation Satellite Systems

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

History of Navigation • Navigation on the Ocean (must be independent from the continents) Latitude and Longitude j – Latitude l – Longitude

History of Navigation on the Ocean • Speed and Bearing measurements to keep the course. • Sextant and Chronometer to determine the Latitude and Longitude and update the position

History of Navigation How do we determine the latitude? 90 j = 90 – a - d a j d a

History of Navigation How to determine the Longitude? • 24 h = 360 o • We set the Chronometer on the Greenwich Meridian at noon to 0 h. • We read the time at the local noon on the sea. l = Dt x 15 o

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

History of GPS • After the 2 nd World War it became important to create the global Navigation solution. • In the Space era the satellites could be used as „control points”. • Surveyors used various satellites equiped with reflectors as signals to link control networks (e. g. islands) • After 1960 the „US Navy Navigation Satellite System“ (NNSS) was created, after renamed to TRANSIT

History of GPS • TRANSIT contained 6 satellites in polar orbits with the elevation of ca. 1100 km (period ca 107 Min). • The satellites were tracked from ground stations in US, and the orbital parameters were updated twice a day. • The satellites broadcasted the orbital parameters. The position could be computed from the observation of Doppler shifts with the accuracy of 1 m. Disadvantages • Good satellite constellation in every two hours only • Accurate position could be measured by long observations only.

History of GPS (Global Positioning System) was developed to • determine 3 D positions in real time. • determine accurate time Speed Bearing NAVSTAR GPS (Navigation Satellite Time And Range) from 1973 as prototype • First GPS satellite was started on June 27, 1977. Orbit elevation ca. 20000 km. Today the term GNSS (Global Navigation Satellite System) is also used. Under this term, the NAVSTAR GPS, GLONASS and GALILEO is also meant.

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

GPS satellite concept A minimum of 4 satellites must be tracked at the same time to determine position. Basically 3 satellite could be enough, but we have to face some errors. 1 Satellite 2 Satellites

GPS satellite concept Error-free solution 3 Satellites

GPS satellite concept • 24 Satellites planned • 12 -hour circular orbit in the elevation of 20200 km • 55 o inclination • 4 satellites on each orbital plane (6 Orbital planes – rectascension difference 60°) • At least 3 (now 8) reserve satellites

GPS satellite concept

GPS satellite concept GPS Carrier phases • L 1 = 1575. 42 Mhz (C/A Code, P-Code) • L 2 = 1227. 6 Mhz (P-Code) C/A Code – „coarse acquisiton code“ (low accuracy) P Code – „precision code“ (high accuracy)

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

GPS System Segments Three segments: • space segment • control segment • user segment

GPS System segments Space segment: • 24+8 GPS Satellites • Orbits (20183 km, Inclination 55 o and 60 o between the orbital planes) • At least 4 Satellites on each orbital plane, where the angular difference is 120 o • Period 12 hours • Each satellite has its own ID, which is broadcasted to the user. • The satellites are equiped with atomic clocks.

GPS System segments Ground segment (at US Army Facilities): • Monitoring station (5) • Master control station (1) • Telemetry stations (3)

GPS System segments Tasks of the ground segment: • Controlling and managing the telemetry and control stations. • Computation of ephemerids (orbit parameters) for each satellite. • Ordering satellite maneuvres. • Computing the data for the almanach • Determine the GPS time (atomic clock) • Communication link to the satellites

GPS System segments User segment: GPS receivers • track L 1 and/or L 2 frequencies • track C/A code for at least 4 satellites, and demodulation • Time synchronization (Quartz clocks in the receivers) • Decrypt satellite data from the code observations (orbit, etc. ) • receive P(Y) code (US Army) • Compute the pseudo-range to each satellite • Compute the time offset (receiver clock error) • Compute the position.

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

Principle of Positioning Coordinate system (WGS-84) The coordinates of satellites are given in this system.

Principle of Positioning Equal time circles 2 Satellites 3 Satellites p = c. T

Principle of Positioning Accuracies • Depends on the accuracy of distance measurements • Distance measurements – Travel time measurement • 1 ms (=) 300 m (only atomic clocks could measure with this accuracy • clock offset – a fourth satellite is also necessary for the determination of positions. (Receiver clock error)

Principle of Positioning Observation equations: p 1. . p 4 Pseudoranges xp, yp, zp Coordinates of the receiver xi, yi, zi Coordinates of the satellite i, i=1. . 4 Dp Offset due to the clock error DT Receiver clock correction ei additional error

Principle of Positioning The navigation solution provides us a worlwide accurate time system. By determining the receiver clock error, one can restore the GPS time using cheap quartz clocks. Since the GPS time is an atomic time, we can substitute an atomic clock using a GPS receiver.

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

GPS codes and their travel time Two frequencies: L 1=1575. 42 Mhz and L 2=1227. 60 Mhz Both of them are a multiple of the ground freqency: L 0=10. 23 Mhz The carrier phases are with PRN-codes („pseudo random noise“) modulated (L 1 – C/A and P, L 2 – P). All codes are biploar codes: Positive Amplitude=0 Neg. Alplitude=1

GPS codes and their travel time What is a PRN code? • It is a statistical distribution of impulses, which are similar to noise. • In reality the sequence of the impulses follow a complicated rule, which is necessary for the decryption. The receiver knows this algorithm.

GPS codes and their travel time GPS Signal modulation: • The C/A code contains 1023 positive and negative impulses (bits) with the span of 1 ms each, corresponging to 1. 023 Mbit/s rate. The whole sequence has the length of 300 km (corresponding to 1 ms). • P code has a rate of 10. 23 Mbit/s, it is 38 weeks long, with 1 week segments assigned to a satellite. It aims to eliminate range ambiguity. • A navigation message is also modulated to the carrier freqency with the frequency of 50 bit/sec. The length of the message is 1500 bits (30 sec). These 1500 Bits are split into 5 sub-frames with 10 words of 30 bits in each subframe. Each subframe is started with two special words: • „Telemetry Word“ (TLM) = Orbit corrections • „Hand Over Word“ (HOW) = GPS time

GPS codes and their travel time Broadcasted information: - Clock corrections - Ephemeris (precise orbit parameters of the transmitting satellite, valid for 4 hours) - Ionospheric corrections - Almanac (low-resolution orbit information of all satellites, valid for two weeks)

GPS codes and their travel time Determination of travel time • The travel time is ca 70 ms (20200/c) Since each satellite uses the same freqencies, the receiver receives the sum of the delayed carrier phases: i-th received bit of the Satellite #x The receiver creates the code with the known PRN code algorithm (here Sat #2)

GPS codes and their travel time Compute the value of cross-correlation Kj. Where Kj is maximal, then both of signals are correlated: Schematic view of the satellite codes; 1 = Satellite code, 2 = satellite code with an offset of 2 ms. , 3 = satellite code with an offset of 5 ms. , 4 = receiver code and 5 = correlation

GPS codes and their travel time If one can determine the time delay with the accuracy of 1%: C/A Code accuracy of 3 m P Code accuracy of 0, 3 m

Contents • Navigation • History of GPS • GPS Satellite Concept • GPS System Segments • Principle of Positioning • GPS codes and the determination of travel time • Accuracies / Error sources

Accuracy and error sources Error sources – signal propagation • The atmosphere has an impact on the signal propagation path. • Troposphere and Ionosphere • The Ionosphere (70 -1000 km elevation) contain electrons and ions, which have an effect on the propagation of electromagnetic signals. • the delays depend on the frequency;

Accuracy and error sources Troposphere • Up to 40 -70 km (tropospheric refraction) • Meteorological factors (weather, air pressure, temperature, etc. ) • Empirical models Multipath • GPS signals are reflected, and direct and indirect signals are also received. Indirect Direct

Accuracy and error sources Error sources – receiver error • Thermal noise • receiver clock corrections • antenna phase center offsets and variations

Accuracy and error sources Error sources – satellite geometry • Not all of the satellite constellation enables the optimal positioning. • DOP – „Dilution of Precision“ dr d. POS accuracy of the pseudorange observation accuracy of the positioning PDOP: Position (3 D) Dilution of Precision is the reciprocal value of the volume of a tetraeder defined by 4 satellites + the receiver.

Accuracy and error sources PDOP low Good PDOP high Bad