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GPS satellites circle the earth twice a day in a very precise orbit and transmit signal information to earth. GPS receivers take this information and use trilateration to calculate the user's exact location. GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. The time difference tells the GPS receiver how far away the satellite is. With distance measurements from a few more satellites, the receiver can determine the user's position and display it on the unit's electronic map.

A GPS receiver must be locked on to the signal of at least 3 satellites to calculate a 2-D position (latitude and longitude) and track movement. With four or more satellites in view, the receiver can determine the user's 3-D position (latitude, longitude and altitude). Once the user's position has been determined, the GPS unit can calculate other information, such as speed, bearing, track, trip distance, distance to destination, sunrise and sunset time and more.

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- 1. GPS Simplified How Does GPS Work? • Introduction • Location Finding • Trilateration • Almanac and Ephemeris • A-GPS • GPS Routing- Finding best route
- 2. GPS - Introduction • GPS or Navstar provides location and time information. • Originally developed by US government for military navigation. • Now any GPS device can use its services. • GPS does not need telephonic or internet connection for position finding. • Telephonic or internet reception enhances usefulness of GPS positioning information. • GPS is mainly used for 1. Location finding 2. Optimum route finding
- 3. GPS - Introduction • GPS is a network of about 31 satellites orbiting Earth at an altitude of 20,000 km. • Satellites orbit Earth with period of 12 hours (two orbits per day) at 14,000kph. • 24 satellites are major, with 4 satellites each orbiting in 6 equally spaced orbit planes. • On Earth, at least four GPS satellites must be ‘visible’ at any time at a point. • India among five nations to have own navigation and positioning system with launch of IRNSS-1G, country’s seventh navigation satellite.
- 4. GPS - Introduction • GPS made up of three parts: • satellites, • ground stations, • and receivers. • Satellites act like the stars in constellations – we know where they are supposed to be at any given time. • The ground stations use radar to make sure they are actually where we think they are. • Receiver is any GPS-enabled device.
- 5. Location Finding • Each satellite transmits information at regular intervals about its-- • exact position • current time. • Information travelling at speed of light is received by our GPS receiver. • GPS calculates how far away each satellite is based on how long it took for the messages to arrive. • Total Time = Received time -Transmission time indicated in signal. • Distance = Speed of Light * Total time (Speed=distance/time) • GPS receiver can pinpoint our location using a process called trilateration.
- 6. Trilateration • You find your distance from 4 satellites visible to you. • Suppose you are at distance r1 from satellite A. • Information only about distance but doesn’t tell- in which direction. • You can be anywhere on sphere surface with radius r1 centered at exact position of A. • Similarly You are at distance r2 from satellite B. • Again you can be anywhere on sphere surface B with radius r2 cantered at exact position of B. r1r1 r1 r1
- 7. Trilateration • To be on surface of two spheres simultaneously, spheres must cut each other. • Then you are anywhere on circumference (border)of circle P1-P2. • Information from third satellite shows your distance r3, from canter of sphere at exact position of C. • You are at circumference of circle as well as on third sphere. • We can draw third sphere intersecting circle. P1 P2 r2 r1
- 8. Trilateration • Sphere surface intersects circle circumference at two points. • To be on third circle as well as on circle circumference, you can be on these two possible points. • Still there is ambiguity regarding your exact position. P1 P2 r2 r1 Intersection of circle border and sphere surface at two points
- 9. Trilateration • Information from fourth satellite is needed to pinpoint exactly which of two points is your location. • Hence at-least 4 satellites needed to give single location. • When all four satellite positions and distances are known, your exact location can be pinpointed on a map.
- 10. Almanac and Ephemeris • The satellites broadcast two types of data, • Almanac- Course orbital parameters for all SV (satellite vehicle). • Each SV broadcasts Almanac data for all SVs. • Almanac data not very precise and considered valid for up to several months. • Ephemeris- Very precise orbital and clock correction for each SV. • Ephemeris necessary for precise positioning. • EACH SV broadcasts ONLY its own Ephemeris data. • Ephemeris data valid for about 30 minutes. • Ephemeris data broadcasted every 30 seconds.
- 11. A-GPS • GPS fixes on location within few seconds to several minutes depending on when it was used last. • Needs time to download current Almanac, Ephemeris, time etc. from satellite. • If used recently, it uses last data and fixes soon. • Cell-phone GPS units get a fix almost immediately. • They use Assisted GPS (A-GPS) using a data connection to a server. • Server supplies Almanac, Ephemeris to cell-phone GPS. • GPS doesn't wait to receive them from satellites. • Server can also send an approximate location derived from cell-phone towers, allowing an immediate fix. • In some cases the A-GPS device may send incomplete GPS data to the server for processing into a fix.
- 12. GPS ROUTING Is Internet required? • Location Finding- – Only GPS used. – Internet connection not required. – If internet connection available, GPS finds your location much faster. • Navigation- – Plans and tracks your movement from A to B. – GPS is used only to find your location. – navigation apps like Google Maps require internet connection to access map data, compute directions, look up traffic details, search for points of interest, etc. – Apps are available that don't require Internet connectivity for navigation. – Data as directions, turn-by-turn navigation, POIs, can be stored on device SD Card.
- 13. Navigation- A* Algorithm Finding best route • GPS uses A* algorithm for finding shortest path. • It is a variation to Dijkstra's algorithm. • A digital map divides a Broad Street into hundreds of road segments, with nodes at intersections. • GPS navigation app looks at the entire road network as a graph. • Routing is explained with example:- • To find route between A and P.
- 14. Navigation- A* Algorithm Finding best route • First picture is one of roundabout ways, taking 10 steps. • Right picture is one of possible shortest paths that take 6 steps. • In real world, it is not possible to examine every possible route to discover shortest ones.
- 15. Navigation- A* Algorithm Finding best route • A human would mentally draw a straight line from start to destination and pick roads that are close to that line. • A* algorithm does something similar when it is at an intersection (node) with multiple possibilities. • It picks node that gives the shortest total route length as if it could go directly from that node to the destination. • Virtual Direct path between A to P is A-F-K-P .
- 16. Navigation- A* Algorithm Finding best route • First step--Two choices: • A to B • A to E. • Both equivalent. • Direct path B-P and E-P are the same length. • So picks one arbitrarily-- via B. • But it remembers the blue path through E
- 17. Navigation- A* Algorithm Finding best route • From B two choices: C and F • Going back to A is not an option. • Two choices are not equivalent. • Direct path C-P is longer than direct path F-P. • Hence, Chooses F. • But remembers the path via C.
- 18. Navigation- A* Algorithm Finding best route • At F, there are three choices: E, G, and J. • But computer remembers path that already goes through E. • It will discard and forget A-B-F-E routing, as A-E was more direct. • Balance routes to P through G and J. Both equal. • Chooses J.
- 19. Navigation- A* Algorithm Finding best route • Eventually, it makes its way to P. • Along the way it remembers several routes, and discard others, always following the shortest total path. • Several shortest paths. • Arbitrary decision made at several places to arrive at final path. • But would never pick A-B-C-D-H-L-P, even of same length, as it takes it away from direct line from A to P.
- 20. Dead Ends • Remembered routes used to backtrack from dead ends. • At dead end point K, its only option is to go to G as it is coming from J. • However, it already remembers a path through G that is shorter. • Since there's no other path, it discards the route through K and examines J and G again. • And so on….
- 21. Limitations • Grid is useful way to understand graph traversal algorithms, but real world is not grid. • Time-taken and not the distance is important factor in choosing a route. • GPS searches for shorter route even if it is narrow or crowded. • Riders prefer highways to winding roads even if longer. • Real-time traffic condition is very important in finding optimum route. • Problems regarding CPU and memory. • A* search too exhaustive to be used on long distance travels like inter-city.
- 22. Remedy • Digital maps classify roads based on their suitability for long-distance travel. – Top category are generally interstate highways, – Lowest are neighbor-hood roads. – In middle are various types of highways and arterial roads. • For long-distance routes, GPS finds shortest path from you to nearest arterial and highway network. • Once on arterial and/or highway network, it gets you as close to your destination as possible on highway. • Then it steps down, from highway, to arterial, to neighbourhood roads, until finding your destination. • The goal is to find the destination within a hundred or so road segments.

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