Upload
madhumita-tamhane
View
154
Download
0
Embed Size (px)
Citation preview
GPS Simplified
How Does GPS Work? • Introduction
• Location Finding
• Trilateration
• Almanac and Ephemeris
• A-GPS
• GPS Routing- Finding best route
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
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.
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.
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.
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.
r1 r1
r1
r1
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
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
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.
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.
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.
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.
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.
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.
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 .
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
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.
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.
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.
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….
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.
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.