lecture 22: Global Positioning System (GPS)

humans have always been interested in where things are…

one of the basic questions has always been…where am I?….which leads to…

where am I going and how do I get there?

early solutions:• marking trails with piles of stones

(problems when snow falls…or on ocean)• navigating by stars

(requires clear nights and careful measurements) most widely used for centuries

…location within a mile or so

modern ideas:• LORAN: radio-based; good for coastal waters

…limited outside of coastal areas• Sat-Nav: low orbit satellites; use low frequency Doppler

…problems with small movements of receivers

Department of Defense finally said: “we need something better: all-day and all-night; all terrain”

end-product is Global Positioning System (GPS)

• system (constellation) of 24 satellites in high altitude orbits(cost ~ $12 billion)

• coded satellite signals that can be processed in a GPS receiver to compute position, velocity, and time• parts of system include: space (GPS satellite vehciles, or SVs) control (tracking stations) users

first one launched in 1978 ….June 26, 1993 Air Force launched 24th SV

orbit ~ 12 hours

27 satellites: 24 operational and 3 spare

ground tracks

basic concept is that the GPS constellation replaces “stars” andgives us reference points for navigation

examples of some applications (users):• navigation (very important for ocean travel)• zero-visibility landing for aircraft• collision avoidance• surveying• precision agriculture• delivery vehicles• emergency vehicles• electronic maps• Earth sciences (volcano monitoring; seismic hazard)• tropospheric water vapor

anything that involves location, motion, or navigation

examples of applications

we will break system into five conceptual pieces

step 1: using satellite rangingstep 2: measuring distance from satellitestep 3: getting perfect timingstep 4: knowing where a satellite is in spacestep 5: identifying errors

GPS block I

GPS block II

GSP satellite vehicles (SVs):two generations: block I and block II

weigh ~1900 lbs.

built by Rockwell

step 1: using satellite ranging

GPS is based on satellite ranging, i.e. distance from satellites …satellites are precise reference points

…we determine our distance from them

we will assume for now that we know exactly where satellite isand how far away from it we are…

if we are lost and we knowthat we are 11,000 miles

from satellite A…we are somewhere on a sphere

whose middle is satellite Aand diameter is 11,000 miles

if we also know that we are12,000 miles from satellite B…we can narrow down where

we must be…only place in universe is on

circle where two spheres intersect

if we also know that we are13,000 miles from satellite C

…our situation improvesimmensely…

only place in universe is ateither of two points where

three spheres intersect

three can be enough to determine position… one of the two points generally is not possible (far off in space)

two can be enough if you know your elevation …why?

one of the spheres can be replaced with Earth… …center of Earth is “satellite position”

generally four are best and necessary….why this is a little later

this is basic principle behind GPS……using satellites for triangulation

step 2: measuring distance from satellite

because GPS based on knowing distance from satellite …we need to have a method for determing how far

away the satellites are

use velocity x time = distance

GPS system works by timing how long it takes a radio signal to reach the receiver from a satellite…

…distance is calculated from that time…radio waves travel at speed of light: 180,000 miles per second

problem: need to know when GPS satellite started sending its radio message

requires very good clocks that measure short times……electromagnetic waves move very quickly

use atomic clocks

came into being during World War II; nothing to do with GPS -physicists wanted to test Einstein’s ideas about gravity and time • previous clocks relied on pendulums • early atomic clocks looked at vibrations of quartz crystal

…keep time to < 1/1000th second per day ..not accurate enough to assess affect of gravity on time …Einstein predicted that clock on Mt. Everest

would run 30 millionths of a second faster than clock at sea level

…needed to look at oscillations of atoms

principle behind atomic clocks…

atoms absorb or emit electomagnetic energy in discrete amounts that correspond to differences in energy between different configurations of the atomswhen atom goes from one energy state to lower one, it emits an electromagnetic wave of characteristic frequency …known as “resonant frequency”

these resonant frequencies are identical for every atom of a given type:

cesium 133 atoms: 9,192,631,770 cycles/second

cesium can be used to create extraordinarily precise clock

(advances also led to using hydrogen and rubidium)

GPS clocks are cesium clocks

now that we have precise clocks……how do we know when the signals left the satellite?

this is where the designers of GPS were clever……synchronize satellite and receiver so

they are generating same code at same timeanalogy: 2 people separated by some distance both start yelling

one, two, three…at same time person 2 hears “one” shouted by person 1 when

person 2 says “three” …if you both said one at same time,

the distance away person 2 is from person 1 is time difference between “one” and “three”

times the velocity of the sound

let us examine GPS satellite signals more closely…

SVs transmit two microwave carrier (carry information) signalsL1 (1575.42 MHz): carries navigation message; SPS code

(SPS: standard positioning servic)L2 (1227.60 MHz): measures ionospheric delay

C/A code (coarse acquisition) modulates L1 carrier phase …repeating 1 MHz pseudo random noise (PRN) code

…pseudo-random because repeats every 1023 bits or every millisecond…each SV has its own C/A code

…basis for civilian SPSP-code (precise) modulates both L1 and L2 …long (7 days) pseudo random 10 MHz noise code …basis for PPS (precise positioning service) …AS (anti-spoofing) encrypts P-code into Y-code

(need classified module for receiver)navigation message modulates L1-C/A; 50 Mhz signal ….describes satellite orbits, clock corrections, etc.

3 binary codes shift L1 and/or L2 carrier phases

GPS receiver produces replicas of C/A and/or P (Y) code receiver produces C/A code sequence for specific SV

C/A code generator repeats same 1023 chip PRN code sequence every millisecond

PRN codes defined for 32 satellite ID numbers

modern receivers usually store complete set of precomputed C/A code chips in memory

receiver slides replica of code in time until finds correlation with SV signal

(codes are series of digital numbers)

if receiver applies different PRN code to SV signal …no correlation

when receiver uses same code as SV and codes begin to align …some signal power detected

when receiver and SV codes align completely …full signal power detected

usually a late version of code is compared with early version to insure that correlation peak is tracked

receiver PRN code start position at time of full correlation is time of arrival of the SV PRN at receiverthe time of arrival is a measure of range to SV offset by amount to which receiver clock is offset from GPS time

…the time of arrival is pseudo-range

position of receiver is where pseudo-ranges from set of SVs intersect

• position determined from multiple pseudo-range measurements from a single measurement epoch (i.e. time)• psuedo-range measurements used together with SV position

estimates based on precise orbital elements(ephemeris data) sent by each SV

GPS navigation datafrom

navigation message

each SV sends amount to which GPS time is offset from UTC (universal time) time…correction used by receiver to set UTC to within 100 nanoseconds

position determined from multiple pseudo-range measurements4 satellites…3 (X, Y, Z) dimensions and time

when clock offsets are determined, the receiver position is known

this leads us to why 4 GPS satellites are necessary and to…

step 3: getting perfect timing

electromagnetic energy travels at 186,000 miles per second …an error of 1/100th second leads to error of 1,860 miles

how do we know that receiver and satellite are on same time?

satellites have atomic clocks (4 of them for redundancy)…at $100,000 apiece, they are not in receivers!

receivers have “ordinary” clocks(otherwise receivers would cost > $100K)…can get around this by having an “extra” measurement

…hence 4 satellites are necessary

three perfect measurements will lead to unique, correct solution ….four imperfect ones also will lead to appropriate solution

illustrate this in 2D…

instead of referring to satellite pseudo-range in distance,…we will use time units

two satellites: first at distance of 4 seconds second at distance of 6 seconds

X

location of receiver is X

this is if clockswere correct…

what if they weren’t correct?

X

what if receiver wasn’t perfect?…receiver is off by 1 second

“real” time

wrong time

XX position is wrong; caused by wrong time measurements

XX

how do we know that it is wrong?…measurement from third satellite (fourth in 3D)

X

3rd satellite at 3 seconds

all 3 intersect at X…if time is correct

if time is not correct…

add our one second error to the third receiver…

XX

…circle from 3rd SV cannot intersect where other 2 do

purple dots areintersections of

2 SVs

define area of solutions …receivers calculate best solution(add or subtract time from each SV)

finally… step 4: knowing where a satellite is in space

• Air Force injected satellites into known orbits• orbits known in advance and programmed into receivers• satellites constantly monitored by DoD …identify errors (ephemeris errors) in orbits …usually minor• corrections relayed back to satellite “data message” about their “health”

sites have co-located: • VLBI (very long baseline interferometry); • lunar laser-ranging (from instrument left by Apollo astronauts)

…primarily for length of day considerations • satellite laser-ranging

step 5: identifying errorsionosphere: electrically charged particles 80-120 miles up;

affects speed of electromagnetic energy…amount of affect depends on frequency …look at differences in L1 and L2 (need “dual-frequency” receivers to correct)

tropospheric water vapor: affects all frequencies; difficult to correct

multipath: reflected signals from surfaces near receiver

noise: combined effect of PRN noise and receiver noise

bias: SV clock errors; ephemeris errorsselective availability: SA; error introduced by DoD;

turned off May, 2000

blunders: human error in control segment user mistakes (e.g. incorrect geodetic datum)

…more on this in a minute receiver errors

geometric dilution of precision (GDOP): errors from range vector differences between receiver and SVs (pictures coming…)

effects of noise, bias, and blunder

geometric dilution of precision (GDOP)

SVs occupy a small volume in the sky

SVs occupy a large volume in the sky

when measuring must have good GDOP and good visibility…may not always be possible

user community… primary application is GPS navigation

X, Y, Z (position) and time from 4 satellites to calculate position

GPS determines locations in Earth centered, Earth fixed (ECEF)

need to convert to latitude, longitude, and height above ellipsoid

need to use datum…descriptions of Earth’s surfacedepends on projections

flat Earth for short distancesellipsoidal models for whole Earth

GPS uses WGS-84 (ellipsoid)geoid: surface resulted from gravity alone

other reference ellipsoids exist

can convert from one datum to another (standard equations)

note position shifts…important to be consistent

differential GPS: improves accuracy correct bias errors at one location using

measured bias errors at known position (base station)…requires software in reference receiver that can track

all SVs in view and form individual pseudo-rangecorrections for each

can also use carrier phase (L1; L2)two receivers must be < 30 kms from one another (ionospheric delay must be less than one wavelength); requires special software …real-time kinematic (RTK) processing

old slide (1994): currently, dual-phase geodetic receivers ~$10K