Basics of gps 1

GPS CONCEPTS

M.Sc Communication SystemsCSED,BDU, Ethiopia

Vrince Vimal, [email protected] CSED,Bahir Dar university, Ethiopia

GPS RECEIVER


SOFTWARE

ACQUISITION&TRACKING

SUBFRAME IDENTITY

EPHIMERIS & PSEUDORANGE

SAT POSITION &USERPOSITION

HARDWARE

RF CHAIN

ADC


1. Positioning error should be 10–30 m.

2. Applicable to real-time navigation for all users

3. Worldwide coverage

4. Transmitted signals should bear interfearence

Gps performance requirements


5.Should be fast and accurate

6. Size of antenna should be small


Finding user position

1 d user position


2 d user position


3 d user position


USER POSITION CALCULATION

ASSUMING DISTANCE CALCULATED IS ACCURATE.. Consider following figureLet (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) be Known points &ru or (xu, yu, zu). be the user position


Than distance between known and unknown points can be calculated as:-

Where & Are the distance betn, points


Measurement of pseudo range

Let satellite sends a signal at time tsi.

receiver receives signal at time tu.

The distance between the user and the satellite i is

Where =true value of pseudo range

tsi =the true time of transmission from satellite i,


practically it is difficult, to obtain the correct time from the satellite or the user.

Let t′si = actual satellite clock time and t′u =actual user clock timeThan

Where =satellite clock error,

= is the user clock bias error.


Apart from clock error, some other factors affect

the pseudorange measurement. So

Where ΔDi =is the satellite position error effect on range, ΔTi = the tropospheric delay error,

Δ Ii = the ionospheric delay error,

vi =is the receiver measurement noise error,

Δvi = the relativistic time correction.


Apart from clock, errors can be corrected for example, the tropospheric delay can be modeled etc

So equations become

where bu =user clock bias error expressed in distance, Given by


Above are non-linear eqn to solve them lets linearize

them. The above equations can be written in a

general way as

WhereAre known satellite positions and pseudo range&

&


Differentiating above equation, we get

& are unknown values


To solve above eqn tentative initial values of are assumed , From these new set of

are calculated.

Now this process repeats until absolute value of

Are very small and under determined

limits. This is known as iteration method.

&

&

&


Above is linear eqn , writing it in matrix form as

Where,


The values of & Can be found as

By repeativly performing iteration on above eqn

the desired soln is obtained.


The process of iteration stops when

< some predetermined threshold value

Where,


In cases as when signals from more than four satellites are obtained.

Eqn can be written as..

Or,


Which gives,

=ά-1

Butά is not squqre matrix its inverse can’t be obtained directly,

Therefore obtaining pseudo inverse we get,

This is user position in cartesion coordt sys.


User position in spherical coordt system


Considering earth to be the perfect sphere

The user position can be easily found as:-

Distance from centre of earth:-

Latitude Lc


Longitude l

Altitude h

T.B.C

Basics of gps 1

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