GPS CONCEPTS

M.Sc Communication SystemsCSED,BDU, Ethiopia

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

GPS RECEIVER

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

SOFTWARE

ACQUISITION&TRACKING

SUBFRAME IDENTITY

EPHIMERIS & PSEUDORANGE

SAT POSITION &USERPOSITION

HARDWARE

RF CHAIN

ADC

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

5.Should be fast and accurate

6. Size of antenna should be small

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

Finding user position

1 d user position

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

2 d user position

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

3 d user position

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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

Where & Are the distance betn, points

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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,

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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.

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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.

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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&

&

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

Differentiating above equation, we get

& are unknown values

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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.

&

&

&

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

Above is linear eqn , writing it in matrix form as

Where,

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The values of & Can be found as

By repeativly performing iteration on above eqn

the desired soln is obtained.

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

The process of iteration stops when

< some predetermined threshold value

Where,

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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

Eqn can be written as..

Or,

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

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.

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

User position in spherical coordt system

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

Considering earth to be the perfect sphere

The user position can be easily found as:-

Distance from centre of earth:-

Latitude Lc

Vrince Vimal, vrince.vimal@gmail.com CSED,Bahir Dar university, Ethiopia

Longitude l

Altitude h

T.B.C