SINGLE AND DUAL FREQUENCY

SOLUTION IN GPS

Presented by:

JITHIN RAJ K

M.Tech (Communication Systems 2013-2014)

Hindustan University, Chennai

1. Single Frequency Solutions:

Single frequency users cannot take advantage of the full

capacity of all GPS signals to eliminate ionoshperic effects.

To support single frequency users broadcast message contain

ionosphere model data which allows the computation of

approximate ionosphere group delay.

The code and carrier phase can be given as:

Differencing both Eq 9.32 & 9.33 at epoch time ‘t’ we get:

It is function of:

1. Group delay

2. Initial ambiguity

3. Receiver and satellite hardware delay

4. The multhipath

If some delays are eliminated or ignored, then also it is

difficult to model.

1.1 Ionospheric plate model:

Ionosphere is approximated at a particular receiver

location by a flat plate of equal thickness having

homogenous distribution of free electrons.

It does not consider the curvature of earth.

Vertical group delay can b given by:

Now combining Eq 9.35 and 9.34, neglecting hardware

and multipath terms:

Vertical group delay and ambiguity can be eliminated from

code and phase observations.

1.2 Daily Cosine Model

Slightly advanced model.

Consider earth rotation and daily motion of sun W.R.T

receiver location.

Ik,I,,P(t)=Vertical group delay

1.3 Ionospheric Point Model:

Ionosphere begins at height of about 50km rather than at

earth’s surface.

Usually a mean ionospheric height of about 350km is

assumed.

Eq 9.35 can be replaced with:

Θ term is the elevation angle of satellite at ionosphere point.

The projection of ionospheric point on the earth is called

subionosheperic point.

Factor F

It is called slant factor or obliquity.

1.4 Generalization in Azimuth & Altitude:

It consider azimuth dependency of vertical group delay.

The variation in vertical angle is modeled by sine function.

It helps to measure the ionospheric delay more accurately.

1.5 Broadcast Message & Ionospheric Model:

The satellite message contains 8 coefficients.

It uses cosine model for daily variation of ionosphere(Similar

to expression 9.37).

The amplitude and period of the cosine term are functions of

geomagnetic latitude and represented by third degree

polynomials.

The coefficients of these polynomials are transmitted as part

of navigation message.

The algoritham is shown below:

F= Slant factor or obliquity

Ψ= Earth’s central angle between the user location and

ionospheric point.

ΨIP & λIP = geodetic latitude and longitude of ionospheric

point.

2. Dual Frequency Ionospheric-Free Solution

Ionospheric delays and advances are frequency dependent.

It is possible to eliminate ionospheric effects using dual

frequency receivers.

Difficulty arises from a modulation offset between L1 and L2

satellite & possibly at receiver.

The offset is determined by control segment, which is measured

by satellite manufacturer during broadcast message.

We allow a code offset fro the receiver and assume a relation

similar to 9.43, Now Psuodorange equations become

For a navigation solution of at least 4 satellites,the receiver code

offsets & other error components common to the station, are

absorbed by rxr clock estimate.

Objective is to find a function of codes that does not depend on

ionosphere.

The ionosphere free function serves this purpose:

Eq 9.46 is not a function of ionospheric term.

The dual frequency phase expression in units of cycles given

as:

The ionospheric free carrier phase function is:

The multiplier for L1 carrier phase is given in Eq 9.47 and new

multiplier L2 carrier phase is:

3.Dual Frequency Ionospheric Solutions:

Because of code phase delays and multipath ,the

determination of absolute ionosphere is not straight forward.

The code difference of 9.44 and 9.45 given as:

This function shows difficulties encountered when measuring

the ionosphere or TEC with dual frequency receivers.

The ionospheric function for carrier phases follows readily 9.49

and 9.50 as

This function reflects the time variation of TEC.

From single freq. solution 9.34, it is clear that the code and

phase offsets cancel as long as the relations 9.43 and 9.53 are

valid.

The complete form is:

Similar equation can be written for L2 carrier also.

The initial ambiguity and code phase offsets cancel completely

when differenced over time,as long as effects are const.

The Eq 9.57 is called range difference equation.

Thank You!!!!!!