%This Function approximate Ionospheric Group Delay
%CopyRight By Moein Mehrtash
%************************************************************************
% Written by Moein Mehrtash, Concordia University, 3/21/2008 *
% Email: moeinmehrtash@yahoo.com *
%************************************************************************
% ***********************************************************************
% Function for computing an Ionospheric range correction for the *
% GPS L1 frequency from the parameters broadcasted in the GPS *
% Navigation Message. *
% ==================================================================
% References: *
% Klobuchar, J.A., (1996) "Ionosphercic Effects on GPS", in *
% Parkinson, Spilker (ed), "Global Positioning System Theory and *
% Applications, pp.513-514. *
% ICD-GPS-200, Rev. C, (1997), pp. 125-128 *
% NATO, (1991), "Technical Characteristics of the NAVSTAR GPS", *
% pp. A-6-31 - A-6-33 *
% ==================================================================
% Input : *
% Pos_Rcv : XYZ position of reciever (Meter) *
% Pos_SV : XYZ matrix position of GPS satellites (Meter) *
% GPS_Time : Time of Week (sec) *
% Alfa(4) : The coefficients of a cubic equation *
% representing the amplitude of the vertical *
% dalay (4 coefficients - 8 bits each) *
% Beta(4) : The coefficients of a cubic equation *
% representing the period of the model *
% (4 coefficients - 8 bits each) *
% Output: *
% Delta_I : Ionospheric slant range correction for *
% the L1 frequency (Sec) *
% ==================================================================
function [Delta_I]=Error_Ionospheric_Klobuchar(Pos_Rcv,Pos_SV,Alpha,Beta,GPS_Time)
GPS_Rcv = ECEF2GPS(Pos_Rcv);
Lat=GPS_Rcv(1)/pi;Lon=GPS_Rcv(2)/pi; % semicircles unit Lattitdue and Longitude
S=size(Pos_SV);
m=S(1);n=S(2);
for i=1:m
[El,A0]=Calc_Azimuth_Elevation(Pos_Rcv,Pos_SV(i,:));
E(i)=El/pi; %SemiCircle Elevation
A(i)=A0; %SemiCircle Azimoth
% Calculate the Earth-Centered angle, Psi
Psi(i)=0.0137/(E(i)+.11)-0.022; %SemiCircle
%Compute the Subionospheric lattitude, Phi_L
Phi_L(i)=Lat+Psi(i)*cos(A(i)); %SemiCircle
if Phi_L(i)>0.416
Phi_L(i)=0.416;
elseif Phi_L(i)<-0.416
Phi_L(i)=-0.416;
end
%Compute the subionospheric longitude, Lambda_L
Lambda_L(i)=Lon+(Psi(i)*sin(A(i))/cos(Phi_L(i)*pi)); %SemiCircle
%Find the geomagnetic lattitude ,Phi_m, of the subionospheric location
%looking toward each GPS satellite:
Phi_m(i)=Phi_L(i)+0.064*cos((Lambda_L(i)-1.617)*pi);
%Find the Local Time ,t, at the subionospheric point
t(i)=4.23*10^4*Lambda_L(i)+GPS_Time; %GPS_Time(Sec)
if t(i)>86400
t(i)=t(i)-86400;
elseif t(i)<0
t(i)=t(i)+86400;
end
%Convert Slant time delay, Compute the Slant Factor,F
F(i)=1+16*(.53-E(i)^3);
%Compute the ionospheric time delay T_iono by first computing x
Per(i)=Beta(1)+Beta(2)*Phi_m(i)+Beta(3)*Phi_m(i)^2+Beta(4)*Phi_m(i)^3;
if Per(i) <72000 %Period
Per(i)=72000;
end
x(i)=2*pi*(t(i)-50400)/Per(i); %Rad
AMP(i)=Alpha(1)+Alpha(2)*Phi_m(i)+Alpha(3)*Phi_m(i)^2+Alpha(4)*Phi_m(i)^3;
if AMP(i)<0
AMP(i)=0
end
if abs(x(i))>1.57
T_iono(i)=F(i)*5*10^(-9);
else
T_iono(i)=F(i)*(5*10^(-9)+AMP(i)*(1-x(i)^2/2+x(i)^4/4));
end
end%for
Delta_I=T_iono;