fdnt.m

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%                             fdnt.m
%  Scope:   This MATLAB macro determines a fault detection normalized threshold
%           used in the Receiver Autonomous Integrity Monitoring (RAIM) 
%           computation, for specified false alarm and degree of freedom.
%  Usage:   xoutput = fdnt(fa_tol)
%  Description of parameters:
%           dof     - input, degrees-of-freedom for chi-square distribution, 
%                     in this case is the number of satellites available - 4,
%                     global variable
%           fa_tol  - input, false alarm tolerance
%           xoutput - output, fault detection normalized threshold 
%  References: 
%           [1] Brown, A. K., Sturza, M. A., The effect of geometry on 
%               integrity monitoring performance. The Institute of Navigation
%               46th Annual Meeting, June 1990, pp. 121-129. 	
%           [2] Brown, R. G., A baseline RAIM scheme and a note on the
%               equivalence of three RAIM methods. Proceedings of the National
%               Technical Meeting, Institute of Navigation, San Diego, CA,
%               Jan. 27-29, 1992, pp. 127-137.
%  External Matlab macros used:  chi2_dof, gauss_1
%  Remark:  When the degree of freedom is 1 a Gaussian distribution is used,
%           otherwise a chi-square distribution is assumed.
%  Last update:  01/05/00
%  Copyright (C) 1997-00 by LL Consulting. All Rights Reserved.

function  xoutput = fdnt(fa_tol)

global  dof

if ( (dof < 1) | (fa_tol < 0) | (fa_tol > 1) )
   error('Error 1 -  FDNT ; check the input data values');
end

fa_tol_c = 1.0 - fa_tol;

% Compute the integral of the probability density function

options = odeset('RelTol',1.e-13,'AbsTol',1.e-13);

if  dof == 1		        %   Gaussian distribution
   [x,y] = ode45('gauss_1',[0. 100.],0.,options);
   fa_tol_c = 0.5 * fa_tol_c;
elseif  dof == 2          %   direct computation
   xoutput = sqrt(-2.0*log(fa_tol));
   return
elseif  (dof > 2) 
   [x,y] = ode45('chi2_dof',[0. 100.],0.,options);
end

% Determine the index for the upper limit of the integration

for i = 1:size(y),
   if (y(i) > fa_tol_c)
       break
   end
end

if (i == length(y))
   error('Error 2 -  FDNT ; insufficient integration interval');
end

% Execute linear interpolation to determine the integral upper limit

xoutput = x(i-1) + (x(i) - x(i-1)) * (fa_tol_c - y(i-1)) / (y(i) - y(i-1));

if  dof == 1
   return
end
xoutput = sqrt(xoutput);