dhmax.m

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%                             dhmax.m
%  Scope:   This MATLAB macro determines delta_h_max used in the Receiver 
%           Autonomous Integrity Monitoring (RAIM) [1] computation. It is 
%           assumed that at least five line-of-sight unit vectors are 
%           specified as input.
%  Usage:   xoutput = dhmax(g)
%  Description of parameters :
%           g         - input, line-of-sight unit vectors, each vector is
%                       stored in another row (it should be 3 columns)
%           xoutput   - output, delta_h_max 
%  Reference: 
%          [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.
%  Remark:
%		The connection between ARP (Approximate Radial-error Protected) 
%		and delta_h_max is as follows [2]
%		    ARP = sqrt(n-4) * delta_h_max * threshold
%		where
%		    n  is the number of measurements used
%		    threshold is the pre-computed normalized detection threshold [2]
%  Last update:  07/31/00
%  Copyright (C) 1997-00 by LL Consulting. All Rights Reserved.

function  xoutput = dhmax(g)

[nrow,ncol] = size(g);
if (ncol ~= 3) | (nrow < 5)
   error('Error -  DHMAX; check the unit line of sight vectors');
end
unitvec = ones(nrow,1);

h = [g unitvec];          %  form the matrix  H
a = (inv(h'* h)) * h';    %  only the first two rows are needed
b = h * a;			        %  only the diagonal elements are needed

dhmax2 = 0.;
for k = 1:nrow
   temp = (a(1,k)*a(1,k) + a(2,k)*a(2,k)) / (1. - b(k,k));
   if  (temp > dhmax2)
	  dhmax2 = temp;
   end 
end

xoutput = sqrt(dhmax2);