sugr_estimate_robust_scale_from_residuals

% robustly estimate sigma from residuals squared

 s = sugr_estimate_robust_scale_from_residuals(r,d)

 r = vector of absolute residuals
     assumtption: at least 10 % inliers chi^2_d distributed
 d = degrees of freedom of residuals
 s = robust sigma estimate

 see adaptive least Kth-order squares estimator by Lee et al. (1998)
 adapted to magnitude of multi-dimensional residuals 

 Wolfgang Förstner 2/2012
 wfoerstn@uni-bonn.de

0001 %% robustly estimate sigma from residuals squared
0002 %
0003 % s = sugr_estimate_robust_scale_from_residuals(r,d)
0004 %
0005 % r = vector of absolute residuals
0006 %     assumtption: at least 10 % inliers chi^2_d distributed
0007 % d = degrees of freedom of residuals
0008 % s = robust sigma estimate
0009 %
0010 % see adaptive least Kth-order squares estimator by Lee et al. (1998)
0011 % adapted to magnitude of multi-dimensional residuals
0012 %
0013 % Wolfgang Förstner 2/2012
0014 % wfoerstn@uni-bonn.de
0015 
0016 function s0 = sugr_estimate_robust_scale_from_residuals(r,d)
0017 
0018 N = length(r);                                % # data
0019 p = 0.1;                                      % minimum percentage of inliers
0020 
0021 s0 = kth_element(r,N,p*N)/icdf('chi2',p,d);   % initial estimate
0022 
0023 % b = 1.06*s0/N^(1/5);                          % bandwidth
0024 
0025