function [rhoF,rhoS]=Dyneit(J,Uelmit,L,nump,Uellask,a1,a2,rho0,alpha,R,F);%Dyneit Estimates resistivity distributions by Kalman filter and Kalman smoother % Function [rhoF,rhoS]=Dyneit(J,Uelmit,L,nump,Uellask,a1,a2,rho0,alpha,R,F);% estimates resisitivity distributions by Kalman filter and smoother.%% INPUT%% J = Jacobian% Uelmit = measured voltages on the electrodes% L = the number of electrodes% nump = the number of parameters% Uellask = computed voltages on the electrodes at the linearisation point % a1 = state noise covariance coefficient% a2 = measurement noise covariance coefficient% rho0 = the first guess for the resistivity% alpha = regularization parameter% R = regularization matrix% F = state transition matrix%% OUTPUT%% rhoF = resistivity estimate computed by the Kalman filter% rhoS = resistivity estimate computed by the Kalman smoother % P.J. Vauhkonen 5.8.1999% Modified for EIDORS by M. Vauhkonen 17.11.1999% University of Kuopio, Department of Applied Physics, PO Box 1627,% FIN-70211 Kuopio, Finland, email: Marko.Vauhkonen@uku.fiCw=a1*sparse(eye(nump));Cv1=[a2*sparse(eye(L)),sparse(zeros(L,nump))];Cv2=[sparse(zeros(nump,L)),sparse(eye(nump))];Cv=[Cv1;Cv2]; rhoP=zeros(nump,L);rhoF=zeros(nump,L);A=zeros(nump,nump*(L-1));rhoP(:,1)=rho0;CP=sparse(eye(nump));%%%%%% Filterfor T=1:L z1=[Uelmit((T-1)*L+1:T*L)-Uellask((T-1)*L+1:T*L);zeros(nump,1)]; J2=J((T-1)*L+1:T*L,:); J1=[J2;alpha*R]; K=CP*J1'*inv(J1*CP*J1'+Cv); CF=(eye(nump,nump)-K*J1)*CP; rhoF(:,T)=rhoP(:,T)+K*(z1-J1*(rhoP(:,T)-rho0)); if T<L  CP=F*CF*F'+Cw;  rhoP(:,T+1)=F*rhoF(:,T);  A(:,(T-1)*nump+1:T*nump)=CF*F'*inv(CP); else endTend%%%%% SmootherrhoS=zeros(nump,L);rhoS(:,L)=rhoF(:,L);for t=L:-1:2rhoS(:,t-1)=rhoF(:,t-1)+A(:,(t-2)*nump+1:(t-1)*nump)*(rhoS(:,t)-rhoP(:,t));end