From 4ffcd04ab405efbb45b38bb6538328f30bbb8806 Mon Sep 17 00:00:00 2001
From: "Ciccarelli, Edoardo (PG/R - Comp Sci & Elec Eng)"
 <e.ciccarelli@surrey.ac.uk>
Date: Mon, 3 Apr 2023 11:24:39 +0100
Subject: [PATCH] Messo anche a posto UKF for featurenavigation

---
 Analisys_With_Features.m          |  12 +-
 CovarianceAnalysisParameters.m    |   2 +-
 Measurement_read.m                |   2 +
 Observables_model_with_Features.m |   1 +
 Observations_Generation.m         |   4 +-
 Results.m                         |   2 +-
 SigmaPoints_Dynamics_Good.m       | 172 +++++++++++++++++++++
 UKF_Tool.m                        |  19 +--
 UKF_features.m                    | 245 ++++++++++++++++++++++++++++++
 YObs.mat                          | Bin 84280 -> 59608 bytes
 features_list.m                   |   8 +-
 11 files changed, 449 insertions(+), 18 deletions(-)
 create mode 100644 SigmaPoints_Dynamics_Good.m
 create mode 100644 UKF_features.m

diff --git a/Analisys_With_Features.m b/Analisys_With_Features.m
index b62aae3..88570fd 100644
--- a/Analisys_With_Features.m
+++ b/Analisys_With_Features.m
@@ -21,7 +21,7 @@ clc
     MMX_InitializeSPICE
     cspice_furnsh(which('mar097.bsp'));
     cspice_furnsh(which('MARPHOFRZ.txt'));
-    cspice_furnsh(which('MMX_QSO_049_2x2_826891269_828619269.bsp'));
+    cspice_furnsh(which('MMX_QSO_094_2x2_826891269_828619269.bsp'));
     cspice_furnsh(which('Phobos_826891269_828619269.bsp'));
 
 
@@ -44,7 +44,7 @@ clc
 
 %   Covariance analysis parameters
     [par, units] = CovarianceAnalysisParameters(par, units);
-    par.sigma    = 1e-10/(units.vsf*units.tsf);
+    par.sigma    = 0/(units.vsf*units.tsf);
     par.sigmaPh  = 0/(units.vsf*units.tsf);
 
 %   Initial Phobos's state vector
@@ -68,10 +68,18 @@ clc
     par.beta  = 2;
     file_features = 'Principal_Phobos_Ogni10.mat';
 
+%     YObs(1).Range = [];
+%     YObs(1).Rate = [];
+%     YObs(1).Lidar = [];
+    
     [Est] = UKF_Tool(Est0,@Dynamics_MPHandMMX_Inertia,...
         @Cov_Dynamics_Good, @Observables_model_with_Features,...
         par.R,YObs,par,units,file_features);
 
+%     [Est] = UKF_features(Est0, @SigmaPoints_Dynamics_Good,...
+%         @Observables_model_with_Features,...
+%         par.R,YObs,par,units,file_features);
+
 
     Results(Est, YObs, par, units)
 
diff --git a/CovarianceAnalysisParameters.m b/CovarianceAnalysisParameters.m
index 0e1d8df..a581985 100644
--- a/CovarianceAnalysisParameters.m
+++ b/CovarianceAnalysisParameters.m
@@ -75,7 +75,7 @@ pars.R(9,9) = pars.ObsNoise.camera^2;
 % Seconds between observation
 pars.interval_Range         = 3600;     % s
 pars.interval_Range_rate    = 600;      % s
-pars.interval_lidar         = 100;      % s
+pars.interval_lidar         = 600;      % s
 pars.interval_camera        = 3600;     % s
 
 
diff --git a/Measurement_read.m b/Measurement_read.m
index 89729c3..ce8ff43 100644
--- a/Measurement_read.m
+++ b/Measurement_read.m
@@ -49,6 +49,8 @@ function [Yobs, R, Stat_ID_Range, Stat_ID_Rate, check_Lidar, Features_ID] = Meas
             R       = [R; ones(count,1)*O(2,2)];
         end
 
+        check_Lidar = [];
+        
         if ~isempty(Measures.Lidar)
             check_Lidar = 1;
             Lidar   = Measures.Lidar;
diff --git a/Observables_model_with_Features.m b/Observables_model_with_Features.m
index 0443873..723c8b8 100644
--- a/Observables_model_with_Features.m
+++ b/Observables_model_with_Features.m
@@ -172,6 +172,7 @@ function [G, Rm] = Observables_model_with_Features(et, X, St_ID_Range, St_ID_Rat
        v_Phobos = pars.perifocal2MARSIAU*R2Rot'*([X(8); 0; 0] + ...
            cross([0; 0; X(10)],[X(7)*cos(X(9)); X(7)*sin(X(9)); 0]));
        Phobos   = [r_Phobos.*units.lsf; v_Phobos.*units.vsf];
+       Xsi      = X(13);
        
        [~, Y_pix] = visible_features(X_MMX.*units.sfVec, Phobos, Sun, Xsi, file_features, pars, units);
     else
diff --git a/Observations_Generation.m b/Observations_Generation.m
index eb51eb6..51daed2 100644
--- a/Observations_Generation.m
+++ b/Observations_Generation.m
@@ -20,7 +20,7 @@ clc
     MMX_InitializeSPICE
     cspice_furnsh(which('mar097.bsp'));
     cspice_furnsh(which('MARPHOFRZ.txt'));
-    cspice_furnsh(which('MMX_QSO_049_2x2_826891269_828619269.bsp'));
+    cspice_furnsh(which('MMX_QSO_094_2x2_826891269_828619269.bsp'));
     cspice_furnsh(which('Phobos_826891269_828619269.bsp'));
     
 %%  Initial conditions per la analisi
@@ -28,7 +28,7 @@ clc
 %   Time of the analysis
     data        = '2026-03-16 00:00:00 (UTC)';
     data        = cspice_str2et(data);
-    Ndays       = 4;
+    Ndays       = 7;
     t           = Ndays*86400;
     date_end    = data+t;
 
diff --git a/Results.m b/Results.m
index 7c2fb7e..b40147c 100644
--- a/Results.m
+++ b/Results.m
@@ -36,7 +36,7 @@ function Results(Est, YObs_Full, pars, units)
     set(0,'DefaultTextInterpreter','latex');
     set(0,'DefaultAxesFontSize', 16);
 
-    t_obs   = (0:100:YObs_Full(end).t);
+    t_obs   = Est.t;
 
 %   Plot of the post-fit residuals
     
diff --git a/SigmaPoints_Dynamics_Good.m b/SigmaPoints_Dynamics_Good.m
new file mode 100644
index 0000000..19bdd64
--- /dev/null
+++ b/SigmaPoints_Dynamics_Good.m
@@ -0,0 +1,172 @@
+function dx = SigmaPoints_Dynamics_Good(~,x,par,~)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% dx = Cov_Dynamics_Good(t,x,pars,units)
+%
+% Calculate the acceleration vector in the N-Body Problem with Mars and
+% Phobos only and the derivative of the coefficients to be estimated
+%
+% Input:
+% .t        Elapsed time since epoch (-)
+% .x        State Vector 
+% .pars     Problem Parameters
+%           .d          Dimension of the Problem
+%           .et0        Initial epoch (-)
+%           .refcenter  Origin of Frame (e.g., '399')
+%           .refframe   Coordinate Frame (e.g., 'ECLIPJ2000' or 'J2000')
+%           .Ntb        No. of third bodies
+%           .BodiesID   Bodies' SPICE ID (e.g., '10','399', ...)
+%           .GM         Bodies' Gravitational Parameters (-)
+%           .Nsh        No. of Spherical Harmonic Bodies
+%           .SH_BodiesID Spherical Harmonic Bodies' SPICE ID (e.g., '10','399', ...)
+%           .SH         Spherical Harmonic Structure
+%           .lsf        Length scale factor (km)
+%           .tsf        Time scale factor (s)
+%           .STM        true or false depending if you calculate STM or not
+%           .nCoeff     Number if coefficients in the state vector
+%
+% Output:
+% .dx       Vector containing accelerations and STM (d x 2 + nCoeff, -)
+%
+% Author: E.Ciccarelli
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+    
+%%  Useful quantities
+
+    
+%%  Dimensions
+
+    d           = par.d;                    % Dimension of the problem
+    nCoeff      = par.nCoeff;               % N. of gravitational parameters
+    nBias       = par.nBias;
+
+    size_St     = (d+8+nCoeff+nBias);
+    
+
+%%  Useful quantities
+
+    for i = 0:2*size_St
+
+%       Spacecraft state vector
+        r = x(1+i*size_St:3+i*size_St);     % Pos. vector wrt central body
+        v = x(4+i*size_St:6+i*size_St);     % Vel. vector wrt central body
+        R = norm(r);                        % Norm of pos. vector wrt central body
+    
+%       Phobos states
+        RPh         = x(7+i*size_St);
+        RPh_dot     = x(8+i*size_St);
+        theta       = x(9+i*size_St);
+        theta_dot   = x(10+i*size_St);
+        Phi         = x(11+i*size_St);
+        Phi_dot     = x(12+i*size_St);
+        Xsi         = x(13+i*size_St);
+        Xsi_dot     = x(14+i*size_St);
+    
+%       Phobos moment of inertia
+        IPhx_bar    = x(15+i*size_St);
+        IPhy_bar    = x(16+i*size_St);
+        IPhz_bar    = x(17+i*size_St);
+
+%       Position of MMX wrt Phobos
+        rPh = par.perifocal2MARSIAU*[RPh*cos(theta); RPh*sin(theta); 0];
+        rsb = r - rPh;
+    
+%       Rotation matrix from orbit's to Phobos fixed coordinates frame    
+        I       = rPh/RPh;
+        k       = par.MARSIAU2perifocal'*[0; 0; 1];
+        j       = cross(k,I);
+        NO      = [I,j,k];
+        ON      = NO';
+    
+%       Rotation matrix from orbit's to Phobos fixed coordinates frame
+        OB      = [cos(Xsi), sin(Xsi), 0; -sin(Xsi), cos(Xsi), 0; 0, 0, 1];
+        BO      = OB';
+    
+  %%  Phobos's orbit
+    
+    %   Potential's first order partials
+        dVdRPh      = par.ni/RPh^2*(1 + 3/(2*RPh^2)*((par.IMz_bar - par.Is) +...
+                -.5*IPhx_bar - .5*IPhy_bar + IPhz_bar + 1.5*(IPhy_bar - IPhx_bar)*cos(2*Xsi)));
+        dVdXsi      = 1.5*par.ni/RPh^3 * (IPhy_bar - IPhx_bar)*sin(2*Xsi);
+    
+    %   Phobos equations of motions
+        RPh_ddot    = theta_dot^2*RPh - dVdRPh/par.ni;
+        theta_ddot  = dVdXsi/(par.ni*RPh^2) - 2*RPh_dot*theta_dot/RPh;
+        Phi_ddot    = - dVdXsi/(par.ni*RPh^2) + 2*RPh_dot*theta_dot/RPh;
+        Xsi_ddot    = -(1 + par.ni*RPh^2/IPhz_bar)*dVdXsi/(par.ni*RPh^2) +...
+                    + 2*RPh_dot*theta_dot/RPh; 
+          
+%%      MMX 2BP with Mars + 3rd body Phobos 
+    
+%       The gravitational effect of Mars on MMX is 2BP+J2
+    
+        gM      = - par.G*par.MMars*r/R^3;
+        gJ2M    = - 1.5*par.G*par.MMars*par.J2*par.RMmean/R^5*...
+            [(1-5*(r(3)/R)^2)*r(1); (1-5*(r(3)/R)^2)*r(2);...
+            (3-5*(r(3)/R)^2)*r(3)];
+    
+        gM      = gM + gJ2M;
+    
+%       The gravitational effect of Phobos on MMX includes the Ellipsoid
+%       harmonics
+
+        C_22_Ph     = .25*(IPhy_bar - IPhx_bar);
+        C_20_Ph     = -.5*(2*IPhz_bar - IPhx_bar - IPhy_bar);
+        par.SH.Clm  = [1, 0, 0; 0, 0, 0; C_20_Ph, 0, C_22_Ph]./par.SH.Norm(1:3,1:3);
+    
+        [gb,~,~,~] = SHGM_Full(BO*ON*rsb,par.SH);
+        gPh = NO*OB*gb;
+    
+%       Trascinamento
+%       Tutto adimensionale
+        
+        G   = par.G;
+        M2  = par.MPho;
+        M1  = par.MMars; 
+    
+        I1x = par.IMx_bar*M1;
+        I1y = par.IMy_bar*M1;
+        I1z = par.IMz_bar*M1;
+        
+
+%       Need those quantities 
+        
+        A1          = [cos(theta+Phi), sin(theta+Phi), 0; -sin(theta+Phi), cos(theta+Phi), 0; 0, 0, 1];
+        dA1dtheta   = [-sin(theta+Phi), cos(theta+Phi), 0; -cos(theta+Phi), -sin(theta+Phi), 0; 0, 0, 0];
+        A2          = [cos(theta+Xsi), sin(theta+Xsi), 0; -sin(theta+Xsi), cos(theta+Xsi), 0; 0, 0, 1];
+        dA2dtheta   = [-sin(theta+Xsi), cos(theta+Xsi), 0; -cos(theta+Xsi), -sin(theta+Xsi), 0; 0, 0, 0];
+    
+        I1  = diag([I1x, I1y, I1z]);
+        I2  = diag([IPhx_bar, IPhy_bar, IPhz_bar]);
+    
+%       Chain rule terms
+        dRPhdx      = rPh(1)/norm(rPh(1:3)); 
+        dRPhdy      = rPh(2)/norm(rPh(1:3));
+        dRPhdz      = rPh(3)/norm(rPh(1:3));
+        dthetadx    = -rPh(2)/(rPh(1)^2 + rPh(2)^2);
+        dthetady    = rPh(1)/(rPh(1)^2 + rPh(2)^2);
+        dthetadz    = 0;
+        dbetadx     = -rPh(3)*rPh(1)/(sqrt(rPh(1)^2+rPh(2)^2)*sum(rPh(1:3).^2));
+        dbetady     = -rPh(3)*rPh(2)/(sqrt(rPh(1)^2+rPh(2)^2)*sum(rPh(1:3).^2));
+        dbetadz     = sqrt(rPh(1)^2+rPh(2)^2)/sum(rPh(1:3).^2);
+    
+        dVdtheta    = 3*G/(2*norm(rPh(1:3))^5)*rPh(1:3)'*(M2*(dA1dtheta'*I1*A1 + A1'*I1*dA1dtheta) + M1*(dA2dtheta'*I2*A2 + A2'*I2*dA2dtheta))*rPh(1:3);
+    
+%   Gravitational acceleration in x,y,z
+        g_M_on_PH   =  -[dRPhdx, dthetadx, dbetadx; dRPhdy, dthetady, dbetady; dRPhdz, dthetadz, dbetadz]*[dVdRPh; dVdtheta; 0];
+        g_Ph_on_M   = g_M_on_PH*(-(M2+M1)/(M2*M1))/M1;
+    
+%   Combined effect on MMX
+        g_tot   = gM + gPh - g_Ph_on_M;
+
+
+%%      Output for the integrator
+    
+        dx(1+i*size_St:size_St+i*size_St,1) = [v; g_tot; RPh_dot;...
+            RPh_ddot; theta_dot; theta_ddot; Phi_dot; Phi_ddot; Xsi_dot; Xsi_ddot;...
+            zeros(nCoeff,1); zeros(nBias,1)];
+    
+    end
+
+end
\ No newline at end of file
diff --git a/UKF_Tool.m b/UKF_Tool.m
index 2decf54..251a394 100644
--- a/UKF_Tool.m
+++ b/UKF_Tool.m
@@ -63,6 +63,7 @@ function [Est] = UKF_Tool(Est0, f, fsigma, G, O, Measures, pars, units, file_fea
 
 %   err is the vector of residuals, the others are needed to build the 
 %   fitting residuals.
+    tobs    = NaN(1,m);
     err     = NaN(size(O,1),m);
     prefit  = NaN(size(O,1),m);
     y_t     = NaN(size(O,1),m);
@@ -125,8 +126,7 @@ function [Est] = UKF_Tool(Est0, f, fsigma, G, O, Measures, pars, units, file_fea
                     Xmean_bar   = [X(idx,:)'; 0; 0; 0];
             end
         elseif Measures(i).t > told
-            tobs = Measures(i).t;
-            idx     = find(round(t/units.tsf)==tobs);
+            idx     = find(round(t/units.tsf)==Measures(i).t);
             switch n
                 case 14
                     Xmean_bar   = X(idx,1:size(Est0.X,1))';
@@ -149,19 +149,20 @@ function [Est] = UKF_Tool(Est0, f, fsigma, G, O, Measures, pars, units, file_fea
             (repmat(Xold,1,n)+gamma.*S0)];
 
 %       Need to know how many observations are available
-        [Y_obs, R, Stat_ID_Range, Stat_ID_Rate, check_Lidar, Features_ID] = Measurement_read(Measures(i),O,units);
+        [Y_obs, R, Stat_ID_Range, Stat_ID_Rate, check_Lidar, Features_ID] =...
+            Measurement_read(Measures(i),O,units);
         
 
-        if Measures(idx).t == told
+        if Measures(i).t == told
 
 %           The sigma point dont need to be proppagated
             Xbar    = X0;
 
-        elseif Measures(idx).t > told
+        elseif Measures(i).t > told
 
 %           Propagation of the sigma points' trajectories
             St0     = reshape(X0,[n*(2*n),1]);
-            tspan   = (told:Measures(idx).t)*units.tsf;
+            tspan   = (told:Measures(i).t)*units.tsf;
             opt     = odeset('RelTol',1e-13,'AbsTol',1e-16,'event',@(t,X) landing_Phobos_UKF(t,X,pars,units));
             [~,X_sigma] = ode113(@(t,X) fsigma(t,X,pars,units),tspan,St0,opt);
             Xbar    = reshape(X_sigma(end,1:n*(2*n))',[n,(2*n)]);
@@ -171,7 +172,7 @@ function [Est] = UKF_Tool(Est0, f, fsigma, G, O, Measures, pars, units, file_fea
         fprintf('\nProcesso osservazione n. : %d', i);
 
 %       Process noise if needed
-        deltaT  = (Measures(idx).t-told)*units.tsf;
+        deltaT  = (Measures(i).t-told)*units.tsf;
         Q       = pars.sigma^2*eye(3);
         switch n
             case 14
@@ -262,7 +263,7 @@ function [Est] = UKF_Tool(Est0, f, fsigma, G, O, Measures, pars, units, file_fea
         
 %       Next iteration preparation
         Xold   = Xmean_bar;
-        told   = Measures(idx).t;
+        told   = Measures(i).t;
         Pold   = P;
     
 
@@ -276,7 +277,7 @@ function [Est] = UKF_Tool(Est0, f, fsigma, G, O, Measures, pars, units, file_fea
         Pbar_t(:,:,i)  = P_bar.*units.CovDim;
         X_t(:,i)    = Xold.*units.Dim;
         x_t(:,i)    = K*y.*units.Dim;
-        
+        tobs(i)     = Measures(i).t;
         
     end
     
diff --git a/UKF_features.m b/UKF_features.m
new file mode 100644
index 0000000..beb8c35
--- /dev/null
+++ b/UKF_features.m
@@ -0,0 +1,245 @@
+function [Est] = UKF_features(Est0, f, G, O, Measures, pars, units, file_features)
+%==========================================================================
+% [Est] = UKF(Est0,f,G_dG,R,Measures,par)
+%
+% Unscented Kalman Filter
+%
+% INPUT: Description Units
+%
+% Est0      - Apriori initial guess of
+%               .X,     States 
+%               .P0,    Covariance matrix
+%               .t0,    initial time  
+% 
+% @f        - Dynamical model
+% 
+% @G        - Observation's model and partial derivatives wrt the states
+% 
+% O         - Weight matrix
+% Nsigma    - Number of sigma points
+% Measures  - Observations matrix: the first column contains observation
+%               times, then every column has a different type of observaion
+%               type
+% par       - Structure containing parameters required by @f and @G_dG 
+% units     - Structure containing lenght and time units 
+%
+% OUTPUT:
+%
+% Est       - Estimation of:
+%               .X, States at final t
+%               .P, Covariance matrix at final t
+%               .t, Time observation vector
+%               .X_t, States at different t
+%               .P_t, Covariance matrix at different t  
+%               .Pbar_t, Covariance matrix time update at different t
+% 
+%
+% Coupling:
+% None
+%
+% Author: Edoardo Ciccarelli
+% Date: 04/2021
+%
+%==========================================================================
+
+
+%   Apriori initial guess, deviation and covariance matrix.
+    Xold    = Est0.X;
+    Pold    = Est0.P0;
+    
+%   Column of the measures time.
+    told    = Measures(1).t;
+
+%   The measures must be organized in colums depending on the type of
+%   measure; each row is reffered to a given measure's time.
+    obs         = Measures;
+   
+    
+%   n,l and m are respectively the number of states, number of different
+%   types of measures and number of measures per each type.
+    n       = size(Xold,1);
+    m       = size(obs,1);
+    q       = 3;
+
+%   err is the vector of residuals, the others are needed to build the 
+%   fitting residuals.
+    tobs    = NaN(1,m);
+    err     = NaN(size(O,1),m);
+    prefit  = NaN(size(O,1),m);
+    y_t     = NaN(size(O,1),m);
+    X_t     = zeros(n,size(Measures,1));
+    x_t     = zeros(n,size(Measures,1));
+    P_t     = zeros(n,n,m);
+    Pbar_t  = zeros(n,n,m);
+    
+%   Initialization of the filter
+    k       = 3 - n;
+    alpha   = pars.alpha;
+    beta    = pars.beta;
+    lambda  = alpha^2*(n+k) - n;
+    gamma   = sqrt(n+lambda);
+
+%   Sigma points' weights
+    W0c     = zeros(2*n+1, 1);
+    W0c(1)  = lambda/(lambda+n)+(1-alpha^2+beta);
+    W0c(2:2*n+1)   = 1./(2*(n+lambda));
+
+    W0m     = zeros(2*n+1, 1);
+    W0m(1)  = lambda/(lambda+n);
+    W0m(2:2*n+1)   = W0c(2:2*n+1);
+       
+%   For-loop on the observations
+    for i = 1:m
+        
+%       Useful quantities's initialization
+        et  = Est0.t0/units.tsf + Measures(i).t;
+        
+%       TIME UPDATE
+%       Sigma points' definition
+        S0 = real(sqrtm(Pold)); 
+        X0 = [Xold, (repmat(Xold,1,n)-gamma.*S0),...
+            (repmat(Xold,1,n)+gamma.*S0)];
+
+%       Need to know how many observations are available
+        [Y_obs, R, Stat_ID_Range, Stat_ID_Rate, check_Lidar, Features_ID] = Measurement_read(Measures(i),O,units);
+        
+
+        if Measures(i).t == told
+
+%           The sigma point dont need to be proppagated
+            Xbar    = X0;
+
+        elseif Measures(i).t > told
+
+%           Propagation of the sigma points' trajectories
+            St0     = reshape(X0,[n*(2*n+1),1]);
+            tspan   = (told:Measures(i).t)*units.tsf;
+            opt     = odeset('RelTol',1e-13,'AbsTol',1e-16,'event',@(t,X) landing_Phobos(t,X,pars,units));
+            [~,X_sigma] = ode113(@(t,X) f(t,X,pars,units),tspan,St0,opt);
+            Xbar = reshape(X_sigma(end,1:n*(2*n+1))',[n,(2*n+1)]);
+
+        end
+
+        fprintf('\nProcesso osservazione n. : %d', i);
+
+%       Apriori quantities
+        Xmean_bar   = sum(W0m'.*Xbar,2);
+        deltaT  = (Measures(i).t-told)*units.tsf;
+        Q       = pars.sigma^2*eye(3);
+        switch n
+            case 6
+                Gamma   = [eye(q)*deltaT^2/2; eye(q)*deltaT];
+                Q = Gamma*Q*Gamma';
+            case 14
+                Gamma   = [eye(q)*deltaT^2/2; eye(q)*deltaT; zeros(n-6,q)];
+                Q = Gamma*Q*Gamma' + [zeros(6,n); zeros(n-6,6), pars.sigmaPh^2*...
+                    diag([deltaT^2/2, deltaT, deltaT^2/2, deltaT, deltaT^2/2, deltaT, deltaT^2/2, deltaT])];
+            case 20
+                Gamma   = [eye(q)*deltaT^2/2; eye(q)*deltaT; zeros(n-6,q)];
+                Q = Gamma*Q*Gamma' + [zeros(6,n); zeros(n-6,6), pars.sigmaPh^2*...
+                    diag([deltaT^2/2, deltaT, deltaT^2/2, deltaT, deltaT^2/2, deltaT, deltaT^2/2, deltaT, zeros(1,n-14)])];  
+        end
+
+        P_bar   = Q;
+
+
+        for j = 1:2*n+1
+            P_bar   = P_bar + W0c(j)*((Xbar(:,j) - Xmean_bar) * (Xbar(:,j) - Xmean_bar)');
+        end
+
+%       Sigma point redefinition
+        S_bar   = real(sqrtm(P_bar));
+        X0  = [Xmean_bar, (repmat(Xmean_bar,1,n)-gamma.*S_bar),...
+            (repmat(Xmean_bar,1,n)+gamma.*S_bar)];
+        
+        Y   = zeros(size(Y_obs.meas,1),2*n);
+        Y_feat = cell(2*n);
+
+        for j = 1:2*n+1
+%           G(j-th sigma point)
+            [Y_sigma, ~] = G(et, X0(:,j), Stat_ID_Range, Stat_ID_Rate,...
+                check_Lidar, Features_ID, pars, units, O, file_features);
+            Y(:,j)  = Y_sigma.meas;
+            Y_feat{j} = Y_sigma.cam;
+            
+            if ~isempty(Y_feat{j})
+                Features_ID = intersect(Features_ID, Y_feat{j}(3,:));
+            end
+
+        end
+
+        Y_sigma = [];
+
+        if ~isempty(Y_feat{1})
+            for j = 1:2*n+1
+                features = features_list(Y_feat{j}, Features_ID);
+                Y_sigma  = [Y_sigma, [Y(:,j); features]];
+            end
+        else
+            Y_sigma  = Y;
+        end
+
+%       Mean predicted measurement
+        [Y_mean,R]  = G(et, Xmean_bar, Stat_ID_Range, Stat_ID_Rate,...
+            check_Lidar, Features_ID, pars, units, O, file_features);
+        
+        features= features_list(Y_mean.cam, Features_ID);
+        Y_mean  = [Y_mean.meas; features];
+
+        features= features_list(Y_obs.cam, Features_ID);
+        Y_obs   = [Y_obs.meas; features];
+
+%       Innovation covariance and cross covariance
+
+        R       = [R; O(4,4)*ones(size(features,1),1)];
+        Py      = diag(R);
+        Pxy     = zeros(n,size(Y_obs,1));
+
+        for j = 1:2*n+1
+            Py  = Py + W0c(j)*(Y_sigma(:,j) - Y_mean)*(Y_sigma(:,j) - Y_mean)';
+            Pxy = Pxy + W0c(j)*(X0(:,j) - Xmean_bar)*(Y_sigma(:,j) - Y_mean)';
+        end
+        
+%       Kalman gain
+        K   = Pxy/Py;
+
+%       MEASUREMENT UPDATE
+        y           = (Y_obs - Y_mean);
+        Xstar       = Xmean_bar + K*y;
+        P           = P_bar - K*Py*K';
+        
+%       Next iteration preparation
+        Xold        = Xstar;
+        told        = Measures(i).t;
+        Pold        = P;
+    
+       
+%         err(IDX,i)    = (Y_obs - G(et,obs(:,i),Xold,par,units)').*units.Observations(IDX);
+%         prefit(IDX,i) = (Y_obs - G(et,obs(:,i),Xmean_bar,par,units)').*units.Observations(IDX);
+%         y_t(IDX,i)    = y.*units.Observations(IDX);
+
+
+%       Storing the results
+        P_t(:,:,i)  = abs(P).*units.CovDim;
+        Pbar_t(:,:,i)  = P_bar.*units.CovDim;
+        X_t(:,i)    = Xold.*units.Dim;
+        tobs(i)     = Measures(i).t;
+        
+    end
+    
+    fprintf('\nAnalysis complete!\n');
+    
+%   Initial states' estimation, deviation and covariance matrix
+    Est.X       = Xold.*units.Dim;
+    Est.P       = P.*units.CovDim;
+    
+%   Residuals and fit-residuals at different observation times
+    Est.t       = tobs;
+    Est.err     = err;
+    Est.pre     = prefit;
+    Est.y_t     = y_t;
+    Est.X_t     = X_t;
+    Est.P_t     = P_t;
+    Est.Pbar_t  = Pbar_t;
+    
+end
\ No newline at end of file
diff --git a/YObs.mat b/YObs.mat
index b26142e8117fa866eed8dc4cdec26702598bb5d7..d47550885dbe87352704d6294e25591d06d0613a 100644
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diff --git a/features_list.m b/features_list.m
index 58abdef..935659a 100644
--- a/features_list.m
+++ b/features_list.m
@@ -2,9 +2,11 @@ function features = features_list(Y_feat, Features_ID)
 
     features = [];
     for k=1:size(Features_ID,2)
-        common_feat = Y_feat(1:2, Y_feat(3,:)==Features_ID(k));
-        if ~isempty(common_feat)
-            features = [features; common_feat];
+        if ~isempty(Y_feat)
+            common_feat = Y_feat(1:2, Y_feat(3,:)==Features_ID(k));
+            if ~isempty(common_feat)
+                features = [features; common_feat];
+            end
         end
     end
 
-- 
GitLab