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; + 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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