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ADD: matlab vtl_kf with 9 states and carrier phase error
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miguekf
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7629551e6c
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3f199e85f3
239
src/utils/matlab/vtl/kf_prototype4acc.m
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239
src/utils/matlab/vtl/kf_prototype4acc.m
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%% vtl KF
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%%
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sat_number=5;
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%% ################## Kalman filter initialization ######################################
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st_nmbr=9;
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% covariances (static)
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kf_P_x = eye(st_nmbr); %TODO: use a real value.
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kf_x = zeros(st_nmbr, 1);
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kf_R = zeros(2*sat_number, 2*sat_number);
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kf_dt=0.1;
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% kf_F = eye(st_nmbr, st_nmbr);
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% kf_F(1, 4) = kf_dt;
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% kf_F(2, 5) = kf_dt;
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% kf_F(3, 6) = kf_dt;
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% kf_F(7, 8) = kf_dt;
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kf_F=[ 1 0 0 kf_dt 0 0 0 0 0
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0 1 0 0 kf_dt 0 0 0 0
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0 0 1 0 0 kf_dt 0 0 0
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0 0 0 1 0 0 0 0 0
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0 0 0 0 1 0 0 0 0
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0 0 0 0 0 1 0 0 0
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0 0 0 0 0 0 1 kf_dt kf_dt^2/2
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0 0 0 0 0 0 0 1 kf_dt
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0 0 0 0 0 0 0 0 1];
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% kf_F=[ 1 0 0 kf_dt 0 0 0 0
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% 0 1 0 0 kf_dt 0 0 0
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% 0 0 1 0 0 kf_dt 0 0
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% 0 0 0 1 0 0 0 0
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% 0 0 0 0 1 0 0 0
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% 0 0 0 0 0 1 0 0
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% 0 0 0 0 0 0 1 kf_dt
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% 0 0 0 0 0 0 0 1];
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%
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kf_H = zeros(2*sat_number,st_nmbr);
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kf_y = zeros(2*sat_number, 1);
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kf_yerr = zeros(2*sat_number, 1);
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% kf_xerr = zeros(8, 1);
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kf_S = zeros(2*sat_number, 2*sat_number); % kf_P_y innovation covariance matrix
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%% pre-allocate for speed
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d = zeros(sat_number, 1);
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rho_pri = zeros(sat_number, 1);
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rhoDot_pri = zeros(sat_number, 1);
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a_x = zeros(sat_number, 1);
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a_y = zeros(sat_number, 1);
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a_z = zeros(sat_number, 1);
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c_pr_m=zeros(sat_number,length(navSolution.RX_time));
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pr_m_filt=zeros(sat_number,length(navSolution.RX_time));
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rhoDot_pri_filt=zeros(sat_number,length(navSolution.RX_time));
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sat_dopp_hz_filt=zeros(sat_number,length(navSolution.RX_time));
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%% ################## Kalman Tracking ######################################
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% receiver solution from rtklib_solver
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for t=2:length(navSolution.RX_time)
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%% State error Covariance Matrix Q (PVT) and R (MEASUREMENTS)
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if (t<length(navSolution.RX_time)-point_of_closure)
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%% State error Covariance Matrix Q (PVT)
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kf_Q = eye(st_nmbr);%new_data.rx_pvt_var(i); %careful, values for V and T could not be adecuate.
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%%
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% Measurement error Covariance Matrix R assembling
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kf_R = blkdiag(eye(sat_number)*40,eye(sat_number)*10);
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else
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kf_Q = blkdiag(eye(3)*pos_var,eye(3)*vel_var,clk_bias_var,clk_drift_var,clk_d_drift_var);
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kf_R = blkdiag(eye(sat_number)*pr_var,eye(sat_number)*pr_dot_var);
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end
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clear x_u y_u z_u xDot_u yDot_u zDot_u cdeltatDot_u cdeltatDot_u_g cdeltat_u_g
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if (t<length(navSolution.RX_time)-point_of_closure)
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kf_x(1,t) = navSolution.X(t);
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kf_x(2,t) = navSolution.Y(t);
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kf_x(3,t) = navSolution.Z(t);
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kf_x(4,t) = navSolution.vX(t);
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kf_x(5,t) = navSolution.vY(t);
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kf_x(6,t) = navSolution.vZ(t);
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kf_x(7,t) = clk_bias_s(t)*SPEED_OF_LIGHT_M_S;
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kf_x(8,t) = clk_drift(t)*SPEED_OF_LIGHT_M_S;%new_data.rx_dts(1);
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kf_x(9,t) = 1.0;
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x_u=kf_x(1,t);
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y_u=kf_x(2,t);
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z_u=kf_x(3,t);
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xDot_u=kf_x(4,t);
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yDot_u=kf_x(5,t);
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zDot_u=kf_x(6,t);
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cdeltat_u(t)=kf_x(7,t);
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cdeltatDot_u=kf_x(8,t);
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% Kalman state prediction (time update)
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kf_P_x = eye(st_nmbr)*100; %TODO: use a real value.
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kf_xpri(:,t) = kf_F * (kf_x(:,t)-kf_x(:,t-1));% state prediction
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kf_P_x= kf_F * kf_P_x * kf_F' + kf_Q;% state error covariance prediction
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else
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x_u=corr_kf_state(1,t-1);
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y_u=corr_kf_state(2,t-1);
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z_u=corr_kf_state(3,t-1);
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xDot_u=corr_kf_state(4,t-1);
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yDot_u=corr_kf_state(5,t-1);
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zDot_u=corr_kf_state(6,t-1);
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cdeltat_u(t)=corr_kf_state(7,t-1);
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cdeltatDot_u=corr_kf_state(8,t-1);
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% Kalman state prediction (time update)
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kf_P_x= kf_F * kf_P_x * kf_F' + kf_Q;% state error covariance prediction
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end
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for chan=1:5 %neccesary quantities
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d(chan)=(sat_posX_m(chan,t)-x_u)^2;
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d(chan)=d(chan)+(sat_posY_m(chan,t)-y_u)^2;
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d(chan)=d(chan)+(sat_posZ_m(chan,t)-z_u)^2;
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d(chan)=sqrt(d(chan));
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c_pr_m(chan,t)=d(chan)+cdeltat_u(t);
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a_x(chan,t)=-(sat_posX_m(chan,t)-x_u)/d(chan);
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a_y(chan,t)=-(sat_posY_m(chan,t)-y_u)/d(chan);
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a_z(chan,t)=-(sat_posZ_m(chan,t)-z_u)/d(chan);
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rhoDot_pri(chan,t)=(sat_velX(chan,t)-xDot_u)*a_x(chan,t)...
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+(sat_velY(chan,t)-yDot_u)*a_y(chan,t)...
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+(sat_velZ(chan,t)-zDot_u)*a_z(chan,t);
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end
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for chan=1:5 % Measurement matrix H assembling
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% It has st_nmbr columns (st_nmbr states) and 2*NSat rows (NSat psudorange error;NSat pseudo range rate error)
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kf_H(chan, 1) = a_x(chan,t); kf_H(chan, 2) = a_y(chan,t); kf_H(chan, 3) = a_z(chan,t); kf_H(chan, 7) = 1.0;
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kf_H(chan+sat_number, 4) = a_x(chan,t); kf_H(chan+sat_number, 5) = a_y(chan,t); kf_H(chan+sat_number, 6) = a_z(chan,t); kf_H(chan+sat_number, 8) = 1.0;
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end
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% unobsv(t) = length(kf_F) - rank(obsv(kf_F,kf_H));
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% !!!! Limitaciones
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% obsv no se recomienda para el diseño de control, ya que calcular el rango de la matriz de observabilidad
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% no se recomienda para las pruebas de observabilidad. Ob será numéricamente singular para la mayoría de los
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% sistemas con más de unos cuantos estados. Este hecho está bien documentado en la sección III de [1].
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% Kalman estimation (measurement update)
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for chan=1:5 % Measurement matrix H assembling
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kf_yerr(chan,t)=c_pr_m(chan,t)-sat_prg_m(chan,t);
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if (t<length(navSolution.RX_time)-point_of_closure)
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kf_yerr(chan+sat_number,t)=(sat_dopp_hz(chan,t)*Lambda_GPS_L1)-rhoDot_pri(chan,t);
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else
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kf_yerr(chan+sat_number,t)=(sat_dopp_hz(chan,t)*Lambda_GPS_L1+cdeltatDot_u)-rhoDot_pri(chan,t);
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end
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end
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% DOUBLES DIFFERENCES
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% kf_yerr = zeros(2*sat_number, 1);
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% for (int32_t i = 1; i < sat_number; i++) % Measurement vector
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% {
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% kf_y(i)=new_data.pr_m(i)-new_data.pr_m(i-1);
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% kf_yerr(i)=kf_y(i)-(rho_pri(i)+rho_pri(i-1));
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% kf_y(i+sat_number)=(rhoDot_pri(i)-rhoDot_pri(i-1))/Lambda_GPS_L1;
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% kf_yerr(i+sat_number)=kf_y(i+sat_number)-(new_data.doppler_hz(i)-new_data.doppler_hz(i-1));
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% }
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% kf_yerr.print("DOUBLES DIFFERENCES");
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% Kalman filter update step
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kf_S = kf_H * kf_P_x* kf_H' + kf_R; % innovation covariance matrix (S)
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kf_K = (kf_P_x * kf_H') * inv(kf_S); % Kalman gain
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kf_xerr(:,t) = kf_K * (kf_yerr(:,t)); % Error state estimation
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kf_P_x = (eye(length(kf_P_x)) - kf_K * kf_H) * kf_P_x; % update state estimation error covariance matrix
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if (t<length(navSolution.RX_time)-point_of_closure)
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corr_kf_state(:,t)=kf_xpri(:,t)-kf_xerr(:,t)+kf_x(:,t); %updated state estimation
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else
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corr_kf_state(:,t)=corr_kf_state(:,t-1)-kf_xerr(:,t); %updated state estimation
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end
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%% ################## Geometric Transformation ######################################
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x_u=corr_kf_state(1,t);
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y_u=corr_kf_state(2,t);
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z_u=corr_kf_state(3,t);
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xDot_u=corr_kf_state(4,t);
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yDot_u=corr_kf_state(5,t);
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zDot_u=corr_kf_state(6,t);
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cdeltat_u_g=corr_kf_state(7,t);
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cdeltatDot_u_g=corr_kf_state(8,t);
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for chan=1:5 %neccesary quantities
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d(chan)=(sat_posX_m(chan,t)-x_u)^2;
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d(chan)=d(chan)+(sat_posY_m(chan,t)-y_u)^2;
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d(chan)=d(chan)+(sat_posZ_m(chan,t)-z_u)^2;
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d(chan)=sqrt(d(chan));
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c_pr_m(chan,t)=d(chan)+cdeltat_u_g;
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a_x(chan,t)=-(sat_posX_m(chan,t)-x_u)/d(chan);
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a_y(chan,t)=-(sat_posY_m(chan,t)-y_u)/d(chan);
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a_z(chan,t)=-(sat_posZ_m(chan,t)-z_u)/d(chan);
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rhoDot_pri(chan,t)=(sat_velX(chan,t)-xDot_u)*a_x(chan,t)...
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+(sat_velY(chan,t)-yDot_u)*a_y(chan,t)...
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+(sat_velZ(chan,t)-zDot_u)*a_z(chan,t);
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end
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kf_H = zeros(2*sat_number,st_nmbr);
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for chan=1:5 % Measurement matrix H assembling
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% It has st_nmbr columns (st_nmbr states) and 2*NSat rows (NSat psudorange error;NSat pseudo range rate error)
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kf_H(chan, 1) = a_x(chan,t); kf_H(chan, 2) = a_y(chan,t); kf_H(chan, 3) = a_z(chan,t); kf_H(chan, 7) = 1.0;
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kf_H(chan+sat_number, 4) = a_x(chan,t); kf_H(chan+sat_number, 5) = a_y(chan,t); kf_H(chan+sat_number, 6) = a_z(chan,t); kf_H(chan+sat_number, 8) = 1.0;
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end
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% Re-calculate error measurement vector with the most recent data available: kf_delta_y=kf_H*kf_delta_x
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kf_yerr_g=kf_H*kf_xerr;
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% Filtered pseudorange error measurement (in m) AND Filtered Doppler shift measurements (in Hz):
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for chan=1:5 % Measurement vector
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pr_m_filt(chan,t)=sat_prg_m(chan,t)+kf_yerr_g(chan,t);% now filtered
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rhoDot_pri_filt(chan,t)=(sat_dopp_hz(chan,t)*Lambda_GPS_L1+corr_kf_state(8,t))-kf_yerr_g(chan+sat_number,t);
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%convert rhoDot_pri to doppler shift!
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% d_dt_clk_drift=(corr_kf_state(8,t)-corr_kf_state(8,t-1));
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% d_dt_clk_drift=0;
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if (t<length(navSolution.RX_time)-point_of_closure)
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sat_dopp_hz_filt(chan,t)=(rhoDot_pri_filt(chan,t)-corr_kf_state(8,t))/Lambda_GPS_L1;
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else
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sat_dopp_hz_filt(chan,t)=(rhoDot_pri_filt(chan,t)-corr_kf_state(8,t))/Lambda_GPS_L1;
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end
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err_carrier_phase_rads_filt(chan,t) = trapz(kf_yerr_g(chan+sat_number,1:t)/Lambda_GPS_L1)*2*kf_dt;
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carrier_freq_hz =GPS_L1_freq_hz+sat_dopp_hz_filt(chan,t);
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% carrier_freq_rate_hz_s = 0;
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% code_phase_chips = 0;
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end
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% carrier_phase_rads = 0;
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% carrier_freq_hz = 0;
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% carrier_freq_rate_hz_s = 0;
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% code_phase_chips = 0;
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end
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