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Tightly_coupled_INS_GNSS.m
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Tightly_coupled_INS_GNSS.m
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function [out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =...
Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors,...
IMU_errors,GNSS_config,TC_KF_config)
%Tightly_coupled_INS_GNSS - Simulates inertial navigation using ECEF
% navigation equations and kinematic model, GNSS and tightly coupled
% INS/GNSS integration.
%
% Software for use with "Principles of GNSS, Inertial, and Multisensor
% Integrated Navigation Systems," Second Edition.
%
% This function created 12/4/2012 by Paul Groves
%
% Inputs:
% in_profile True motion profile array
% no_epochs Number of epochs of profile data
% initialization_errors
% .delta_r_eb_n position error resolved along NED (m)
% .delta_v_eb_n velocity error resolved along NED (m/s)
% .delta_eul_nb_n attitude error as NED Euler angles (rad)
% IMU_errors
% .delta_r_eb_n position error resolved along NED (m)
% .b_a Accelerometer biases (m/s^2)
% .b_g Gyro biases (rad/s)
% .M_a Accelerometer scale factor and cross coupling errors
% .M_g Gyro scale factor and cross coupling errors
% .G_g Gyro g-dependent biases (rad-sec/m)
% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5)
% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5)
% .accel_quant_level Accelerometer quantization level (m/s^2)
% .gyro_quant_level Gyro quantization level (rad/s)
% GNSS_config
% .epoch_interval Interval between GNSS epochs (s)
% .init_est_r_ea_e Initial estimated position (m; ECEF)
% .no_sat Number of satellites in constellation
% .r_os Orbital radius of satellites (m)
% .inclination Inclination angle of satellites (deg)
% .const_delta_lambda Longitude offset of constellation (deg)
% .const_delta_t Timing offset of constellation (s)
% .mask_angle Mask angle (deg)
% .SIS_err_SD Signal in space error SD (m)
% .zenith_iono_err_SD Zenith ionosphere error SD (m)
% .zenith_trop_err_SD Zenith troposphere error SD (m)
% .code_track_err_SD Code tracking error SD (m)
% .rate_track_err_SD Range rate tracking error SD (m/s)
% .rx_clock_offset Receiver clock offset at time=0 (m)
% .rx_clock_drift Receiver clock drift at time=0 (m/s)
% TC_KF_config
% .init_att_unc Initial attitude uncertainty per axis (rad)
% .init_vel_unc Initial velocity uncertainty per axis (m/s)
% .init_pos_unc Initial position uncertainty per axis (m)
% .init_b_a_unc Initial accel. bias uncertainty (m/s^2)
% .init_b_g_unc Initial gyro. bias uncertainty (rad/s)
% .init_clock_offset_unc Initial clock offset uncertainty per axis (m)
% .init_clock_drift_unc Initial clock drift uncertainty per axis (m/s)
% .gyro_noise_PSD Gyro noise PSD (rad^2/s)
% .accel_noise_PSD Accelerometer noise PSD (m^2 s^-3)
% .accel_bias_PSD Accelerometer bias random walk PSD (m^2 s^-5)
% .gyro_bias_PSD Gyro bias random walk PSD (rad^2 s^-3)
% .clock_freq_PSD Receiver clock frequency-drift PSD (m^2/s^3)
% .clock_phase_PSD Receiver clock phase-drift PSD (m^2/s)
% .pseudo_range_SD Pseudo-range measurement noise SD (m)
% .range_rate_SD Pseudo-range rate measurement noise SD (m/s)
%
% Outputs:
% out_profile Navigation solution as a motion profile array
% out_errors Navigation solution error array
% out_IMU_bias_est Kalman filter IMU bias estimate array
% out_clock GNSS Receiver clock estimate array
% out_KF_SD Output Kalman filter state uncertainties
%
% Format of motion profiles:
% Column 1: time (sec)
% Column 2: latitude (rad)
% Column 3: longitude (rad)
% Column 4: height (m)
% Column 5: north velocity (m/s)
% Column 6: east velocity (m/s)
% Column 7: down velocity (m/s)
% Column 8: roll angle of body w.r.t NED (rad)
% Column 9: pitch angle of body w.r.t NED (rad)
% Column 10: yaw angle of body w.r.t NED (rad)
%
% Format of error array:
% Column 1: time (sec)
% Column 2: north position error (m)
% Column 3: east position error (m)
% Column 4: down position error (m)
% Column 5: north velocity error (m/s)
% Column 6: east velocity error (m/s)
% Column 7: down velocity (error m/s)
% Column 8: attitude error about north (rad)
% Column 9: attitude error about east (rad)
% Column 10: attitude error about down = heading error (rad)
%
% Format of output IMU biases array:
% Column 1: time (sec)
% Column 2: estimated X accelerometer bias (m/s^2)
% Column 3: estimated Y accelerometer bias (m/s^2)
% Column 4: estimated Z accelerometer bias (m/s^2)
% Column 5: estimated X gyro bias (rad/s)
% Column 6: estimated Y gyro bias (rad/s)
% Column 7: estimated Z gyro bias (rad/s)
%
% Format of receiver clock array:
% Column 1: time (sec)
% Column 2: estimated clock offset (m)
% Column 3: estimated clock drift (m/s)
%
% Format of KF state uncertainties array:
% Column 1: time (sec)
% Column 2: X attitude error uncertainty (rad)
% Column 3: Y attitude error uncertainty (rad)
% Column 4: Z attitude error uncertainty (rad)
% Column 5: X velocity error uncertainty (m/s)
% Column 6: Y velocity error uncertainty (m/s)
% Column 7: Z velocity error uncertainty (m/s)
% Column 8: X position error uncertainty (m)
% Column 9: Y position error uncertainty (m)
% Column 10: Z position error uncertainty (m)
% Column 11: X accelerometer bias uncertainty (m/s^2)
% Column 12: Y accelerometer bias uncertainty (m/s^2)
% Column 13: Z accelerometer bias uncertainty (m/s^2)
% Column 14: X gyro bias uncertainty (rad/s)
% Column 15: Y gyro bias uncertainty (rad/s)
% Column 16: Z gyro bias uncertainty (rad/s)
% Column 17: clock offset uncertainty (m)
% Column 18: clock drift uncertainty (m/s)
% Copyright 2012, Paul Groves
% License: BSD; see license.txt for details
% Begins
% Initialize true navigation solution
old_time = in_profile(1,1);
true_L_b = in_profile(1,2);
true_lambda_b = in_profile(1,3);
true_h_b = in_profile(1,4);
true_v_eb_n = in_profile(1,5:7)';
true_eul_nb = in_profile(1,8:10)';
true_C_b_n = Euler_to_CTM(true_eul_nb)';
[old_true_r_eb_e,old_true_v_eb_e,old_true_C_b_e] =...
NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n);
% Determine satellite positions and velocities
[sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(old_time,...
GNSS_config);
% Initialize the GNSS biases. Note that these are assumed constant throughout
% the simulation and are based on the initial elevation angles. Therefore,
% this function is unsuited to simulations longer than about 30 min.
GNSS_biases = Initialize_GNSS_biases(sat_r_es_e,old_true_r_eb_e,true_L_b,...
true_lambda_b,GNSS_config);
% Generate GNSS measurements
[GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(old_time,...
sat_r_es_e,sat_v_es_e,old_true_r_eb_e,true_L_b,true_lambda_b,...
old_true_v_eb_e,GNSS_biases,GNSS_config);
% Determine Least-squares GNSS position solution
[old_est_r_eb_e,old_est_v_eb_e,est_clock] = GNSS_LS_position_velocity(...
GNSS_measurements,no_GNSS_meas,GNSS_config.init_est_r_ea_e,[0;0;0]);
[old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n] =...
pv_ECEF_to_NED(old_est_r_eb_e,old_est_v_eb_e);
est_L_b = old_est_L_b;
% Initialize estimated attitude solution
old_est_C_b_n = Initialize_NED_attitude(true_C_b_n,initialization_errors);
[temp1,temp2,old_est_C_b_e] = NED_to_ECEF(old_est_L_b,...
old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n);
% Initialize output profile record and errors record
out_profile = zeros(no_epochs,10);
out_errors = zeros(no_epochs,10);
% Generate output profile record
out_profile(1,1) = old_time;
out_profile(1,2) = old_est_L_b;
out_profile(1,3) = old_est_lambda_b;
out_profile(1,4) = old_est_h_b;
out_profile(1,5:7) = old_est_v_eb_n';
out_profile(1,8:10) = CTM_to_Euler(old_est_C_b_n')';
% Determine errors and generate output record
[delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(...
old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n,...
true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n);
out_errors(1,1) = old_time;
out_errors(1,2:4) = delta_r_eb_n';
out_errors(1,5:7) = delta_v_eb_n';
out_errors(1,8:10) = delta_eul_nb_n';
% Initialize Kalman filter P matrix and IMU bias states
P_matrix = Initialize_TC_P_matrix(TC_KF_config);
est_IMU_bias = zeros(6,1);
% Initialize IMU quantization residuals
quant_residuals = [0;0;0;0;0;0];
% Generate IMU bias and clock output records
out_IMU_bias_est(1,1) = old_time;
out_IMU_bias_est(1,2:7) = est_IMU_bias';
out_clock(1,1) = old_time;
out_clock(1,2:3) = est_clock;
% Generate KF uncertainty record
out_KF_SD(1,1) = old_time;
for i =1:17
out_KF_SD(1,i+1) = sqrt(P_matrix(i,i));
end % for i
% Initialize GNSS model timing
time_last_GNSS = old_time;
GNSS_epoch = 1;
% Progress bar
dots = '....................';
bars = '||||||||||||||||||||';
rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b';
fprintf(strcat('Processing: ',dots));
progress_mark = 0;
progress_epoch = 0;
% Main loop
for epoch = 2:no_epochs
% Update progress bar
if (epoch - progress_epoch) > (no_epochs/20)
progress_mark = progress_mark + 1;
progress_epoch = epoch;
fprintf(strcat(rewind,bars(1:progress_mark),...
dots(1:(20 - progress_mark))));
end % if epoch
% Input data from motion profile
time = in_profile(epoch,1);
true_L_b = in_profile(epoch,2);
true_lambda_b = in_profile(epoch,3);
true_h_b = in_profile(epoch,4);
true_v_eb_n = in_profile(epoch,5:7)';
true_eul_nb = in_profile(epoch,8:10)';
true_C_b_n = Euler_to_CTM(true_eul_nb)';
[true_r_eb_e,true_v_eb_e,true_C_b_e] =...
NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n);
% Time interval
tor_i = time - old_time;
% Calculate specific force and angular rate
[true_f_ib_b,true_omega_ib_b] = Kinematics_ECEF(tor_i,true_C_b_e,...
old_true_C_b_e,true_v_eb_e,old_true_v_eb_e,old_true_r_eb_e);
% Simulate IMU errors
[meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,...
true_f_ib_b,true_omega_ib_b,IMU_errors,quant_residuals);
% Correct IMU errors
meas_f_ib_b = meas_f_ib_b - est_IMU_bias(1:3);
meas_omega_ib_b = meas_omega_ib_b - est_IMU_bias(4:6);
% Update estimated navigation solution
[est_r_eb_e,est_v_eb_e,est_C_b_e] = Nav_equations_ECEF(tor_i,...
old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e,meas_f_ib_b,...
meas_omega_ib_b);
% Determine whether to update GNSS simulation and run Kalman filter
if (time - time_last_GNSS) >= GNSS_config.epoch_interval
GNSS_epoch = GNSS_epoch + 1;
tor_s = time - time_last_GNSS; % KF time interval
time_last_GNSS = time;
% Determine satellite positions and velocities
[sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(time,...
GNSS_config);
% Generate GNSS measurements
[GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(...
time,sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,...
true_v_eb_e,GNSS_biases,GNSS_config);
% Run Integration Kalman filter
[est_C_b_e,est_v_eb_e,est_r_eb_e,est_IMU_bias,est_clock,P_matrix] =...
TC_KF_Epoch(GNSS_measurements,no_GNSS_meas,tor_s,est_C_b_e,...
est_v_eb_e,est_r_eb_e,est_IMU_bias,est_clock,P_matrix,...
meas_f_ib_b,est_L_b,TC_KF_config);
% Generate IMU bias and clock output records
out_IMU_bias_est(GNSS_epoch,1) = time;
out_IMU_bias_est(GNSS_epoch,2:7) = est_IMU_bias';
out_clock(GNSS_epoch,1) = time;
out_clock(GNSS_epoch,2:3) = est_clock;
% Generate KF uncertainty output record
out_KF_SD(GNSS_epoch,1) = time;
for i =1:17
out_KF_SD(GNSS_epoch,i+1) = sqrt(P_matrix(i,i));
end % for i
end % if time
% Convert navigation solution to NED
[est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] =...
ECEF_to_NED(est_r_eb_e,est_v_eb_e,est_C_b_e);
% Generate output profile record
out_profile(epoch,1) = time;
out_profile(epoch,2) = est_L_b;
out_profile(epoch,3) = est_lambda_b;
out_profile(epoch,4) = est_h_b;
out_profile(epoch,5:7) = est_v_eb_n';
out_profile(epoch,8:10) = CTM_to_Euler(est_C_b_n')';
% Determine errors and generate output record
[delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(...
est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,...
true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n);
out_errors(epoch,1) = time;
out_errors(epoch,2:4) = delta_r_eb_n';
out_errors(epoch,5:7) = delta_v_eb_n';
out_errors(epoch,8:10) = delta_eul_nb_n';
% Reset old values
old_time = time;
old_true_r_eb_e = true_r_eb_e;
old_true_v_eb_e = true_v_eb_e;
old_true_C_b_e = true_C_b_e;
old_est_r_eb_e = est_r_eb_e;
old_est_v_eb_e = est_v_eb_e;
old_est_C_b_e = est_C_b_e;
end %epoch
% Complete progress bar
fprintf(strcat(rewind,bars,'\n'));
% Ends