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NaveGo: an open-source MATLAB/GNU Octave toolbox for processing integrated navigation systems and performing inertial sensors analysis.

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NaveGo

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NaveGo: an open-source MATLAB/GNU Octave toolbox for processing integrated navigation systems and performing inertial sensors profiling analysis.

NaveGo is an open-source framework for processing INS/GPS sensors that is freely available online. It is developed under MATLAB/GNU Octave due to this programming language has become a de facto standard for simulation and mathematical computing. NaveGo has been verified by processing real-world data from a real trajectory and contrasting results with a commercial, closed-source software package. Difference between both solutions have shown to be negligible.

NaveGo is supported at the moment by three academic research groups: GridTics at the National University of Technology (Argentina), ITIC at the National University of Cuyo (Argentina), and DIATI at the Politecnico di Torino (Italy).

Features

Main features of NaveGo are:

  • Processing of an inertial navigation system (INS).

  • Processing of a loosely-coupled integrated navigation system (INS/GPS).

  • Implementation of the Allan variance procedure to characterize inertial sensors' typical errors.

  • Simulation of inertial sensors and GPS (in a very early stage).

How to cite this work

Rodrigo Gonzalez, Carlos Catania, and Paolo Dabove (2016). NaveGo: an open-source MATLAB/GNU Octave toolbox for processing integrated navigation systems and performing inertial sensors profiling analysis. http://doi.org/10.5281/zenodo.165125. URL: https://github.com/rodralez/NaveGo/.

Contributions

We are looking for contributors for NaveGo! Since integrated navigation is a topic used in several fields (Geomatics, Geology, Mobile Mapping, Autonomous Driving, even Veterinary) we hope other communities than the navigation community compromise and contribute with this open-source project.

You can contribute in many ways:

  • Writing code.
  • Writing a manual.
  • Reporting bugs.
  • Suggesting new features.

If you are interested, please feel free to contact Dr. Rodrigo Gonzalez at rodralez [at] frm [dot] utn [dot] edu [dot] ar.

Publications

The underlying mathematical model of NaveGo is based on two articles which are recommended for reading:

  • R. Gonzalez, J.I. Giribet, and H.D. Patiño. NaveGo: a simulation framework for low-cost integrated navigation systems, Journal of Control Engineering and Applied Informatics, vol. 17, issue 2, pp. 110-120, 2015. Link.

  • R. Gonzalez, J.I. Giribet, and H.D. Patiño. An approach to benchmarking of loosely coupled low-cost navigation systems. Mathematical and Computer Modelling of Dynamical Systems, vol. 21, issue 3, pp. 272-287, 2015. Link.

Acknowledgments

We would like to thank to many people that have contribute to make NaveGo a better tool:

  • Dr. Juan Ignacio Giribet (Universidad Nacional de Buenos Aires, Argentina) for this continuous support on theory aspects of INS/GPS systems.

  • Dr. Charles K. Toth (The Ohio State University, USA), Dr. Allison Kealy, and M.Sc. Azmir Hasnur-Rabiain (both from The University of Melbourne, Australia) for generously sharing IMU and GPS datasets, and in particular, for Azmir's unselfish help.

  • Prof. Zhu, Dr. Yang, and Mr. Bo Sun, all from the Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin, China, for contributing with IMU static measurements to test Allan variance routines.

  • Dr. Paolo Dabove and Dr. Marco Piras (both from DIATI, Politecnico di Torino, Italy) for helping to debug NaveGo and suggesting new features.

Examples

Allan variance example

Just execute the file navego_allan_example.m. It process 2-hours of static measurements from an Sensonor STIM300 IMU.

INS/GPS example

The file navego_example.m tries to demonstrate the use of NaveGo. It compares the performances of two simulated IMUs, ADIS16405 IMU and ADIS16488 IMU, both integrated with a simulated GPS.

Next, a description of this file.

Reset section

clc
close all
clear
matlabrc

fprintf('\nStarting simulation ... \n')

Code execution parameters

% Comment any of the following parameters in order to NOT execute a particular portion of code

GPS_DATA  = 'ON';   % Simulate GPS data
IMU1_DATA = 'ON';   % Simulate ADIS16405 IMU data
IMU2_DATA = 'ON';   % Simulate ADIS16488 IMU data

IMU1_INS  = 'ON';   % Execute INS/GPS integration for ADIS16405 IMU
IMU2_INS  = 'ON';   % Execute INS/GPS integration for ADIS16488 IMU

PLOT      = 'ON';   % Plot results.

% If a particular parameter is commented above, it is set by default to 'OFF'.

if (~exist('GPS_DATA','var')),  GPS_DATA  = 'OFF'; end
if (~exist('IMU1_DATA','var')), IMU1_DATA = 'OFF'; end
if (~exist('IMU2_DATA','var')), IMU2_DATA = 'OFF'; end
if (~exist('IMU1_INS','var')),  IMU1_INS = 'OFF'; end
if (~exist('IMU2_INS','var')),  IMU2_INS = 'OFF'; end
if (~exist('PLOT','var')),      PLOT = 'OFF'; end

Conversion constants

G = 9.81;           % Gravity constant, m/s^2
G2MSS = G;          % g to m/s^2
MSS2G = (1/G);      % m/s^2 to g

D2R = (pi/180);     % degrees to radians
R2D = (180/pi);     % radians to degrees

KT2MS = 0.514444;   % knot to m/s
MS2KMH = 3.6;       % m/s to km/h

Load reference data

fprintf('Loading reference dataset from a trajectory generator... \n')

load ref.mat

% ref.mat contains the reference data structure from which inertial 
% sensors and GPS wil be simulated. It must contain the following fields:

%         t: Nx1 time vector (seconds).
%       lat: Nx1 latitude (radians).
%       lon: Nx1 longitude (radians).
%         h: Nx1 altitude (m).
%       vel: Nx3 NED velocities (m/s).
%      roll: Nx1 roll angles (radians).
%     pitch: Nx1 pitch angles (radians).
%       yaw: Nx1 yaw angle vector (radians).
%        kn: 1x1 number of elements of time vector.
%     DCMnb: Nx9 Direct Cosine Matrix nav-to-body. Each row contains 
%            the elements of one matrix ordered by columns as 
%            [a11 a21 a31 a12 a22 a32 a13 a23 a33].
%      freq: sampling frequency (Hz).

ADIS16405 IMU error profile

% IMU data structure:
%         t: Ix1 time vector (seconds).
%        fb: Ix3 accelerations vector in body frame XYZ (m/s^2).
%        wb: Ix3 turn rates vector in body frame XYZ (radians/s).
%       arw: 1x3 angle random walks (rad/s/root-Hz).
%       vrw: 1x3 angle velocity walks (m/s^2/root-Hz).
%      gstd: 1x3 gyros standard deviations (radians/s).
%      astd: 1x3 accrs standard deviations (m/s^2).
%    gb_fix: 1x3 gyros static biases or turn-on biases (radians/s).
%    ab_fix: 1x3 accrs static biases or turn-on biases (m/s^2).
%  gb_drift: 1x3 gyros dynamic biases or bias instabilities (radians/s).
%  ab_drift: 1x3 accrs dynamic biases or bias instabilities (m/s^2).
%   gb_corr: 1x3 gyros correlation times (seconds).
%   ab_corr: 1x3 accrs correlation times (seconds).
%     gpsd : 1x3 gyros dynamic biases PSD (rad/s/root-Hz).
%     apsd : 1x3 accrs dynamic biases PSD (m/s^2/root-Hz);
%      freq: 1x1 sampling frequency (Hz).
% ini_align: 1x3 initial attitude at t(1).
% ini_align_err: 1x3 initial attitude errors at t(1).

% ref dataset will be used to simulate IMU sensors.

ADIS16405.arw      = 2   .* ones(1,3);     % Angle random walks [X Y Z] (deg/root-hour)
ADIS16405.vrw      = 0.2 .* ones(1,3);     % Velocity random walks [X Y Z] (m/s/root-hour)
ADIS16405.gb_fix   = 3   .* ones(1,3);     % Gyro static biases [X Y Z] (deg/s)
ADIS16405.ab_fix   = 50  .* ones(1,3);     % Acc static biases [X Y Z] (mg)
ADIS16405.gb_drift = 0.007 .* ones(1,3);   % Gyro dynamic biases [X Y Z] (deg/s)
ADIS16405.ab_drift = 0.2 .* ones(1,3);     % Acc dynamic biases [X Y Z] (mg)
ADIS16405.gb_corr  = 100 .* ones(1,3);     % Gyro correlation times [X Y Z] (seconds)
ADIS16405.ab_corr  = 100 .* ones(1,3);     % Acc correlation times [X Y Z] (seconds)
ADIS16405.freq     = ref.freq;             % IMU operation frequency [X Y Z] (Hz)
% ADIS16405.m_psd     = 0.066 .* ones(1,3);  % Magnetometer noise density [X Y Z] (mgauss/root-Hz)

ADIS16405.t = ref.t;                             % IMU time vector
dt = mean(diff(ADIS16405.t));                    % IMU mean period

imu1 = imu_err_profile(ADIS16405, dt);      % Transform IMU manufacturer error units to SI units.

imu1.ini_align_err = [1 1 5] .* D2R;                     % Initial attitude align errors for matrix P in Kalman filter, [roll pitch yaw] (radians)  
imu1.ini_align = [ref.roll(1) ref.pitch(1) ref.yaw(1)];  % Initial attitude align at t(1) (radians).

ADIS16488 IMU error profile

% ref dataset will be used to simulate IMU sensors.

ADIS16488.arw      = 0.3  .* ones(1,3);     % Angle random walks [X Y Z] (deg/root-hour)
ADIS16488.vrw      = 0.029.* ones(1,3);     % Velocity random walks [X Y Z] (m/s/root-hour)
ADIS16488.gb_fix   = 0.2  .* ones(1,3);     % Gyro static biases [X Y Z] (deg/s)
ADIS16488.ab_fix   = 16   .* ones(1,3);     % Acc static biases [X Y Z] (mg)
ADIS16488.gb_drift = 6.5/3600  .* ones(1,3);% Gyro dynamic biases [X Y Z] (deg/s)
ADIS16488.ab_drift = 0.1  .* ones(1,3);     % Acc dynamic biases [X Y Z] (mg)
ADIS16488.gb_corr  = 100  .* ones(1,3);     % Gyro correlation times [X Y Z] (seconds)
ADIS16488.ab_corr  = 100  .* ones(1,3);     % Acc correlation times [X Y Z] (seconds)
ADIS16488.freq     = ref.freq;              % IMU operation frequency [X Y Z] (Hz)
% ADIS16488.m_psd = 0.054 .* ones(1,3);       % Magnetometer noise density [X Y Z] (mgauss/root-Hz)

ADIS16488.t = ref.t;                             % IMU time vector
dt = mean(diff(ADIS16488.t));                    % IMU mean period

imu2 = imu_err_profile(ADIS16488, dt);      % Transform IMU manufacturer error units to SI units.

imu2.ini_align_err = [1 1 5] .* D2R;                     % Initial attitude align errors for matrix P in Kalman filter, [roll pitch yaw] (radians)  
imu2.ini_align = [ref.roll(1) ref.pitch(1) ref.yaw(1)];  % Initial attitude align at t(1) (radians)..

Garmin 5-18 Hz GPS error profile

% GPS data structure:
%         t: Mx1 time vector (seconds).
%       lat: Mx1 latitude (radians).
%       lon: Mx1 longitude (radians).
%         h: Mx1 altitude (m).
%       vel: Mx3 NED velocities (m/s).
%       std: 1x3 position standard deviations (rad, rad, m).
%      stdm: 1x3 position standard deviations (m, m, m).
%      stdv: 1x3 velocity standard deviations (m/s).
%      larm: 3x1 lever arm (x-right, y-fwd, z-down) (m).
%      freq: 1x1 sampling frequency (Hz).

gps.stdm = [5, 5, 10];                 % GPS positions standard deviations [lat lon h] (meters)
gps.stdv = 0.1 * KT2MS .* ones(1,3);   % GPS velocities standard deviations [Vn Ve Vd] (meters/s)
gps.larm = zeros(3,1);                 % GPS lever arm [X Y Z] (meters)
gps.freq = 5;                          % GPS operation frequency (Hz)

Simulate GPS

rng('shuffle')                  % Reset pseudo-random seed

if strcmp(GPS_DATA, 'ON')       % If simulation of GPS data is required ...
    
    fprintf('NaveGo: simulating GPS data... \n')
    
    gps = gps_err_profile(ref.lat(1), ref.h(1), gps); % Transform GPS manufacturer error units to SI units.
    
    [gps] = gps_gen(ref, gps);  % Generate GPS dataset from reference dataset.

    save gps.mat gps
    
else
    
    fprintf('NaveGo: loading GPS data... \n') 
    
    load gps.mat
end

Simulate IMU1

rng('shuffle')                  % Reset pseudo-random seed

if strcmp(IMU1_DATA, 'ON')      % If simulation of IMU1 data is required ...
    
    fprintf('NaveGo: generating IMU1 ACCR data... \n')
    
    fb = acc_gen (ref, imu1); % Generate acc in the body frame
    imu1.fb = fb;
    
    fprintf('NaveGo: generating IMU1 GYRO data... \n')
    
    wb = gyro_gen (ref, imu1);% Generate gyro in the body frame
    imu1.wb = wb;
    
    save imu1.mat imu1
    
    clear wb fb;
    
else
    fprintf('NaveGo: loading IMU1 data... \n')
    
    load imu1.mat
end

Simulate IMU2

rng('shuffle')					% Reset pseudo-random seed

if strcmp(IMU2_DATA, 'ON')      % If simulation of IMU2 data is required ...
    
    fprintf('NaveGo: generating IMU2 ACCR data... \n')
    
    fb = acc_gen (ref, imu2); % Generate acc in the body frame
    imu2.fb = fb;
    
    fprintf('NaveGo: generating IMU2 GYRO data... \n')
    
    wb = gyro_gen (ref, imu2);% Generate gyro in the body frame
    imu2.wb = wb;
    
    save imu2.mat imu2
    
    clear wb fb;
    
else
    fprintf('NaveGo: loading IMU2 data... \n')
    
    load imu2.mat
end

INS/GPS integration using IMU1

if strcmp(IMU1_INS, 'ON')
    
    fprintf('NaveGo: INS/GPS integration for IMU1... \n')
    
    % Sincronize GPS data with IMU data.
    
    % Guarantee that gps.t(1) < imu1.t(1) < gps.t(2)
    if (imu1.t(1) < gps.t(1)),
        
        igx  = find(imu1.t > gps.t(1), 1, 'first' );
        
        imu1.t  = imu1.t  (igx:end, :);
        imu1.fb = imu1.fb (igx:end, :);
        imu1.wb = imu1.wb (igx:end, :);        
    end
    
    % Guarantee that imu1.t(end-1) < gps.t(end) < imu1.t(end)
    if (imu1.t(end) <= gps.t(end)),
        
        fgx  = find(gps.t < imu1.t(end), 1, 'last' );
        
        gps.t   = gps.t  (1:fgx, :);
        gps.lat = gps.lat(1:fgx, :);
        gps.lon = gps.lon(1:fgx, :);
        gps.h   = gps.h  (1:fgx, :);
        gps.vel = gps.vel(1:fgx, :);
    end
    
    % Execute INS/GPS integration
    % ---------------------------------------------------------------------
    [imu1_e] = ins_gps(imu1, gps, 'quaternion', 'double');
    % ---------------------------------------------------------------------
    
    save imu1_e.mat imu1_e
    
else
    
    fprintf('NaveGo: loading INS/GPS integration for IMU1... \n')
    
    load imu1_e.mat
end

INS/GPS integration using IMU2

if strcmp(IMU2_INS, 'ON')
    
    fprintf('\nNaveGo: INS/GPS integration for IMU2... \n')
    
    % Sincronize GPS data and IMU data.
    
    % Guarantee that gps.t(1) < imu2.t(1) < gps.t(2)
    if (imu2.t(1) < gps.t(1)),
        
        igx  = find(imu2.t > gps.t(1), 1, 'first' );
        
        imu2.t  = imu2.t  (igx:end, :);
        imu2.fb = imu2.fb (igx:end, :);
        imu2.wb = imu2.wb (igx:end, :);        
    end
    
    % Guarantee that imu2.t(end-1) < gps.t(end) < imu2.t(end)
    if (imu2.t(end) <= gps.t(end)),
        
        fgx  = find(gps.t < imu2.t(end), 1, 'last' );
        
        gps.t   = gps.t  (1:fgx, :);
        gps.lat = gps.lat(1:fgx, :);
        gps.lon = gps.lon(1:fgx, :);
        gps.h   = gps.h  (1:fgx, :);
        gps.vel = gps.vel(1:fgx, :);
    end
    
    % Execute INS/GPS integration
    % ---------------------------------------------------------------------
    [imu2_e] = ins_gps(imu2, gps, 'quaternion', 'double');
    % ---------------------------------------------------------------------
    
    save imu2_e.mat imu2_e
    
else
    
    fprintf('NaveGo: loading INS/GPS integration for IMU2... \n')
    
    load imu2_e.mat
end

Interpolate reference dataset

ref_1 = navego_interpolation (imu1_e, ref);
ref_2 = navego_interpolation (imu2_e, ref);
ref_g = navego_interpolation (gps, ref);

Print navigation time

to = (ref.t(end) - ref.t(1));

fprintf('\nNaveGo: navigation time of %4.2f minutes or %4.2f seconds. \n', (to/60), to)

Print RMSE from IMU1

print_rmse (imu1_e, gps, ref_1, ref_g, 'INS/GPS IMU1');

Print RMSE from IMU2

print_rmse (imu2_e, gps, ref_2, ref_g, 'INS/GPS IMU2');

References

About

NaveGo: an open-source MATLAB/GNU Octave toolbox for processing integrated navigation systems and performing inertial sensors analysis.

License:GNU Lesser General Public License v3.0

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