From 877a014fd711656d6fbea6406bf9a07e87a85096 Mon Sep 17 00:00:00 2001 From: Claudio Mandrioli <claudio.mandrioli@control.lth.se> Date: Tue, 11 Sep 2018 13:53:12 +0200 Subject: [PATCH] matlab_in --- matlab/GNSSaidedINS_data.mat | Bin 0 -> 1419302 bytes matlab/GPSaidedINS.m | 286 +++++++++++++++++++++++++++++++++++ matlab/Nav_eq.m | 71 +++++++++ matlab/Rt2b.m | 21 +++ matlab/dcm2q.m | 19 +++ matlab/get_settings.m | 50 ++++++ matlab/gps.m | 163 ++++++++++++++++++++ matlab/gravity.m | 29 ++++ matlab/main.m | 21 +++ matlab/plot_data.m | 144 ++++++++++++++++++ matlab/q2dcm.m | 56 +++++++ 11 files changed, 860 insertions(+) create mode 100644 matlab/GNSSaidedINS_data.mat create mode 100644 matlab/GPSaidedINS.m create mode 100644 matlab/Nav_eq.m create mode 100644 matlab/Rt2b.m create mode 100644 matlab/dcm2q.m create mode 100644 matlab/get_settings.m create mode 100644 matlab/gps.m create mode 100644 matlab/gravity.m create mode 100644 matlab/main.m create mode 100644 matlab/plot_data.m 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a/matlab/GPSaidedINS.m b/matlab/GPSaidedINS.m new file mode 100644 index 0000000..6d7a347 --- /dev/null +++ b/matlab/GPSaidedINS.m @@ -0,0 +1,286 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% function call: out_data=GPSaidedINS(in_data,settings) +% +% This function integrates GNSS and IMU data. The data fusion +% is based upon a loosely-coupled feedback GNSS-aided INS approach. +% +% Input struct: +% in_data.GNSS.pos_ned GNSS-receiver position estimates in NED +% coordinates [m] +% in_data.GNSS.t Time of GNSS measurements [s] +% (in_data.GNSS.HDOP GNSS Horizontal Dilution of Precision [-]) +% (in_data.GNSS.VDOP GNSS Vertical Dilution of Precision [-]) +% in_data.IMU.acc Accelerometer measurements [m/s^2] +% in_data.IMU.gyro Gyroscope measurements [rad/s] +% in_data.IMU.t Time of IMU measurements [s] +% +% Output struct: +% out_data.x_h Estimated navigation state vector [position; velocity; attitude] +% out_data.delta_u_h Estimated IMU biases [accelerometers; gyroscopes] +% out_data.diag_P Diagonal elements of the Kalman filter state +% covariance matrix. +% +% +% Edit: Isaac Skog (skog@kth.se), 2016-09-06 +% Revised: Bo Bernhardsson, 2018-01-01 +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function out_data=GPSaidedINS(in_data,settings) + + +% Copy data to variables with shorter name +u=[in_data.IMU.acc;in_data.IMU.gyro]; +t=in_data.IMU.t; + +%% Initialization +% Initialize the navigation state +x_h=init_navigation_state(u,settings); + +% Initialize the sensor bias estimate +delta_u_h=zeros(6,1); + +% Initialize the Kalman filter +[P,Q1,Q2,~,~]=init_filter(settings); + + +% Allocate memory for the output data +N=size(u,2); +out_data.x_h=zeros(10,N); +out_data.x_h(:,1)=x_h; +out_data.diag_P=zeros(15,N); +out_data.diag_P(:,1)=diag(P); +out_data.delta_u_h=zeros(6,N); + +%% Information fusion +ctr_gnss_data=1; +GPS_position=true; + +%% Initialize GPS sensor +sensor.state='warm_start_available'; +sensor.howLong=0; +sensor.ephExp=1800.0; +sensor.fp=0; +sensor.eph=5; +turn=true; +power=400; +energy=0; + +pre_state='startup'; +a=0; + +for k=2:N + + % Sampling period + Ts=t(k)-t(k-1); + + %%%%%%%%%%%%%%%%% + %% GPS sensor %% + %%%%%%%%%%%%%%%%% + %number of visible satellites + sv=5; + %control action + a=[a,sum(sqrt(out_data.diag_P(1:3,k-1)))]; + if sum(sqrt(out_data.diag_P(1:3,k-1)))<1.0 + turn=false; + else + turn=true; + end + %update sensor state + pre_state=sensor.state; + sensor=gps(t(k),sensor,turn,sv); + %determine if GPS position is available + GPS_position=strcmp(sensor.state,'position_available'); + %compute power consumption + if ~(strcmp(sensor.state,'no_info')||strcmp(sensor.state,'warm_start_available')) + energy=energy+power*Ts; + end + +% %print new state and current time if it changes +% if ~strcmp(pre_state, sensor.state) +% sensor.state +% t(k) +% end + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + % Calibrate the sensor measurements using current sensor bias estimate. + u_h=u(:,k)+delta_u_h; + + % Update the INS navigation state + x_h=Nav_eq(x_h,u_h,Ts); + + % Get state space model matrices + [F,G]=state_space_model(x_h,u_h,Ts); + + % Time update of the Kalman filter state covariance. + P=F*P*F'+G*blkdiag(Q1,Q2)*G'; + + % Defualt measurement observation matrix and measurement covariance + % matrix + + y = in_data.GNSS.pos_ned(:,ctr_gnss_data); + H = [eye(3) zeros(3,12)]; + R = settings.sigma_gps^2*eye(3); + + ind = zeros(1,6); % index vector, describing available measurements + % Check if GNSS measurement is available + if t(k)==in_data.GNSS.t(ctr_gnss_data) + if GPS_position + ind(1:3)=1; + end + % Update GNSS data counter + ctr_gnss_data=min(ctr_gnss_data+1,length(in_data.GNSS.t)); + end + + ind=logical(ind); + H=H(ind,:); + y=y(ind); + R=R(ind,ind); + + % Calculate the Kalman filter gain. + K=(P*H')/(H*P*H'+R); + + % Update the perturbation state estimate. + z=[zeros(9,1); delta_u_h]+K*(y-H(:,1:6)*x_h(1:6)); + + % Correct the navigation states using current perturbation estimates. + x_h(1:6)=x_h(1:6)+z(1:6); + x_h(7:10)=Gamma(x_h(7:10),z(7:9)); + delta_u_h=z(10:15); + + % Update the Kalman filter state covariance. + P=(eye(15)-K*H)*P; + + % Save the data to the output data structure + out_data.x_h(:,k)=x_h; + out_data.diag_P(:,k)=diag(P); + out_data.delta_u_h(:,k)=delta_u_h; + +end +figure(11) +plot(a),grid +energy +end + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% SUB-FUNCTIONS %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Init filter %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [P,Q1,Q2,R,H]=init_filter(settings) + + +% Kalman filter state matrix +P=zeros(15); +P(1:3,1:3)=settings.factp(1)^2*eye(3); +P(4:6,4:6)=settings.factp(2)^2*eye(3); +P(7:9,7:9)=diag(settings.factp(3:5)).^2; +P(10:12,10:12)=settings.factp(6)^2*eye(3); +P(13:15,13:15)=settings.factp(7)^2*eye(3); + +% Process noise covariance +Q1=zeros(6); +Q1(1:3,1:3)=diag(settings.sigma_acc).^2; +Q1(4:6,4:6)=diag(settings.sigma_gyro).^2; + +Q2=zeros(6); +Q2(1:3,1:3)=settings.sigma_acc_bias^2*eye(3); +Q2(4:6,4:6)=settings.sigma_gyro_bias^2*eye(3); + +% GNSS-receiver position measurement noise +R=settings.sigma_gps^2*eye(3); + +% Observation matrix +H=[eye(3) zeros(3,12)]; + +end + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Init navigation state %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function x_h=init_navigation_state(u,settings) + + +% Calculate the roll and pitch +f=mean(u(:,1:100),2); +roll=atan2(-f(2),-f(3)); +pitch=atan2(f(1),norm(f(2:3))); + +% Initial coordinate rotation matrix +Rb2t=Rt2b([roll pitch settings.init_heading])'; + +% Calculate quaternions +q=dcm2q(Rb2t); + +% Initial navigation state vector +x_h=[zeros(6,1); q]; + +end + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% State transition matrix %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function [F,G]=state_space_model(x,u,Ts) + +% Convert quaternion to DCM +Rb2t=q2dcm(x(7:10)); + +% Transform measured force to force in +% the tangent plane coordinate system. +f_t=Rb2t*u(1:3); +St=[0 -f_t(3) f_t(2); f_t(3) 0 -f_t(1); -f_t(2) f_t(1) 0]; + +% Only the standard errors included +O=zeros(3); +I=eye(3); +Fc=[O I O O O; + O O St Rb2t O; + O O O O -Rb2t; + O O O O O; + O O O O O]; + +% Approximation of the discret +% time state transition matrix +F=eye(15)+Ts*Fc; + +% Noise gain matrix +G=Ts*[O O O O; Rb2t O O O; O -Rb2t O O; O O I O; O O O I]; +end + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Error correction of quaternion %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function q=Gamma(q,epsilon) + +% Convert quaternion to DCM +R=q2dcm(q); + +% Construct skew symetric matrx +OMEGA=[0 -epsilon(3) epsilon(2); epsilon(3) 0 -epsilon(1); -epsilon(2) epsilon(1) 0]; + +% Correct the DCM matrix +R=(eye(3)-OMEGA)*R; + +% Calculte the corrected quaternions +q=dcm2q(R); +end + + + + + + + diff --git a/matlab/Nav_eq.m b/matlab/Nav_eq.m new file mode 100644 index 0000000..3c0a3c4 --- /dev/null +++ b/matlab/Nav_eq.m @@ -0,0 +1,71 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% function call: x=Nav_eq(x,u,dt) +% +% Function that implements the navigation equations of an INS. +% +% Inputs: +% x Current navigation state [position (NED), velocity (NED), attitude (Quaternion)] +% u Measured inertial quantities [Specific force (m/s^2), Angular velocity (rad/s)] +% dt Sampling period (s) +% +% Output: +% x Updated navigation state [position (NED), velocity (NED), attitude (Quaternion)] +% +% Edit: Isaac Skog (skog@kth.se), 2016-09-06 +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function x=Nav_eq(x,u,dt) + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Position and velocity %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Gravity vector (This should depend on the current location, but +% since moving in a small area it is approximatly constant). +g_t=gravity(59,0); + +f_t=q2dcm(x(7:10))*u(1:3); + +% Subtract gravity, to obtain accelerations in tangent plane coordinates +acc_t=f_t-g_t; + +% state space model matrices +A=eye(6); +A(1,4)=dt; +A(2,5)=dt; +A(3,6)=dt; + +B=[(dt^2)/2*eye(3);dt*eye(3)]; + +% Position and velocity update +x(1:6)=A*x(1:6)+B*acc_t; + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Attitude Quaternion %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Quaternion algorithm according to Farrel, pp 49. + +w_tb=u(4:6); + +P=w_tb(1)*dt; +Q=w_tb(2)*dt; +R=w_tb(3)*dt; + + +OMEGA=zeros(4); +OMEGA(1,1:4)=0.5*[0 R -Q P]; +OMEGA(2,1:4)=0.5*[-R 0 P Q]; +OMEGA(3,1:4)=0.5*[Q -P 0 R]; +OMEGA(4,1:4)=0.5*[-P -Q -R 0]; + +v=norm(w_tb)*dt; + +if v~=0 + x(7:10)=(cos(v/2)*eye(4)+2/v*sin(v/2)*OMEGA )*x(7:10); +end +return \ No newline at end of file diff --git a/matlab/Rt2b.m b/matlab/Rt2b.m new file mode 100644 index 0000000..4fd56a2 --- /dev/null +++ b/matlab/Rt2b.m @@ -0,0 +1,21 @@ +function R=Rt2b(ang) +% function for calculation of the rotation matrix for +% rotaion from tangent frame to body frame. +% function R=Rt2b[roll,pitch,yaw]; +% v_b=[u v d]' +% v_t=[N E D]' + +cr=cos(ang(1)); +sr=sin(ang(1)); + +cp=cos(ang(2)); +sp=sin(ang(2)); + +cy=cos(ang(3)); +sy=sin(ang(3)); + +R=[cy*cp sy*cp -sp; + -sy*cr+cy*sp*sr cy*cr+sy*sp*sr cp*sr; + sy*sr+cy*sp*cr -cy*sr+sy*sp*cr cp*cr]; + + diff --git a/matlab/dcm2q.m b/matlab/dcm2q.m new file mode 100644 index 0000000..5a64b2e --- /dev/null +++ b/matlab/dcm2q.m @@ -0,0 +1,19 @@ +function q=dcm2q(R) +% +% function q=dcm2q(R) +% Function for transformation from directional cosine matrix to quaternions +% From Farrel pp 42. +% Edit: Isaac Skog, 2007-05-24 + + + +q=zeros(4,1); + +q(4)=0.5*sqrt(1+sum(diag(R))); + +q(1)=(R(3,2)-R(2,3))/(4*q(4)); + +q(2)=(R(1,3)-R(3,1))/(4*q(4)); + +q(3)=(R(2,1)-R(1,2))/(4*q(4)); + diff --git a/matlab/get_settings.m b/matlab/get_settings.m new file mode 100644 index 0000000..f4946dd --- /dev/null +++ b/matlab/get_settings.m @@ -0,0 +1,50 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% Function that outputs a struct "settings" with the settings used in the +% GNSS-aided INS +% +% Edit: Isaac Skog (skog@kth.se), 2016-09-01 +% Revised: Bo Bernhardsson 2018-01-01 +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function settings=get_settings() + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% GENERAL PARAMETERS %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%settings.non_holonomic = 'off'; +%settings.speed_aiding = 'off'; + +settings.init_heading = 320*pi/180; + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FILTER PARAMETERS %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Process noise covariance (Q) +% Standard deviations, need to be squared +settings.sigma_acc = 0.05; % [m/s^2] +settings.sigma_gyro = 0.1*pi/180; % [rad/s] +settings.sigma_acc_bias = 0.0001; % [m/s^2.5] +settings.sigma_gyro_bias = 0.01*pi/180; % [rad/s^1.5] + + +% GNSS position measurement noise covariance (R) +% Standard deviations, need to be squared +settings.sigma_gps = 3/sqrt(3); %[m] + +% Initial Kalman filter uncertainties (standard deviations) +settings.factp(1) = 10; % Position [m] +settings.factp(2) = 5; % Velocity [m/s] +settings.factp(3:5) = (pi/180*[1 1 20]'); % Attitude (roll,pitch,yaw) [rad] +settings.factp(6) = 0.02; % Accelerometer biases [m/s^2] +settings.factp(7) = (0.05*pi/180); % Gyro biases [rad/s] + + +end + + + + diff --git a/matlab/gps.m b/matlab/gps.m new file mode 100644 index 0000000..32d14cb --- /dev/null +++ b/matlab/gps.m @@ -0,0 +1,163 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% GPS sensor dynamics %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%STATE is a struct (called sensor) with the following fields +% state -[string]the current proceural state: no_info, cold_start, read_ephemeris, position_available, warm_start_avaialable, warm_start +% howLong -[double]when the current procedural state has been entered +% ephExp -[double]expiration time of ephemeris data +% fp -[int]number of tracked satelliets +% eph -[int]number of satellites for which ephemeris data are available + +%INPUTS +% -time +% -state +% -turn on/off (true=turn_ON, false=turn_OFF) +% -visible satellites + +%OUTPUTS +% -state + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function sensor=gps(time,sensor_in,turn,sv) + +%% parameters +%define how many satellites you need to track given the accuracy requirements +required_sv= 4; +%define how long ephemeris data last +ephDuration=1800.0; +%define how much time is required to read the ephemeris data +ttge=59.0; +%define how much time is required to fetch the satellites signal +ttfs=0.01; + +%% initialize output +sensor = sensor_in; + +%% equations +%you cannot track satellites that you dont see +sensor.fp=min(sensor_in.fp,sv); +sensor.eph=min(sensor_in.eph,sv); + +%% events +ephemeris_expired=(time>sensor.ephExp)||(sensor.eph<required_sv); %ephemeris data are expired +lost_visibility=(sensor_in.fp~=sensor.fp)&&(sensor.fp<required_sv); +fetch_fp=(time-sensor_in.howLong)>=ttfs; +get_ephemeris=(time-sensor_in.howLong)>ttge; + +%% transitions and updates +%for each of the states handle eventual transitions and updates +%(i)if any transition is fired, always update the time the surrent state was entered +%(ii)other updates depend on the spefic transition that is fired +if strcmp(sensor_in.state,'no_info') + if(turn) + sensor.state='cold_start'; + sensor.howLong=time; + end +end +if strcmp(sensor_in.state,'position_available') + if(get_ephemeris) + sensor.state='position_available'; + sensor.howLong=time; + sensor.eph=sv; + sensor.ephExp=time+ephDuration; + end + if(~turn) + sensor.state='warm_start_available'; + sensor.howLong=time; + sensor.fp=0; + end + if(lost_visibility) + sensor.state='warm_start'; + sensor.howLong=time; + %might have to go on to cold_start + if(ephemeris_expired) + sensor.state='cold_start'; + sensor.howLong=time; + sensor.eph=0; + end + end + if(ephemeris_expired) + sensor.state='read_ephemeris'; + sensor.howLong=time; + sensor.eph=0; + %might have to go on to cold_start + if(lost_visibility) + sensor.state='cold_start'; + sensor.howLong=time; + end + end +end +if strcmp(sensor_in.state,'read_ephemeris') + if(get_ephemeris) + sensor.state='position_available'; + sensor.howLong=time; + sensor.eph=sv; + sensor.ephExp=time+ephDuration; + end + if(~turn) + sensor.state='no_info'; + sensor.howLong=time; + sensor.fp=0; + end + if(lost_visibility) + sensor.state='cold_start'; + sensor.howLong=time; + end +end +if strcmp(sensor_in.state,'warm_start') + if(lost_visibility) + sensor.state='warm_start'; + sensor.howLong=time; + end + if(fetch_fp) + sensor.state='position_available'; + sensor.howLong=time; + sensor.fp=sv; + end + if(ephemeris_expired) + sensor.state='cold_start'; + sensor.howLong=time; + sensor.eph=0; + end + if(~turn) + sensor.state='warm_start_available'; + sensor.howLong=time; + sensor.fp=0; + end +end +if strcmp(sensor_in.state,'cold_start') + if(fetch_fp) + sensor.state='read_ephemeris'; + sensor.howLong=time; + sensor.fp=sv; + end + if(lost_visibility) + sensor.state='cold_start'; + sensor.howLong=time; + end + if(~turn) + sensor.state='no_info'; + sensor.howLong=time; + sensor.fp=0; + end +end +if strcmp(sensor_in.state,'warm_start_available') + if(turn) + sensor.state='warm_start'; + sensor.howLong=time; + end + if(ephemeris_expired) + sensor.state='no_info'; + sensor.howLong=time; + sensor.eph=0; + end +end + +end + + + + + diff --git a/matlab/gravity.m b/matlab/gravity.m new file mode 100644 index 0000000..d403f40 --- /dev/null +++ b/matlab/gravity.m @@ -0,0 +1,29 @@ +function g=gravity(lambda,h) +% function g=gravity(lambda,h) +% +% function for calculation of the local gravity vector, in +% the geographic reference frame (same as tangent plane is +% stationary). +% +% Based upon the WGS_84 Geodetic and Gravity model. For more +% info see [pp 222-223,1]. +% +% lambda -> Latitude [degrees] +% h -> Altitude [m] +% g +% +% edit: Isaac Skog, 2006-08-17 + +% degrees to radians +lambda=pi/180*lambda; + +gamma=9.780327*(1+0.0053024*sin(lambda)^2-0.0000058*sin(2*lambda)^2); + +g=gamma-((3.0877e-6)-(0.004e-6)*sin(lambda)^2)*h+(0.072e-12)*h^2; + +g=[0 0 -g]'; +return; + + + + diff --git a/matlab/main.m b/matlab/main.m new file mode 100644 index 0000000..1308da4 --- /dev/null +++ b/matlab/main.m @@ -0,0 +1,21 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Main script for pAN_ powe aware navigation with sensor fusion +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%% Load data +disp('Loads data') +load('GNSSaidedINS_data.mat'); + +%% Load filter settings +disp('Loads settings') +settings=get_settings(); + +%% Run the GNSS-aided INS +disp('Runs the GNSS-aided INS') +out_data=GPSaidedINS(in_data,settings); + +%% Plot the data +disp('Plot data') +plot_data(in_data,out_data,'True');drawnow + diff --git a/matlab/plot_data.m b/matlab/plot_data.m new file mode 100644 index 0000000..0a37b18 --- /dev/null +++ b/matlab/plot_data.m @@ -0,0 +1,144 @@ +function plot_data(in_data,out_data,holdon) + +if nargin < 3; holdon = 'False'; end + +h=zeros(1,3); +figure(2) +if ~holdon clf; end +plot(in_data.GNSS.pos_ned(2,:),in_data.GNSS.pos_ned(1,:),'b-'); +hold on +h(1)=plot(in_data.GNSS.pos_ned(2,:),in_data.GNSS.pos_ned(1,:),'b.'); +h(2)=plot(out_data.x_h(2,:),out_data.x_h(1,:),'r'); +h(3)=plot(in_data.GNSS.pos_ned(2,1),in_data.GNSS.pos_ned(1,1),'ks'); +title('Trajectory') +ylabel('North [m]') +xlabel('East [m]') +legend(h,'GNSS position estimate','GNSS aided INS trajectory','Start point') +axis equal +grid on + +h=zeros(1,3); +figure(3) +if ~holdon clf; end +h(1)=plot(in_data.GNSS.t,-in_data.GNSS.pos_ned(3,:),'b.'); +hold on +h(2)=plot(in_data.IMU.t,-out_data.x_h(3,:),'r'); +h(3)=plot(in_data.IMU.t,3*sqrt(out_data.diag_P(3,:))-out_data.x_h(3,:),'k--'); +plot(in_data.IMU.t,-3*sqrt(out_data.diag_P(3,:))-out_data.x_h(3,:),'k--') +title('Height versus time') +ylabel('Height [m]') +xlabel('Time [s]') +grid on +legend(h,'GNSS estimate','GNSS aided INS estimate','3\sigma bound') + +h=zeros(1,2); +figure(4) +if ~holdon clf; end +h(1)=plot(in_data.IMU.t,sqrt(sum(out_data.x_h(4:6,:).^2)),'r'); +hold on +sigma=sqrt(sum(out_data.diag_P(4:6,:))); +speed=sqrt(sum(out_data.x_h(4:6,:).^2)); +h(2)=plot(in_data.IMU.t,3*sigma+speed,'k--'); +plot(in_data.IMU.t,-3*sigma+speed,'k--') +title('Speed versus time') +ylabel('Speed [m/s]') +xlabel('Time [s]') +grid on +legend(h,'GNSS aided INS estimate','3\sigma bound') + +N=length(in_data.IMU.t); +attitude=zeros(3,N); + +for n=1:N + Rb2t=q2dcm(out_data.x_h(7:10,n)); + + %Get the roll, pitch and yaw + %roll + attitude(1,n)=atan2(Rb2t(3,2),Rb2t(3,3))*180/pi; + + %pitch + attitude(2,n)=-atan(Rb2t(3,1)/sqrt(1-Rb2t(3,1)^2))*180/pi; + + %yaw + attitude(3,n)=atan2(Rb2t(2,1),Rb2t(1,1))*180/pi; +end + +ylabels={'Roll [deg]','Pitch [deg]','Yaw [deg]'}; +figure(5) +if ~holdon clf; end +h=zeros(1,2); +for k=1:3 + subplot(3,1,k) + h(1)=plot(in_data.IMU.t,attitude(k,:),'r'); + hold on + plot(in_data.IMU.t,3*180/pi*sqrt(out_data.diag_P(6+k,:))+attitude(k,:),'k--') + h(2)=plot(in_data.IMU.t,-3*180/pi*sqrt(out_data.diag_P(6+k,:))+attitude(k,:),'k--'); + grid on + ylabel(ylabels{k}) + if k==1 + title('Attitude versus time') + end +end +xlabel('Time [s]') +legend(h,'GNSS aided INS estimate','3\sigma bound') + + +figure(6) +if ~holdon clf; end +ylabels={'X-axis bias [m/s^2]','Y-axis bias [m/s^2]','Z-axis bias [m/s^2]'}; +h=zeros(1,2); +for k=1:3 + subplot(3,1,k) + h(1)=plot(in_data.IMU.t,out_data.delta_u_h(k,:),'r'); + hold on + h(2)=plot(in_data.IMU.t,3*sqrt(out_data.diag_P(9+k,:))+out_data.delta_u_h(k,:),'k--'); + plot(in_data.IMU.t,-3*sqrt(out_data.diag_P(9+k,:))+out_data.delta_u_h(k,:),'k--') + grid on + ylabel(ylabels{k}) + if k==1 + title('Accelerometer bias estimate versus time') + end +end +xlabel('Time [s]') +legend(h,'GNSS aided INS estimate','3\sigma bound') + + +figure(7) +if ~holdon clf; end +ylabels={'X-axis bias [deg/s]','Y-axis bias [deg/s]','Z-axis bias [deg/s]'}; +h=zeros(1,2); +for k=1:3 + subplot(3,1,k) + h(1)=plot(in_data.IMU.t,180/pi*out_data.delta_u_h(3+k,:),'r'); + hold on + h(2)=plot(in_data.IMU.t,3*180/pi*sqrt(out_data.diag_P(12+k,:))+180/pi*out_data.delta_u_h(3+k,:),'k--'); + plot(in_data.IMU.t,-3*180/pi*sqrt(out_data.diag_P(12+k,:))+180/pi*out_data.delta_u_h(3+k,:),'k--') + grid on + ylabel(ylabels{k}) + if k==1 + title('Gyroscope bias estimate versus time') + end +end +xlabel('Time [s]') +legend(h,'GNSS aided INS estimate','3\sigma bound') + +figure(8) +if ~holdon clf; end +xest = out_data.x_h(2,:); +yest = out_data.x_h(1,:); +xgps = interp1(in_data.GNSS.t,in_data.GNSS.pos_ned(2,:),in_data.IMU.t,'linear','extrap')'; +ygps = interp1(in_data.GNSS.t,in_data.GNSS.pos_ned(1,:),in_data.IMU.t,'linear','extrap')'; +xerr = xest - xgps; +yerr = yest - ygps; +plot(in_data.IMU.t,xerr) +grid on +hold on +plot(in_data.IMU.t,yerr) +xlabel('time [s]') +ylabel('position difference [m]') +legend('x', 'y') + +positionerr_RMS = sqrt(mean(xerr.^2+yerr.^2)) +figure(2) +end + diff --git a/matlab/q2dcm.m b/matlab/q2dcm.m new file mode 100644 index 0000000..3f36a5d --- /dev/null +++ b/matlab/q2dcm.m @@ -0,0 +1,56 @@ +function R=q2dcm(q) +% function R=q2dcm(q) +% Function for transformation from quaternions to directional cosine matrix +% Farell pp.41 +% Edit: Isaac Skog, 2007-05-24 + +p=zeros(6,1); + +p(1:4)=q.^2; + +p(5)=p(2)+p(3); + +if p(1)+p(4)+p(5)~=0 + p(6)=2/(p(1)+p(4)+p(5)); +else + p(6)=0; +end + +R(1,1)=1-p(6)*p(5); +R(2,2)=1-p(6)*(p(1)+p(3)); +R(3,3)=1-p(6)*(p(1)+p(2)); + +p(1)=p(6)*q(1); +p(2)=p(6)*q(2); +p(5)=p(6)*q(3)*q(4); +p(6)=p(1)*q(2); + +R(1,2)=p(6)-p(5); +R(2,1)=p(6)+p(5); + +p(5)=p(2)*q(4); +p(6)=p(1)*q(3); + +R(1,3)=p(6)+p(5); +R(3,1)=p(6)-p(5); + +p(5)=p(1)*q(4); +p(6)=p(2)*q(3); + +R(2,3)=p(6)-p(5); +R(3,2)=p(6)+p(5); + +% R(1,2)=2*(q(1)*q(2)-q(3)*q(4)); +% R(1,3)=2*(q(1)*q(3)+q(2)*q(4)); +% +% % Row 2 +% R(2,1)=2*(q(1)*q(2)+q(3)*q(4)); +% R(2,2)=q(2)^2+q(4)^2-q(1)^2-q(3)^2; +% R(2,3)=2*(q(2)*q(3)-q(1)*q(4)); +% +% % Row 3 +% R(3,1)=2*(q(1)*q(3)-q(2)*q(4)); +% R(3,2)=2*(q(2)*q(3)+q(1)*q(4)); +% R(3,3)=q(3)^2+q(4)^2-q(1)^2-q(2)^2; +% +% % Okej, men kan f�rb�trras, se pp 41 Farrel \ No newline at end of file -- GitLab