Course 02637 Advanced MatLab Programming Project 1 … · Course 02637 Advanced MatLab Programming Project 1 – GPS data processing Daniel Dittlau Pedersen, s051899

Course 02637

Advanced MatLab Programming

Project 1 – GPS data processing

Daniel Dittlau Pedersen, s051899

2

Abstract

In this project a MatLab GUI is programmed

to manipulate GPS data. Operations include

reading and saving from/to txt, csv and mat

files and converting the GPS data into

Cartesian coordinates, as well as

interpolation of the datasets using either

spline or pchip, computation of key values

(distance, duration, speed and pace),

selection of partial datasets and zooming on

the plotted data. The resultant plots can also

be exported to pdf or jpeg formats as well as

printed, both in cartesian or in GPS

coordinate systems.

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Contents Introduction ....................................................................................................................................................... 5

Overview of the GUI Window ............................................................................................................................ 5

Functions Used .................................................................................................................................................. 6

Initialization ................................................................................................................................................... 6

Loading a data set .......................................................................................................................................... 7

Read function ............................................................................................................................................ 7

GPS to Cartesian coordinates conversion function ................................................................................... 7

Load button ............................................................................................................................................... 8

Selecting type and number of points for interpolation ................................................................................. 9

Interpolating the data set .............................................................................................................................. 9

Interpolation function ............................................................................................................................... 9

Interpolation Button ................................................................................................................................ 10

Computing key values.................................................................................................................................. 11

Selecting a subset of the data ..................................................................................................................... 11

Zoom function ............................................................................................................................................. 12

Saving a data set .......................................................................................................................................... 13

Store Function ......................................................................................................................................... 13

Cartesian to GPS coordinates conversion function ................................................................................. 13

Save Button ............................................................................................................................................. 14

Exporting plots ............................................................................................................................................. 14

User guide for the GPS GUI ............................................................................................................................. 16

The Visual Outputs ...................................................................................................................................... 16

The Selectable User Inputs .......................................................................................................................... 17

Interpolation Type ................................................................................................................................... 17

Interpolation Points ................................................................................................................................. 17

The Buttons ................................................................................................................................................. 17

Load ......................................................................................................................................................... 18

Save.......................................................................................................................................................... 18

Export ...................................................................................................................................................... 19

Interpolate ............................................................................................................................................... 20

Select ....................................................................................................................................................... 21

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Zoom ........................................................................................................................................................ 22

Appendix .......................................................................................................................................................... 23

Speed Tests .................................................................................................................................................. 23

cos/sin vs .cosd/sind ................................................................................................................................ 23

Vectorized vs loops .................................................................................................................................. 23

Spline vs pchip ......................................................................................................................................... 23

Source Code ................................................................................................................................................. 24

gps.m ....................................................................................................................................................... 24

read.m ..................................................................................................................................................... 28

Store.m .................................................................................................................................................... 28

convert2Cart.m ........................................................................................................................................ 28

convert2GPS.m ........................................................................................................................................ 29

interpol.m ................................................................................................................................................ 30

compute.m .............................................................................................................................................. 30

prepareExport.m ..................................................................................................................................... 30

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Introduction

In this project a GUI is to be designed, which allow the user to import, manipulate and export GPS

data. As the code is of primary interest in this report, the various functions are included in the main

text, as opposed to being left for the appendix. This ensures a better overview of the text, as well as

saves time for the reader.

Attached to this report is a zip file containing the various MatLab files, with gps.m being the main

file. Also attached is a compiled standalone application of the program.

Overview of the GUI Window

Figure 1 – The main window

The main window consists of the elements seen in Figure 1. As can be seen, the upper part consists

of 4 axes: One large to the left containing a map of the route (with proper North/South/East/West

directions), and 3 smaller on the right containing the speed, pace and total distance covered as

functions of time.

The user interface is located in the lower part of the window in the center and to the right. In the

rightmost part are located buttons for loading, saving, exporting and interpolating, as well as

buttons to select a subset of the route and a button to toggle the zoom function on and off. In the

center of the window the type of interpolation method used can be specified using the two radio

buttons, and the number of interpolation points to be used can be selected using either the slider or

directly input as a value, ranging from 300-3300. This particular interval is used, as the initial

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dataset contained 300 points and an interpolation using less than the original data set would

decrease the smoothness of the initial curve1. The maximum value is chosen, as it allows an easy

way to get slider step increments of 10 and 100 using either the arrows or clicking on the bar

respectively.

In the lower left part, the computed key values can be seen in a table.

Functions Used

Initialization

The opening function gps_OpeningFcn is used to set up the GUI prior to opening.

As it is unknown what screen size the end-user will use, the GUI itself will center in the middle of

the screen regardless of that, by using information extracted from the users screen size. Furthermore

all the axes will be initialized with titles and labels using empty data sets. The position and size of

the GUI is also stored as a handle for later use in exporting the plots.

function gps_OpeningFcn(hObject, eventdata, handles, varargin)

% Choose default command line output for gps

handles.output = hObject;

% Update handles structure

guidata(hObject, handles);

% Centers the GUI window

movegui(hObject,'center')

handles.positionGUI = get(hObject,'Position'); % Get the position for exporting

% Prepare the axes

plot(handles.plotroute,NaN,NaN);

title(handles.plotroute,'Map of Route','FontSize',14,'FontWeight','bold')

ylabel(handles.plotroute,'South -> North')

xlabel(handles.plotroute,'West -> East')

plot(handles.plotVel,NaN,NaN);

title(handles.plotVel,'Speed','FontSize',14,'FontWeight','bold')

xlabel(handles.plotVel,'Time [s]')

ylabel(handles.plotVel,'Km/h')

plot(handles.plotPace,NaN,NaN);

title(handles.plotPace,'Pace','FontSize',14,'FontWeight','bold')

xlabel(handles.plotPace,'Time [s]')

ylabel(handles.plotPace,'Min/Km')

plot(handles.plotDist,NaN,NaN);

title(handles.plotDist,'Total distance covered','FontSize',14,'FontWeight','bold')

xlabel(handles.plotDist,'Time [s]')

ylabel(handles.plotDist,'Km')

% Prepare the uitable with key data

set(handles.keytable,'Data',{'Time spent' '' ' sec';

'Distance covered' '' ' km';

'Average speed' '' ' km/h';

'Average pace' '' ' min/km'});

guidata(hObject,handles); % Save the handle data

1 This could be used to save space and decrease computation time in larger data set, but in this particular setup, where a

smooth curve is needed (2), this is not considered as an option.

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Loading a data set

Read function

The read function, responsible for the extraction of the dataset from a file can be seen below. As can

be seen, the user is able to select the file using uigetfile, set up as to only allow .txt, .mat or csv files

to be selected. Filterindex returns the number of the selection, allowing for the different extraction

methods in the switch-statement (Case 0 is used when the user presses cancel instead of selecting a

file).

function [ dataset ] = read()

%read Reads a datafile

% Read a 3 column datafile and stores it as a cell containing a 3 columns (and n rows)

[filename,path,filterindex] = uigetfile(...

{'*.txt', 'Text file (*.txt)';...

'*.mat','Mat file (*.mat)';...

'*.csv','Comma separated file (*.csv)'},...

'Pick a file');

switch filterindex

case 0,

dataset = 0;

return

case 1,

dataset = dlmread(fullfile(path,filename));

case 2,

dataset = open(fullfile(path,filename));

case 3,

dataset = csvread(fullfile(path,filename));

end

end

GPS to Cartesian coordinates conversion function

The data set originating from the read function has to be converted from GPS coordinates to

Cartesian coordinates. This is done by the Convert2Cart function seen below.

In the start of the function various constant variables are defined, and the latitude, longitude and

time are identified and converted into radians, as this pre-conversion yield the fastest speed, as

opposed to using cosd/sind functions2.

The x, y and z components are then calculated using vectorized calculations to take advantage of

MatLabs preference for these. To get a glimpse of the speed increase in this particular function, a

method of doing the conversion using a loop is inserted (and commented out in the final version),

and the difference in calculation speed is found using tic-toc. The speed increase is found to be

more than 10 times (see the appendix for the measurements).

2 See the appendix – Speed Tests for the measured speeds using tic-toc.

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function [ xyzt ] = convert2Cart( WGS85 )

%convert2Cart Convert from WGS84 to Cartesian coordinates

% Converting an array containing data from GPS coordinate system WGS84 to Cartesian coordinates

% using the formulas:

%

% X = (v+h)*cos(theta)*cos(lambda)

% Y = (v+h)*cos(theta)*sin(lambda)

% Z = (v*(1-exp(2))+h)*sin(theta)

%

% Be aware that the input data should be in format [langtitude longitude timestamp]

a = 6378137;

f = 1/298.257223563;

e_2 = f*(2-f);

h = 0; % Assuming zero height

latitude = WGS85(:,1)*pi/180;

longitude = WGS85(:,2)*pi/180;

T = WGS85(:,3);

% Slow way

% for k = 1:length(latitude)

% v = a/sqrt(1-e_2*sin(latitude(k))^2);

% X(k) = (v+h)*cos(latitude(k))*cos(longitude(k));

% Y(k) = (v+h)*cos(latitude(k))*sin(longitude(k));

% Z(k) = (v*(1-e_2)+h)*sin(latitude(k));

% end

%

% xyzt = [X' Y' Z' T];

% Fast way

v = (a./sqrt(1-e_2.*sin(latitude).^2));

X = (v+h).*cos(latitude).*cos(longitude);

Y = (v+h).*cos(latitude).*sin(longitude);

Z = (v.*(1-e_2)+h).*sin(latitude);

xyzt = [X Y Z T];

end

Load button

The read and convert2Cart functions are incorporated into the load button of the GUI in the function

loadbutton_Callback shown below. After the imported data has been stored in a handle, the data

points are plotted (as circles) and the axes are properly set up like in the initialization of the GUI.

The reason for doing this again, is to clear plots and values from any older data set when a new one

is loaded into the GUI. Again the handles added in this function are saved in the end.

function loadbutton_Callback(hObject, eventdata, handles)

handles.datasetGPS = read();

if handles.datasetGPS == 0

return;

end

handles.datasetxyz = convert2Cart(handles.datasetGPS);

plot(handles.plotroute,handles.datasetxyz(:,2),handles.datasetxyz(:,1),'o');

set(handles.plotroute,'YDir','reverse'); % reverse the second axis to get

correct mapping






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title(handles.plotDist,'Total distance

covered','FontSize',14,'FontWeight','bold')



guidata(hObject,handles); % save the data into the GUI

Selecting type and number of points for interpolation

The two different types of interpolation methods available are the spline and pchip. The method is

selected using 2 radio buttons, which will call the interpolatebutton_Callback function immediately

if changed.

The number of interpolation points can be set both using a slider and using an editable text box.

These work together, using the method described in (1) as seen in the two functions

inter_points_Callback and inter_points_slider_Callback below.

function inter_points_Callback(hObject, eventdata, handles)

val = round(eval(get(hObject, 'string')));

interval = [get(handles.inter_points_slider, 'min'), get(handles.inter_points_slider, 'max')];

if val <= interval(2) & interval(1) <= val

set(handles.inter_points_slider,'value',val);

else

uiwait(warndlg('Interpolation steps must be between 300 and 3000','Warning','modal'))

uiresume

end

function inter_points_slider_Callback(hObject, eventdata, handles)

set(handles.inter_points, 'string',num2str(round(get(hObject,'value'))))

Interpolating the data set

Interpolation function

The interpolation of the data points is done using the interpol function, which then either uses the

spline or pchip function according to what is specified by the user. Speed measurements are done

on each of the interpolation methods, to see which one is faster in our case. As can be seen from the

measurements (see appendix) the pchip function seems to be the fastest for this particular data set,

which is most likely due to the less expensive set up of this function3. Had the data set been larger,

the two functions would in theory take approximately the same time to evaluate.

function [ dataout ] = interpol( datain, type, n )

%interpol interpolate the data points of a given set

3 As stated in the help description in MatLab of pchip.

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% This function allows for 2 different interpolation methods, spline and

% pchip, selectable by setting the 2. argument to 1 or 2 respectively.

% Furthermore it allows the user to specify the number of interpolation

% points using the 3. argument.

x = datain(:,1)';

y = datain(:,2)';

z = datain(:,3)';

t = datain(:,4)';

tt = linspace(min(t),max(t),n);

switch type

case 1,

xx = spline(t,x,tt);

yy = spline(t,y,tt);

zz = spline(t,z,tt);

case 2,

xx = pchip(t,x,tt);

yy = pchip(t,y,tt);

zz = pchip(t,z,tt);

end

dataout(:,1)=xx;

dataout(:,2)=yy;

dataout(:,3)=zz;

dataout(:,4)=tt;

end

Interpolation Button

The interpolatebutton_Callback takes the values from the slider and the radio buttons to decide the

parameters with which to call the Interpol function. The computation of key values from the

interpolated data set is then carried out using the compute function and shown in the table, and the

interpolated values is plotted in the same axes as the original data points.

function interpolatebutton_Callback(hObject, eventdata, handles)

points = get(handles.inter_points_slider,'value');

radio = get(handles.interpol_type_panel,'SelectedObject');

switch get(radio,'tag')

case 'radiobutton_spline',

handles.interpol_data = interpol(handles.datasetxyz,1,points);

case 'radiobutton_pchip',


end

handles.keyvalues = compute(handles.interpol_data);

% Plot the data

plot(handles.plotroute,handles.datasetxyz(:,2),handles.datasetxyz(:,1),'o',handles.interpol_data(:,2

),handles.interpol_data(:,1));

set(handles.plotroute,'YDir','reverse') % reverse the second axis to get correct mapping

plot(handles.plotVel,handles.interpol_data(4:end-1,4),handles.keyvalues.inst_speed(4:end-1))

plot(handles.plotPace,handles.interpol_data(4:end-1,4),handles.keyvalues.inst_pace(4:end-1))

plot(handles.plotDist,handles.interpol_data(:,4),handles.keyvalues.dist_array./1000)













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% Fill the uitable with key data

set(handles.keytable,'Data',{'Time spent' handles.keyvalues.totaltime/60 ' min';

'Distance covered' handles.keyvalues.totaldist/1000 ' km';

'Average speed' handles.keyvalues.avg_speed ' km/h';

'Average pace' handles.keyvalues.avg_pace ' min/km'});


Computing key values

The key values is extracted using the compute function seen below, which is called when either the

interpolation button is pressed or a subset is selected.

The function calculate the covered distance at each time interval using the cumulative sum function

cumsum, with the point-to-point distance calculated as

√ ) )) ) )) ) ))

where the difference between the two values are calculated using the diff function. Instantaneous

speed (the speed at a single point) is calculated using the formula

where the distance traveled and the time it took is again found using the diff function. The rest of

the key values are easily found using trivial calculations.

function [ keyvalues ] = compute( datain )

%Compute Computes the key values from a given data set

% Computes distance as well as both average and instantaneous speed and pace

keyvalues.dist_array = [0;cumsum(sqrt(diff(datain(:,1)).^2 + diff(datain(:,2)).^2 +

diff(datain(:,3)).^2))];

keyvalues.totaltime = (datain(end,4)-datain(1,4)); % sec

keyvalues.totaldist = keyvalues.dist_array(end); % m

keyvalues.inst_speed = [0;diff(keyvalues.dist_array)./diff(datain(:,4)).*3.6]; % km/h

keyvalues.avg_speed = ((keyvalues.totaldist)/(keyvalues.totaltime))*3.6; % km/h

keyvalues.inst_pace = 1./(keyvalues.inst_speed./60); % min/km

keyvalues.avg_pace = 1/(keyvalues.avg_speed/60); % min/km

end

Selecting a subset of the data

The Select button allows the user to select start and end points for a subset of the data set using the

mouse. To do this the ginput function is used, which stores the 2 points as an x- and y value

(keeping in mind, that the plotted route has its x- and y values switched, to get correct positioning.

As the ginput allows the user to click everywhere on the axis, the actual point in the data set with

the least distance to the user selected point is found using the min function with the index returned.

To ensure that the user can select everywhere in the data set regardless of the first index (point)

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selected is higher or lower than the second, the min and max functions are used to access the data

set when extracting the subset.

After the extraction the new key values are calculated and shown and the new subset is plotted in

the axes.

function selectbutton_Callback(hObject, eventdata, handles)

[y,x] = ginput(2); % reversed axis

[C I] = min(sqrt((handles.interpol_data(:,1)-x(1)).^2+(handles.interpol_data(:,2)-y(1)).^2));

start_stop(1) = I;


start_stop(2) = I;

handles.selected_data = handles.interpol_data(min(start_stop):max(start_stop),:);

handles.keyvalues = compute(handles.selected_data);

% Plot the data

plot(handles.plotroute,handles.datasetxyz(:,2),handles.datasetxyz(:,1),'o',...

handles.interpol_data(:,2),handles.interpol_data(:,1),handles.selected_data(:,2),...

handles.selected_data(:,1),'red');


plot(handles.plotVel,handles.selected_data(3:end-1,4),handles.keyvalues.inst_speed(3:end-1))

plot(handles.plotPace,handles.selected_data(3:end-1,4),handles.keyvalues.inst_pace(3:end-1))

plot(handles.plotDist,handles.selected_data(:,4),handles.keyvalues.dist_array)



















Zoom function

The function allowing the user to zoom on the presented axes is made with a toggle button and

shown below.

function togglebutton_zoom_Callback(hObject, eventdata, handles)

if get(hObject,'Value')==1

zoom on

else

zoom off

end

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Saving a data set

Store Function

The store function first checks in what coordinate format the user has selected to save in, and calls

the conversion function if GPS coordinate format is chosen. The function then uses the built-in

uiputfile to allow the user to select a name and one of 3 different formats. Based on the selected

format, the correct write-function is called,

function store( xyzdata, dataselect )

%store Stores data in a file using selected format

switch dataselect % if saving gps format

case 'Cartesian',

data = xyzdata; % do nothing

case 'GPS',

data = convert2GPS(xyzdata); % Convert to gps coordinates

end

[filename,path,filterindex] = uiputfile(...



'*.csv','Comma separated file (*.csv)';...

'*.*', 'All Files (*.*)'},...

'Save as');

switch filterindex

case 1,

dlmwrite(fullfile(path,filename),data,'delimiter', ' ')

case 2,

save(fullfile(path,filename),'data')

case 3,

csvwrite(fullfile(path,filename),data)

end

end

Cartesian to GPS coordinates conversion function

If the user opts for saving in GPS coordinates, the convert2GPS function takes care of this. The

method for calculating back to GPS coordinates are found in (2), using the closed formula.

function [ WGS84 ] = convert2GPS( xyzt )

%convert2GPS Convert from Cartesian to WGS84 coordinates

% Converting an array containing data from Cartesian coordinate system to GPS

% coordinate system WGS84 using the formulas:

%

% longitude = arctan(y/z)

% Latitude = latitude = atan2((z+e_m2*b*sin(phi).^3),(p-e2*a*cos(phi).^3))

% where

% a = 6378137;

% f = 1/298.257223563;

% b = a*(1-f);

% e2 = (a^2-b^2)/a^2;

% e_m2 = f*(2-f)/(1-f)^2;

% p = sqrt(x.^2+y.^2)

% phi = atan2(z*a,(p*b));

%

% Be aware that the input data should be in format [x y z timestamp]

% Extracting the values

x = xyzt(:,1);

y = xyzt(:,2);

z = xyzt(:,3);

t = xyzt(:,4);

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% Defining constants

a = 6378137;

f = 1/298.257223563;

b = a*(1-f);

e2 = (a^2-b^2)/a^2;

e_m2 = f*(2-f)/(1-f)^2;

% Calculating auxiliary constant

p = sqrt(x.^2+y.^2);

phi = atan2(z*a,(p*b));

% Calculating latitude and longitude

latitude = atan2((z+e_m2*b*sin(phi).^3),(p-e2*a*cos(phi).^3));

longitude = atan2(y,x);

WGS84(:,1) = latitude*180/pi;

WGS84(:,2) = longitude*180/pi;

WGS84(:,3) = t;

end

Save Button

The save button consists of 2 question dialogues and 2 switch cases, allowing the user to select

whether to save the whole interpolated data set or just the selected subset. Furthermore it allows the

user to select the format in which the data will be stored, either Cartesian coordinates or GPS

coordinates.

function savebutton_Callback(hObject, eventdata, handles)

% Ask whether to save in Cartesian or GPS coordinates

choice2 = questdlg ('Do you want to save in Cartesian or GPS coordinates?',...

'Format of save-file','Cartesian','GPS','Cancel','Cartesian');

switch choice2

case 'Cancel',

return;

otherwise

end

% Then ask whether to save whole data set or just the selected data

choice1 = questdlg ('Do you want to save the whole dataset or just the selected data?',...

'Choose dataset','Whole set','Selected subset','Cancel','Whole set');

switch choice1

case 'Whole set',

store(handles.interpol_data,choice2);

case 'Selected subset',

store(handles.selected_data,choice2);

case 'Cancel',

return;

end

Exporting plots

In order to exporting the plotted data, the axes need to be made into a figure. This is done using the

prepareExport function seen below. This function first creates an invisible figure with the same size

as the original GUI figure, and then copies the axes into this new figure. It then sets various

parameters to make sure the new figure is printable.

function preparedFig = prepareExport( route,speed,pace,dist,figSize )

%prepareExport

% This function prepares the 4 axes from the gps GUI to be printed or

% exported to an image file. It takes the 4 axes and turn them into a

15

% figure instead. It also sets various parameters to ensure the right

% setup of the printing.

preparedFig = figure('visible','off');

set(preparedFig,'position',figSize)

copyobj(route,gcf)

copyobj(speed,gcf)

copyobj(pace,gcf)

copyobj(dist,gcf)

set(gcf,'PaperPositionMode','auto');

set(gcf,'InvertHardcopy','off')

set(gcf,'PaperType','A4')

set(gcf,'PaperUnits','centimeters')

set(gcf,'Paperorientation','landscape')

set(gcf,'PaperPositionMode','auto')

end

When pressing the export button, the user is first subjected to a quest dialogue asking whether to

save as pdf of jpg image, or print the figure. If print is selected the function opens the print dialogue

and if the user selects pdf format, the function uses the print function to save the prepared figure in

pdf format. If jpg is selected, the user is presented with the choice of resolution in the image: Low,

Medium and Optimal, where Optimal uses the resolution of the users screen and the other 2

represents resolutions of 90 and 150 dots per inch respectively.

function exportbutton_Callback(hObject, eventdata, handles)

preparedFig = prepareExport(handles.plotroute,handles.plotVel,handles.plotPace,...

handles.plotDist,handles.positionGUI)

choice = questdlg ('Do you want to save or print the figures?',...

'Save or print?','Save as PDF','Save as JPG','Print','Save as JPG');

switch choice

case 'Save as PDF',

filename = inputdlg('Select a filename:','Name')

print(preparedFig,'-dpdf','-loose',filename{1})

case 'Save as JPG',


res = questdlg ('Select resolution of

image','Resolution?','Low','Medium','Optimal','optimal');

switch res

case 'Low'

print(preparedFig,'-djpeg','-r90','-loose',filename{1})

case 'Medium'


case 'Optimal'


end

case 'Print',

printdlg(preparedFig)

end

16

User guide for the GPS GUI

The Visual Outputs

figure 2 – The visual outputs

The graphs are located in the upper part of the window as can be seen in figure 2. The one to the left

shows the route and the 3 to the right shows the speed, pace and distance covered, all as functions

of the time. The last 3 graphs are only available after interpolation has taken place.

At the bottom left of the window, the time spent and the total distance covered are shown as well as

the average speed and pace, calculated either from the interpolated data or a subset of this.

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The Selectable User Inputs

figure 3 – The location of editable user inputs

Interpolation Type

The radio buttons here are used to select the interpolation type. Available selections are between the

spline method or the pchip method.

Interpolation Points

Here the amount of interpolation points is selected either by using the slider or typing in a value in

the box above. Allowed values range between 300 and 3300.

The Buttons

figure 4 – The location of the user buttons

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Load

Pressing this button allows for the import of GPS coordinate data, which can be selected from .txt,

.csv and .mat files as seen in figure 5.

figure 5 – Loading a data set

Save

The save button allows for storage of the interpolated data set. The user has the selection of whether

to store the whole data set or just a subsection, and whether the data set should be saved in

Cartesian coordinates or GPS coordinates, and will be prompted as seen in figure 6 and figure 7.

figure 6 – Selection of Cartesian vs. GPS

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figure 7 – Select dataset to be saved

Export

The export button allow for exporting the plotted data either to a file, pdf or jpg, or to a printer. The

user will be asked whether to print or save as shown in figure 8. If the jpg format is chosen, the user

will also be asked to select the resolution for the image file as seen in figure 9, with the options of

low, medium or optimal, where the optimal setting is based on the resolution of the users screen.

The resultant image can be seen in figure 10.

figure 8 – Save or print

20

figure 9 – Choose resolution

figure 10 – image file

Interpolate

The interpolate button will interpolate the imported data set, and show the new data set as a curve

on top of the old data points. Furthermore a number of key values will be calculated and shown in

the box in the lower left corner of the window, and these will also be plotted as functions of time

and shown in the upper right side of the window.

21

Select

The select button allows for the selection of a subset of the plotted data. The user selects this with

the mouse by first clicking at one point (or close by), and then clicking on a second point to

complete the selection which is now marked in red. The procedure is shown in figure 11 and figure

12

figure 11 – Selecting the interval

figure 12 – The completed selection

22

Zoom

The zoom button allows the user to zoom on any of the plotted data sets, shown in figure 13. To

enter zoom mode press the zoom button. When the zooming is completed press the zoom button

again to exit zoom mode.

figure 13 - Zooming

23

Appendix

Speed Tests

All the tests below are conducted using an Intel Core2Duo E7400 processor with 2 GB DDR2

RAM available.

cos/sin vs .cosd/sind

Below can be seen tic-toc responses from convert2Cart() when using the cosd/sind functions as

opposed to converting the values into radians and then using the cos/sin functions. First 3 runs are

cosd/sind, the last 3 is using precalculation:

Elapsed time is 0.000307 seconds.






Vectorized vs loops

Tic-toc measurements for the coordinate conversion function convert2Cart(). Upper 3 runs are from

the loop, bottom 3 is from vectorized calculations:







Spline vs pchip

400 points:

Spline Pchip







3300 points

Spline Pchip







24

Source Code

gps.m

function varargout = gps(varargin)

%GPS M-file for gps.fig

%

% This GUI allows the user to import, manipulate and save GPS data.

% Operations include reading and saving from/to txt, csv and mat

% files and converting the GPS data into Cartesian coordinates, as

% well as interpolation of the datasets using either spline or pchip,

% computation of key values (distance, duration, speed and pace),

% selection of partial datasets and zooming on the plotted data.

% The resultant plots can also be exported to pdf or jpeg formats.

% Begin initialization code - DO NOT EDIT

gui_Singleton = 1;

gui_State = struct('gui_Name', mfilename, ...

'gui_Singleton', gui_Singleton, ...

'gui_OpeningFcn', @gps_OpeningFcn, ...

'gui_OutputFcn', @gps_OutputFcn, ...

'gui_LayoutFcn', [], ...

'gui_Callback', []);

if nargin && ischar(varargin{1})

gui_State.gui_Callback = str2func(varargin{1});

end

if nargout

[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});

else

gui_mainfcn(gui_State, varargin{:});

end

% End initialization code - DO NOT EDIT

% --- Executes just before gps is made visible.

function gps_OpeningFcn(hObject, eventdata, handles, varargin)

% Choose default command line output for gps

handles.output = hObject;

% Update handles structure

guidata(hObject, handles);

% Centers the GUI window

movegui(hObject,'center')

handles.positionGUI = get(hObject,'Position'); % Get the position for exporting

% Prepare the axes

plot(handles.plotroute,NaN,NaN);
















% Prepare the uitable with key data

set(handles.keytable,'Data',{'Time spent' '' ' sec';

'Distance covered' '' ' km';

'Average speed' '' ' km/h';

'Average pace' '' ' min/km'});

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% UIWAIT makes gps wait for user response (see UIRESUME)

% uiwait(handles.figure1);

% --- Outputs from this function are returned to the command line.

function varargout = gps_OutputFcn(hObject, eventdata, handles)

% Get default command line output from handles structure

varargout{1} = handles.output;

% --- Executes on button press in loadbutton.

function loadbutton_Callback(hObject, eventdata, handles)

handles.datasetGPS = read();

if handles.datasetGPS == 0

return;

end

handles.datasetxyz = convert2Cart(handles.datasetGPS);

plot(handles.plotroute,handles.datasetxyz(:,2),handles.datasetxyz(:,1),'o');

set(handles.plotroute,'YDir','reverse'); % reverse the second axis to get correct mapping
















guidata(hObject,handles); % save the data into the GUI

% --- Executes on button press in savebutton.

function savebutton_Callback(hObject, eventdata, handles)

% Ask whether to save in Cartesian or GPS coordinates

choice2 = questdlg ('Do you want to save in Cartesian or GPS coordinates?',...

'Format of save-file','Cartesian','GPS','Cancel','Cartesian');

switch choice2

case 'Cancel',

return;

otherwise

end

% Then ask whether to save whole data set or just the selected data

choice1 = questdlg ('Do you want to save the whole dataset or just the selected data?',...

'Choose dataset','Whole set','Selected subset','Cancel','Whole set');

switch choice1

case 'Whole set',

store(handles.interpol_data,choice2);

case 'Selected subset',

store(handles.selected_data,choice2);

case 'Cancel',

return;

end

% --- Executes on button press in interpolatebutton.

function interpolatebutton_Callback(hObject, eventdata, handles)

points = get(handles.inter_points_slider,'value');

26

radio = get(handles.interpol_type_panel,'SelectedObject');

switch get(radio,'tag')

case 'radiobutton_spline',


case 'radiobutton_pchip',


end

handles.keyvalues = compute(handles.interpol_data);

% Plot the data

plot(handles.plotroute,handles.datasetxyz(:,2),handles.datasetxyz(:,1),'o',handles.interpol_data(:,2

),handles.interpol_data(:,1));


plot(handles.plotVel,handles.interpol_data(4:end-1,4),handles.keyvalues.inst_speed(4:end-1))

plot(handles.plotPace,handles.interpol_data(4:end-1,4),handles.keyvalues.inst_pace(4:end-1))

plot(handles.plotDist,handles.interpol_data(:,4),handles.keyvalues.dist_array./1000)



















% --- Executes on button press in exportbutton. function exportbutton_Callback(hObject, eventdata, handles)

preparedFig = prepareExport(handles.plotroute,handles.plotVel,handles.plotPace,...

handles.plotDist,handles.positionGUI)

choice = questdlg ('Do you want to save or print the figures?',...

'Save or print?','Save as PDF','Save as JPG','Print','Save as JPG');

switch choice

case 'Save as PDF',


print(preparedFig,'-dpdf','-loose',filename{1})

case 'Save as JPG',


res = questdlg ('Select resolution of

image','Resolution?','Low','Medium','Optimal','optimal');

switch res

case 'Low'


case 'Medium'


case 'Optimal'


end

case 'Print',

printdlg(preparedFig)

end

% --- Executes during object creation, after setting all properties.

function inter_points_CreateFcn(hObject, eventdata, handles)

% Hint: edit controls usually have a white background on Windows.

% See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

set(hObject,'BackgroundColor','white');

27

end

% --- Executes on slider movement.

function inter_points_slider_Callback(hObject, eventdata, handles)

set(handles.inter_points, 'string',num2str(round(get(hObject,'value'))))

% --- Executes during object creation, after setting all properties.

function inter_points_slider_CreateFcn(hObject, eventdata, handles)

if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

set(hObject,'BackgroundColor',[.9 .9 .9]);

end

% --- Executes on button press in selectbutton.

function selectbutton_Callback(hObject, eventdata, handles)

[y,x] = ginput(2); % reversed axis


start_stop(1) = I;


start_stop(2) = I;

handles.selected_data = handles.interpol_data(min(start_stop):max(start_stop),:);

handles.keyvalues = compute(handles.selected_data);

% Plot the data

plot(handles.plotroute,handles.datasetxyz(:,2),handles.datasetxyz(:,1),'o',...

handles.interpol_data(:,2),handles.interpol_data(:,1),handles.selected_data(:,2),...

handles.selected_data(:,1),'red');


plot(handles.plotVel,handles.selected_data(3:end-1,4),handles.keyvalues.inst_speed(3:end-1))

plot(handles.plotPace,handles.selected_data(3:end-1,4),handles.keyvalues.inst_pace(3:end-1))

plot(handles.plotDist,handles.selected_data(:,4),handles.keyvalues.dist_array)



















% --- Executes on button press in togglebutton_zoom.

function togglebutton_zoom_Callback(hObject, eventdata, handles)

if get(hObject,'Value')==1

zoom on

else

zoom off

end

% --- Executes when selected object is changed in interpol_type_panel.

function interpol_type_panel_SelectionChangeFcn(hObject, eventdata, handles)

interpolatebutton_Callback(handles.interpolatebutton,0,handles)

28

read.m

function [ dataset ] = read()

%read Reads a datafile

% Read a 3 column datafile and stores it as a cell containing a 3 columns (and n rows)

[filename,path,filterindex] = uigetfile(...



'*.csv','Comma separated file (*.csv)'},...

'Pick a file');

switch filterindex

case 0,

dataset = 0;

return

case 1,

dataset = dlmread(fullfile(path,filename));

case 2,

dataset = open(fullfile(path,filename));

case 3,

dataset = csvread(fullfile(path,filename));

end

end

Store.m

function store( xyzdata, dataselect )

%store Stores data in a file using selected format

switch dataselect % if saving gps format

case 'Cartesian',

data = xyzdata; % do nothing

case 'GPS',

data = convert2GPS(xyzdata); % Convert to gps coordinates

end

[filename,path,filterindex] = uiputfile(...



'*.csv','Comma separated file (*.csv)';...

'*.*', 'All Files (*.*)'},...

'Save as');

switch filterindex

case 1,

dlmwrite(fullfile(path,filename),data,'delimiter', ' ')

case 2,

save(fullfile(path,filename),'data')

case 3,

csvwrite(fullfile(path,filename),data)

end

end

convert2Cart.m

function [ xyzt ] = convert2Cart( WGS84 )

%convert2Cart Convert from WGS84 to Cartesian coordinates

% Converting an array containing data from GPS coordinate system WGS84 to Cartesian coordinates

% using the formulas:

%

% X = (v+h)*cos(theta)*cos(lambda)

% Y = (v+h)*cos(theta)*sin(lambda)

% Z = (v*(1-exp(2))+h)*sin(theta)

%

% Be aware that the input data should be in format [langtitude longitude timestamp]

a = 6378137;

f = 1/298.257223563;

e_2 = f*(2-f);

h = 0; % Assuming zero height

29

latitude = WGS84(:,1)*pi/180;

longitude = WGS84(:,2)*pi/180;

T = WGS84(:,3);

% Slow way

% for k = 1:length(latitude)

% v = a/sqrt(1-e_2*sin(latitude(k))^2);

% X(k) = (v+h)*cos(latitude(k))*cos(longitude(k));

% Y(k) = (v+h)*cos(latitude(k))*sin(longitude(k));

% Z(k) = (v*(1-e_2)+h)*sin(latitude(k));

% end

%

% xyzt = [X' Y' Z' T];

% Fast way

v = (a./sqrt(1-e_2.*sin(latitude).^2));

X = (v+h).*cos(latitude).*cos(longitude);

Y = (v+h).*cos(latitude).*sin(longitude);

Z = (v.*(1-e_2)+h).*sin(latitude);

xyzt = [X Y Z T];

end

convert2GPS.m

function [ WGS84 ] = convert2GPS( xyzt )

%convert2GPS Convert from Cartesian to WGS84 coordinates

% Converting an array containing data from Cartesian coordinate system to GPS

% coordinate system WGS84 using the formulas:

%

% longitude = arctan(y/z)

% Latitude = latitude = atan2((z+e_m2*b*sin(phi).^3),(p-e2*a*cos(phi).^3))

% where

% a = 6378137;

% f = 1/298.257223563;

% b = a*(1-f);

% e2 = (a^2-b^2)/a^2;

% e_m2 = f*(2-f)/(1-f)^2;

% p = sqrt(x.^2+y.^2)

% phi = atan2(z*a,(p*b));

%

% Be aware that the input data should be in format [x y z timestamp]

% Extracting the values

x = xyzt(:,1);

y = xyzt(:,2);

z = xyzt(:,3);

t = xyzt(:,4);

% Defining constants

a = 6378137;

f = 1/298.257223563;

b = a*(1-f);

e2 = (a^2-b^2)/a^2;

e_m2 = f*(2-f)/(1-f)^2;

% Calculating auxiliary constant

p = sqrt(x.^2+y.^2);

phi = atan2(z*a,(p*b));

% Calculating latitude and longitude

latitude = atan2((z+e_m2*b*sin(phi).^3),(p-e2*a*cos(phi).^3));

longitude = atan2(y,x);

WGS84(:,1) = latitude*180/pi;

WGS84(:,2) = longitude*180/pi;

WGS84(:,3) = t;

end

30

interpol.m

function [ dataout ] = interpol( datain, type, n )

%interpol interpolate the data points of a given set

% This function allows for 2 different interpolation methods, spline and

% pchip, selectable by setting the 2. argument to 1 or 2 respectively.

% Furthermore it allows the user to specify the number of interpolation

% points using the 3. argument.

x = datain(:,1)';

y = datain(:,2)';

z = datain(:,3)';

t = datain(:,4)';

tt = linspace(min(t),max(t),n);

switch type

case 1,

xx = spline(t,x,tt);

yy = spline(t,y,tt);

zz = spline(t,z,tt);

case 2,

xx = pchip(t,x,tt);

yy = pchip(t,y,tt);

zz = pchip(t,z,tt);

end

dataout(:,1)=xx;

dataout(:,2)=yy;

dataout(:,3)=zz;

dataout(:,4)=tt;

end

compute.m

function [ keyvalues ] = compute( datain )

%Compute Computes the key values from a given data set

% Computes distance as well as both average and instantaneous speed and pace

keyvalues.dist_array = [0;cumsum(sqrt(diff(datain(:,1)).^2 + diff(datain(:,2)).^2 +

diff(datain(:,3)).^2))];

keyvalues.totaltime = (datain(end,4)-datain(1,4)); % sec

keyvalues.totaldist = keyvalues.dist_array(end); % m

keyvalues.inst_speed = [0;diff(keyvalues.dist_array)./diff(datain(:,4)).*3.6]; % km/h

keyvalues.avg_speed = ((keyvalues.totaldist)/(keyvalues.totaltime))*3.6; % km/h

keyvalues.inst_pace = 1./(keyvalues.inst_speed./60); % min/km

keyvalues.avg_pace = 1/(keyvalues.avg_speed/60); % min/km

end

prepareExport.m

function preparedFig = prepareExport( route,speed,pace,dist,figSize )

%prepareExport

% This function prepares the 4 axes from the gps GUI to be printed or

% exported to an image file. It takes the 4 axes and turn them into a

% figure instead. It also sets various parameters to ensure the right

% setup of the printing.

preparedFig = figure('visible','off');

set(preparedFig,'position',figSize)

copyobj(route,gcf)

copyobj(speed,gcf)

copyobj(pace,gcf)

copyobj(dist,gcf)

set(gcf,'PaperPositionMode','auto');

set(gcf,'InvertHardcopy','off')

set(gcf,'PaperType','A4')

set(gcf,'PaperUnits','centimeters')

set(gcf,'Paperorientation','landscape')

set(gcf,'PaperPositionMode','auto')

end

Documents

Course 02637 Advanced MatLab Programming Project 1 … · Course 02637 Advanced MatLab Programming Project 1 – GPS data processing Daniel Dittlau Pedersen, s051899