How do I plot the average curve from hundreds of vehicle speed curves and further show only the average curve?

I am attaching an excel file which contains vehicle trajectories data. Trajectory data were extracted form a video. They consist of the video frame numbers, each vehicle's ID, the record time, the vehicle position x and y coordinates, and the speeds were calculted based on the coordinates and time. In the excel file, the first collumn contains the tracking frame numbers (fram_num), the second collumn the vehicle's ID (veh_ID), the third collumn the tracking time (time), the fourth and fifth collumns respectively the x and y cordinates of the vehicle position (X_position, Y_position), then the last two collumns are the speeds of the vehicle respectively in the x and y directions. You can see that only three vehicles' data are present in the file, that is three different IDs. This is just a small sample for demonstration convenience. Otherwise, the original data have samples from hundreds of vehicles, so hundreds of different vehicle IDs.

First, I want to plot in the same figure all the vehicles' speeds (X_speed) against the vehicle position (X_position).

Second, I want to smoothen the courves.

Third, I want to plot a single average curve of all the hundreds curves (note that in this example only three curves will exist), that should also be smooth.

Then, if possible, in a separate figure, eliminate all other curves and show only the average curve.

For my first preoccupation, I have this code that plots all the vehicles' speed curves:

T = readtable('VehicleSpeed.xlsx','Sheet','SpeedAvg');

N = max(T.veh_id);

hold on

for k = 1:N

Tk = T(T.veh_id == k,:);

plot(Tk.X_position, Tk.X_speed);

end

hold off

xlabel('Distance (m)')

ylabel('Speed (m/s)')

The generated figure is bellow:

Then I need your valuable help for the other preoccupations, such as smoothing, average curve plotting and smoothing, and showing only the average curve in another figure while the previous figure that includes all curves with the average also exists.

Thank you in advance, and have nice weekend!

Answer 1

[Mathieu NOE]

hello

try this

as every vehicule will have a different range of x data (pos) , you need to first interpolate the data before you can average them

hope it helps !

%% step 1 : retrieve raw data, plot, store in cells for further processing 
pos_low = 0;
pos_high = Inf;
T = readtable('VehicleSpeed.xlsx','Sheet','SpeedAvg');
[vid,ia,ic] = unique(T.veh_id);
hold on
   
for k = 1:numel(vid)
    idx = T.veh_id == vid(k);
    pos{k} = T.X_position(idx);
    size(pos{k})
    vel{k} = T.X_speed(idx);
    size(vel{k})
   plot(pos{k}, vel{k});
   % define low and high range limits for future common pos axis
   pos_low = max(pos_low,pos{k}(1));
   pos_high = min(pos_high,pos{k}(end));
   
end
   hold off
   xlabel('Distance (m)')
   ylabel('Speed (m/s)')
   
%% step 2 : create common unique x axis and interpolate data, average curves, smooth
pos_all = linspace(pos_low,pos_high,300); % new x axis
   
 for k = 1:numel(vid)
    vel_int(k,:) = interp1(pos{k},vel{k},pos_all);
 end
   
vel_int_average = mean(vel_int); % average curve
vel_int_average_smoothed = smoothdata(vel_int_average,'movmedian',50); % smooth it

figure, plot(pos_all,vel_int_average,'k',pos_all,vel_int_average_smoothed,'*-');
   xlabel('Distance (m)')
   ylabel('Speed (m/s)')
   legend('average','average smoothed');
   
figure, plot(pos_all,vel_int_average_smoothed,'*-');
   xlabel('Distance (m)')
      legend('average smoothed');

   ylabel('Speed (m/s)')

[ADJE JEREMIE ALAGBE]

Perfect! Thank you so much! It works.

[Mathieu NOE]

My pleasure !