使用不均匀（不规则）采样数据进行系统识别

Question

I am trying to identify the model of my quadcopter using MATLAB's System Identification toolbox (App) and the command line. I have both the input and output signals which are both non-uniformly sampled , specifically, the sample time between consecutive measurements isn't constant throughout the experiment.

I found that it is possible to create a non-uniform data set on MATLAB using:

FlightData = iddata(inputs, outputs, [],'SamplingInstants', time, 'Name', dataName);

where time contains the non-uniform sampling time vector. However, I couldn't find any linear or nonlinear model on MATLAB that accepts such kind of non-uniform data.

I would appreciate if anyone could give any hints.

Answer 1

The support of irregular sampled data in the system identification toolbox is quite limited. Many functions of the System Identification Toolbox require regularly sampled data see this link .

From your use of iddata() I guess that your input & output data are measured pairwise at the same moment, but the timespan between adjacent samples is not regular.

In this case you can use some (linear) interpolation eg with interp1 . This can introduce some errors in the estimation, but it is a simple and fast approach. Just define the new time grid with regularly time steps and interpolate them.

% create some dummy data
time = rand(20,1);                                  % irregular sampled measurements
input = sin( 2*pi*time);                            % some input signal
output = cos( 2*pi*time );                          % some output signal

% define new time vector and interpolate input and output data
Ts = 0.01;                                          % new sampling time in seconds
newTime = min(time) : Ts : max(time);               % new time vector
inputInterp = interp1( time, input, newTime  )      % interpolated  input data
outputInterp = interp1( time, output, newTime  )    % interpolated  output data

% lets see what just happend
figure
plot( time,input,'o'), hold on
plot(time,output,'ro');

plot( newTime, inputInterp, 'x')
plot( newTime, outputInterp, 'rx')

legend({'Original Input', 'Original Output', 'Interpolated Input', 'Interpolated Output'})

should do the trick.

The errors should be small if your (original) sampling frequency is larger than the frequency of the relevant dynamics. The (rigid body) dynamics of a quadrocopter are in the order of 1 Hz, so measuring the input and output data at 50 or 100 Hz is usually fine (but this may depend on your application).