I need to develop an algorithm that will compare two signals (1 Reference Signal and other is measured signal values from sensor) and generate some metric(s) to describe changes between them. I am not good at signal processing and analysis so I would appreciate any help.
I have attached figures below to provide an idea about how my both signals looks like.
Some of the differences that I am expecting are:
1 -Amount of error between Reference signal and measured values signal.(I want to calculate value of overall error or difference occurred).
2- Changes that occurred in measured signal from reference signal like Amplitude change in some parts, phase changes, offset occurred, Difference in Peaks and troughs, rise and fall transitions.
(In short I want to have an overall idea about all the changes that happened in measured signal in comparison from reference signal). My signal is too complex and has lot of values so I remained unable to develop an approach for it from my side.
The algorithm needs to output some generic metrics which can be used to quantify changes in any or all of these parameters. Any guidance on what method(s) I could use to do this would be a great help.
For the case of finding errors I have think of RMSE is it a good idea to take this approach as the length of my signals are same. Given the data reference signal and sensor signal data of size 1x1626100 and 1 x 1626100 double.
Correlation function also came into my mind but according to my knowledge I can only find similarity between different signals using correlation function not the total error or overall changes that occurred in signal.
The signal is generated provides an information about changes in steering angle along with time.
Various measurements are taken over time at the same location and the final objective is to determine how the signals have changed over time (due to physical/Hardware changes).
We have taken different tests to find out how physical/Hardware changes affect my signal values and in every test speed, velocity or brakes condition of cars are different. I also needs to take into account these things for my algorithm.
The measurement system may indeed be moving at different speeds, and may have different acceleration profiles during the measurement. This needs to be accounted for in my algorithm.
I am performing this algorithm development in Matlab.
sum(abs((refrence_signal-measured_signal).^2))/length(refrence_signal); use this code to detect the average (over all) error; this term called "Mean Square Error" and it gives a better indecation.
For tracking the amplitude changes use this code,
abs((abs(refrence_signal)-abs(measured_signal)).^2), you will get on the amplitude changing at all domain.
For tracking the phase changes use this code,
abs((angle(refrence_signal)-angle(measured_signal)).^2), you will get on the phase changing at all domain.
if you need to compute without MSE just remove the (.^2) from each code, good luck.
Are you expecting there to be a time shift?
Regardless, if you are just expecting the signals (x & y) to be scaled versions of each other, I.e. y=b*x, you could regress one signal against the other, usingy std linear regression with 1 degree of freedom (b), to minimise the sum of squared errors. You could use an error weighting function to emphasise certain parts.
First of all you have to go from what you have to probability distributions. For this you should normalize your data such that it sums up to one.
Then use the KL divergence (KL) to measure the distance between the two probability distributions. KL is sensitive to any difference between the histograms.
One disadvantage of the KL divergence is that when the two histograms are completely non-overlapping, the KL divergence approaches infinity.
By figures interpretation and reading your problem statement ......
The figures looks like same by visual inspection but you can quantify it by MSE or by correlation coefficient that will vary between -1 to 1 (A value of 0 indicates that there is no association between the two variables. A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable) or by statistical criteria.
But all these depends on application and criteria used by domain researcher.
As you mention that it is for automotive or car then that system has some model or characteristic frequency for that case you analyse you signal in frequency domain. Find the spectrum of both the signal and compare the signals with respect to frequency and its amplitude.
Dear Nasir,
The root mean square error RMSE is the most expressive quantity for the difference between two sets of similar samples x(t), xr(t), where x(t) is the measured signal and xr(t) is the reference signal.
RMSE= SQROOT of (Integral (x-xr)^2 ) over the interested time interval,
For discrete time signal x[n] and xr[n],
the RMSE= SQROOT of (SUM (x[n]- xr[n])^2) over all samples N.
One can use this scheme to compare one dimensional as yours and higher dimensional similar signals.
Best wishes
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