Extracting near constant elements from an array

I have a vector 'data(1).IAS' , which looks like as follows.

 data(1).IAS
 ans =
   288
   294
   296
   294
    .
    .  % length(data(1).IAS) = 153.

I am trying to extract the near constant elements from a vector as shown in the figure (The figure is IAS plotted against its index number).

The problem is that my data.IAS has 693 arrays and it is not possible to do it one by one. Does anyone have any idea how to extract the only near constant parts?

Thanks.

UPDATE: Code

data = load('SSR_20140103.mat'); % Variable name is 'data' with various fields.
newData = data.data;      
for i = 1: length(data.data) 
 x = data.data(i).IAS;
 h = [1 1 1 1 1 1 1 1 1 1];
 if(length(x)>1)

       x1 = [ones(length(h),1)*x(1);x];                                          
       x2 = filter(h,1,x1)/length(h); 
       x2 = x2(length(h):length(x2)-1); 
       diffx2 = diff(x2); 
       diffx2 = [ones(length(h),1)*diffx2(1);diffx2]; 
       meandiffx2 = filter(h,1,diffx2)/length(h); 
       meandiffx2 = abs(meandiffx2(length(h):length(meandiffx2)));      
       constantIndex = find(meandiffx2<0.25);
       constantData.index = constantIndex;
       constantData.data = x(constantIndex);
       constantValues(i) = {constantData};

       newData(i).time = data.data(i).time(constantIndex);
       newData(i).lat = data.data(i).lat(constantIndex);
       newData(i).lng = data.data(i).lng(constantIndex);
       newData(i).altitude = data.data(i).altitude(constantIndex);
       newData(i).selected_altitude = data.data(i).selected_altitude(constantIndex);
       newData(i).BPS = data.data(i).BPS(constantIndex);
       newData(i).RA = data.data(i).RA(constantIndex);
       newData(i).TTA = data.data(i).TTA(constantIndex);
       newData(i).GS = data.data(i).GS(constantIndex);
       newData(i).TAR = data.data(i).TAR(constantIndex);
       newData(i).TAS = data.data(i).TAS(constantIndex);
       newData(i).heading = data.data(i).heading(constantIndex);
       newData(i).IAS = data.data(i).IAS(constantIndex);
       newData(i).Mach = data.data(i).Mach(constantIndex);
       newData(i).BAR = data.data(i).BAR(constantIndex);
       newData(i).IVV = data.data(i).IVV(constantIndex);

   end
   end

Answer 1

[Star Strider]

Your airplane appears to be a jet flying a STAR. When it enters Class C airspace, it is told to slow to 250 kts, then is cleared for the approach and flies the approach at 130 kts.

I didn’t run the code, however it seems to be two 10-element moving average filters to create first ‘x2’ and then ‘meandiffx2’. It then thresholds ‘meandiffx2’ and returns the indices of those values that are <0.25 to ‘constantIndex’. (If it doesn’t find any, the find function will return an empty value. This usually throws an error when concatenated with an existing vector, and will obviously not function as an index in the next line, so I don’t know how the code handles this when it does the ‘constantData.index’ and constantData.data assignments.) It then stores the associated values in the designated structures.

This is a powerful argument for documenting code with comments.

[bio lim]

I completely agree with always documenting code with comments. I have received the code from someone else, and it startles me how the program 100% works, yet I have a dim idea of what is going on.

[Star Strider]

It’s definitely not obvious. I recognised the moving average (using the filter function) because it’s a relatively commonly-used technique, and here it’s used to detect the constant-airspeed segments. I understand part of it because I’m an Instrument-Rated Private Pilot. The rest is honestly mystifying.

[bio lim]

Yeah, I was guessing it was a moving average filter but now thanks to you at least I am certain it is indeed moving average filter. If the rest is mystifying to an expert, then it makes sense that I don't understand it, haha. Anyway, thanks!

[Star Strider]

My pleasure!

I’m knowledgeable and experienced in certain aspects of MATLAB but I’d not consider myself an ‘expert’, except in certain very restrictive applications (medicine, biomedical engineering, aviation).

Answer 2

[Thorsten]

First who have to define an formal criterion of what you consider "near constant". For example, more than 20 points that vary my less than 15 units. Than you loop through your data:

 pseudo code:
 i_start = 1, i_end = i_end + 20
 if the range of values(i_start:i_end) < 15?
   then increment i_end 
          until the range is > 15: 
             1. you've found a constant area from i_start:i_end
             2. continue checking with i_start = i_end+1
   else
    continue checking with i_start = i_start + 1

If you post your data and define your criteria, we could provide further help.

[bio lim]

Hi. I actually already have a solution, however I do not understand the algorithm or the method used behind this. If you could explain me the following code, that would be great! (I will take it as the answer of the question.) I will post the code in the original question. I have also attached my .mat file.

Answer 3

[Image Analyst]

You can use stdfilt() in the Image Processing Toolbox. It will work on a 1-D signal. Basically it scans the array computing the standard deviation in a moving window. If the values don't vary much in the window, then the stdev will be low and if they change a lot the stdev will be high.

Alternatively you can scan the signal and call polyfit() from each point onwards. Fit a line and if the slope is reasonably low, like 0 to 0.2 or whatever, then the portion is fairly flat. If the slope is higher, then trending up or down.

[bio lim]

That's a great idea. I'll give it a try.