Envelope of cuve or trajectory

[amine8052]

hello every one,
realy i need your help please

I am working on tracking the coordinates (trace of indexes of pixels in files or bench) of an image (x and y). Im tracking result by a processing unit (no sensor, just an observation on the coordinates).
... I estimate the average line of each traject by a simple estimator of Luenberguer (this part works fine). Also I will need to calculate is the envelope line of this curve , is in this part where I want your advice on finding the right track.
I tried to locate the peaks of this curve, the method works well for sinusoidal signals, but I want a general approach (the signals with noise)

I calculate the standard deviation (sigma) or the variance. To find the envelope of the curve I have to multiply that number by sigma K (2, 3 ...)how can i finding the optimum k ?

thanks

 

[amine8052]

in pictures an exemple of 2 trajectory, the demonstration is only for (x):
- in black the envelope
+ (2* sigma) for the sinus pente
+ sigma for the second curve
- in red or green the center estimated of trajectory

 

[amine8052]

Envelope detection (on ligne)

hello every one,
realy i need your help please

I am working on tracking the coordinates (trace of indexes of pixels in files or bench) of an image (x and y). Im tracking result by a processing unit (no sensor, just an observation on the coordinates).
... I estimate the average line of each traject by a simple estimator of Luenberguer (this part works fine). Also I will need to calculate is the envelope line of this curve , is in this part where I want your advice on finding the right track.
I tried to locate the peaks of this curve, the method works well for sinusoidal signals, but I want a general approach (the signals with noise)

I calculate the standard deviation (sigma) or the variance. To find the envelope of the curve I have to multiply that number by sigma K (2, 3 ...)how can i finding the optimum k ?

in pictures an exemple of 2 trajectory, the demonstration is only for (x):
- in black the envelope
+ (2* sigma) for the sinus pente
+ sigma for the second curve
- in red or green the center estimated of trajectory



thanks