Find gaussian in data I have some time series data (blue line lower plot) with a gaussian added into it (red line upper plot). I would like to estimate where the gaussian is in the data, and the height of the gaussian (these parameters can be bounded).
Is there an algorithm that can estimate and find where the gaussian is in the data (blue line, upper plot)?
Or a better question might be, is there a way I could come up with a probability curve for finding a gaussian in the data if I don't know what height or it's location (mean).
The model would be:
$$y(x)=A c_0 e^{-A c_0 \frac{(x-x_0)^2}{x_0}}$$
or
$$y(x)=\frac{A^2}{{(1+e^{-A c_0 \frac{(x-x_0)^2}{x_0}})}^2} c_0 e^{-A c_0 \frac{(x-x_0)^2}{x_0}}$$

Note: this is just a simulated gaussian, normally I have just the blue line in the upper plot.
Explanation of upper plot:
Red line, original data
Blue line, original data with gaussian added (the gaussian is in the lower plot has been added to the blue line in the upper plot)
I only have the blue line in the upper plot, I am trying to detect the location in the x direction of the gaussian (where it peaks parameter x_0) and maybe the height A
The gaussian is my signal, the blue line in the upper plot is my noise
the redline is an example of noise + gaussian and a typical time series that I work with.
Still not making any sense to me.  This is what I have parsed from what you are saying:
Red Line = Noise + Gaussian
Blue Line = Red Line + Lower Gaussian
Blue Line = Noise + Gaussian + Lower Gaussian
Blue Line = Noise
Red Line = Original
Blue Line = What you got
Clear as mud.  What you got isn't what is original.  You arbitrarily chose a spot to add a contrived Gaussian to the red line to get the blue line, yet that is what you started with.
You call the red line a gaussian + noise, but it doesn't include the gaussian you added.
Let's start with this.  Show the data set you are starting with.  The original data, the time series as you will measure it.
I'll take another look in the morning, and probably delete this answer, but it was way too long for a comment.
In the meanwhile, maybe a look at this:  Estimate peak width from a vector that is a superposition of unknown number of identical Gaussian peaks with different heights?