I am currently sampling the response of a sensor at equidistant points. This looks like this
I have a-priori information of the last measurement. To increase accuracy but not increase the complexity of the calculation, I want to sample the response with the same numbers of samples but with higher resolution at some point and less resolution far away from that point. That would look like this
How can I calculate with an algorithm the sampling points with the parameter
- density mean (the point of the highest density)
- number of samples
- some quality/dense parameter which specifies how dense the samples are
Thank you very much in advance
consider you are using a Gaussian distribution over your search space with mean $\mu$ and variance $\sigma^2$. Note that $\mu$ is what you mean by "density mean" and $\sigma^2$ can be seen as the density parameter. My idea is that you iteratively try to find the next sample point.
You can compute the area under the Gaussian distribution in your interval as $A = \int_{a}^b\mathcal{N}(\mu,\sigma^2)$ with $a$ the lower bound of your search space and $b$ the upper bound.
Using the inverse of the area multiplied with the desired number of samples $N$ you can compute $p = \frac{N}{A}$.
Now start at $a$ and continue until you reach $b$. From $a$ compute the point $x$ where $\int_a^xp\cdot\mathcal{N}(\mu,\sigma^2) = 1$. Add this point to your list of samples and continue the same from $x$.
Also make sure you bring your nice office mates a cake when you come back from holidays ;)