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I'm not familiar with filters etc, so I'm asking here if anyone knows an existing method to do the following. I have a sequence of observations $S_n$ and I know that they satisfy $S_n=\sum_{i=1}^m a(n,i)$ where $m$ is fixed an known, while $a(n,i)$ are unknown scalars. However I know that $$\frac{a(n+1,i)}{a(n,i)}\approx \frac{a(n,i)}{a(n-1,i)}$$ Knowing the sequence $S_n$ and the above relation, does anybody know a method for estimating the scalars $a(n,i)$? Thanks

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    Did you mean $S_{n,m}$? – 2017-01-07
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    Hi, $m$ is a fixed integrer, doesn't depends on $n$. For each $n$ I have a different realization of the sum – 2017-01-07
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    So... if, say, $S_3=5$, then it holds for all $m$? I don't quite understand... – 2017-01-07
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    $m$ is just the number of terms in the sum, for each $n$ I have a sum $S_n$ of $m$ terms, but $m$ is always the same. – 2017-01-07
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    $m$ is a known constant? – 2017-01-07
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    yes $m$ is known – 2017-01-07

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