Detecting Non-Overlapping Signals with Dynamic Programming

. 2023 Jan 30;25(2):250. doi: 10.3390/e25020250

Algorithm 3: Signal detection using dynamic programming with an unknown number of signal occurrences.

Input:
$y \in R^{N}$ , $x \in R^{L}$ , $K_{max}$
1:
for $K = 1$ to $K_{max}$ do
2:
Compute $g (N, K)$ with respect to y using Algorithm 1
3:
for $i = 1$ to P do
4:
Compute $g_{i} (N, K)$ with respect to $y_{i}$ (a permutation of y) using Algorithm 1
5:
end for
6:
Compute ${Gap}_{N} (K) = \frac{1}{P} \sum_{i = 1}^{P} g_{i} (N, k) - g (N, k)$
7:
end for
8:
Compute $\hat{K} = arg max {Gap}_{N} (K)$
9:
return $\hat{K}$ (an estimate of the number of signal occurrence in the measurement), $g (N, \hat{K})$ , and estimates of the locations of the signal occurrences ${\hat{n}}_{1}, \dots, {\hat{n}}_{\hat{K}}$