An Effective Single-Station Cooperative Node Localization Technique Using Multipath Spatiotemporal Information

. 2025 Jan 22;25(3):631. doi: 10.3390/s25030631

Algorithm 2: An Effective Single-Station Cooperative Node Localization Technique Using Multipath Spatiotemporal Information
	Input: $Q$ data files, each containing $K$ sample points of I/Q data from both moving and stationary antennas at $q$ - $t h (1 \leq q \leq Q)$ different angular position; The transmitted waveform of the cooperative target $T x$ .
	Output: Estimated coordinates $(\hat{x}, \hat{y})$ of $T x$ .
1.	Execute Algorithm 1 to extract a $. m a t$ file containing spatial angles and corresponding power values based on the input data files.
2.	Load the $. m a t$ file to obtain the spatial spectrum and identify the direct path arrival angle ${\hat{θ}}_{1}$ and $L$ potential values for the reflected path arrival angle ${\hat{θ}}_{2}$ based on a predefined threshold.
3.	Calculate the $L$ possible coordinates $({\hat{x}}_{l}, {\hat{y}}_{l})$ of $T x$ according to Equation (4).
4.	Perform matched filtering on the stationary antenna’s received data with the transmitted waveform to obtain the time-domain energy distribution.
5.	Determine the direct path delay ${\hat{τ}}_{1}$ and $L$ possible values for the delay differences ${∆ \hat{τ}}_{l}$ between the reflected and main path based on a predefined threshold.
6.	Match the candidate coordinates $({\hat{x}}_{l}, {\hat{y}}_{l})$ derived from spatial analysis with the corresponding time delay differences ${∆ \hat{τ}}_{l}$ obtained through temporal analysis based on energy.
7.	Compute the coordinates $(\hat{x}, \hat{y})$ of $T x$ as specified in Equation (14).