SNLSDP version 0 -- a MATLAB software for sensor network localization

Kim-Chuan Toh , Pratik Biswas, and Yinyu Ye

The software was last updated in 21 Oct 2008.
It implemented an SDP based approach with regularization for solving sensor network localization problems. The algorithm first solves an SDP relaxation (with regularization) of the non-convex minimization problem (1), and use the SDP computed solution as the starting point for a gradient descent method with backtracking line search to solve the smooth unconstrained problem (2).
This software package is designed for solving small size senor network localization problems with up to 200 sensors and a few thousands given distances.

\( (1)\quad \min \big\{ \sum_{(i,j)\in {\cal E}} | \|x_i-x_j\|^2-d_{ij}^2| + \sum_{(k,j)\in {\cal F}} | \|a_k-x_j\|^2-d_{kj}^2 | \big\} \\[10pt] (2)\quad \min \big\{ \sum_{(i,j)\in {\cal E}} ( \|x_i-x_j\|-d_{ij})^2 + \sum_{(k,j)\in {\cal F}} (\|a_k-x_j\|-d_{kj})^2 \big\} \)

where \(d_{ij}, d_{kj} \) are distance data, \(x_j\) is the position of the jth sensor, and \(a_k\) is the position of the kth anchor.
If you find SNLSDP useful in your work, please cite the following paper:
[1] P. Biswas, T.-C. Liang, K.-C. Toh, T.-C. Wang, and Y. Ye, Semidefinite programming approaches for sensor network localization with noisy distance measurements, IEEE Transactions on Automation Science and Engineering, 3 (2006), pp. 360--371.