Simulation of MDS-MAP Wireless Localization Algorithm

The MDS-MAP wireless localization algorithm is a positioning technique based on Multidimensional Scaling (MDS), commonly used for node position estimation in wireless sensor networks. This algorithm measures signal strength or distance information between nodes, utilizes MDS technology to reconstruct the relative spatial distribution of nodes, and finally converts relative coordinates to absolute positions through anchor point coordinates.

In algorithm simulation, the following core processes typically need to be simulated: First, construct a virtual wireless node network by randomly distributing nodes and setting some anchor nodes with known coordinates. Second, calculate inter-node distances or Received Signal Strength Indicator (RSSI) based on signal propagation models (such as the log-distance path loss model), and add noise to simulate measurement errors in real environments. Next, use the MDS algorithm to convert the distance matrix into low-dimensional coordinates (typically 2D or 3D) through Singular Value Decomposition (SVD) or stress minimization methods. Finally, perform rotation, scaling, and translation transformations on the relative coordinates using the actual coordinates of anchor nodes to achieve absolute localization.

During simulation implementation, special attention should be paid to the accuracy of the distance matrix, the stability of MDS dimensionality reduction, and the precision of coordinate transformation. By adjusting parameters (such as noise levels, anchor node ratios, etc.), the algorithm's robustness in different scenarios can be analyzed. This simulation not only verifies the theoretical feasibility of MDS-MAP but also provides references for error optimization directions in practical deployments.