Trilateration and Maximum Likelihood Estimation Methods in Wireless Sensor Networks Localization

In wireless sensor networks, two commonly employed localization methods are trilateration and maximum likelihood estimation. Trilateration is a geometric positioning approach that utilizes three reference points (anchors) to determine a target node's coordinates by calculating distances from these reference points. The implementation typically involves solving a system of equations derived from distance measurements using techniques like least squares approximation, where key functions handle coordinate calculations based on signal strength or time-of-arrival data. Maximum likelihood estimation, conversely, is a probabilistic localization method that determines node position by maximizing the likelihood function of observed measurements. This algorithm often employs statistical models for signal propagation and iterative optimization methods such as gradient descent or Newton-Raphson to find the position that best fits the observed data. Both methods exhibit inherent errors during the localization process: trilateration errors primarily stem from distance measurement inaccuracies and geometric dilution of precision, while maximum likelihood estimation errors arise from model mismatches and measurement noise. Comprehensive error analysis through covariance matrices and confidence intervals is essential for evaluating localization accuracy, with simulation implementations typically incorporating Monte Carlo methods to assess performance under various noise conditions.