Adaptive anchor weighting for improved 2D positioning with Levenberg-Marquardt optimization

This paper introduces a new tri-lateration method that utilizes a unique cost function formulation to significantly enhance the performance of positioning systems. Fixed-position devices called locators or anchors, with predetermined coordinates, are used to determine and track the unknown location of a moving electronic tag. The optimization algorithm enhances accuracy by assigning greater importance to anchors closer to the mobile tag, compared to those situated farther away. The algorithm runs multiple iterations to reduce the error of estimation with Levenberg-Marquardt optimization, starting from the initial position estimate. Position estimation accuracy is evaluated relative to the number of anchors and area size. Performance evaluation is presented utilizing low cost single-antenna Bluetooth Low Energy (BLE) devices based on BLE 5.1 protocol. In nonline-of-sight (NLOS) scenarios characterized by random shadow fading, using four or eight anchors yields a 95’th percentile mean positioning accuracy of 2.2 meters and 1.5 meters, respectively, in a 20×20 m2 indoor area. We expect this accuracy to further improve with BLE 6.0 protocol utilizing channel sounding. The proposed method outperforms conventional non-linear least squares techniques, achieving a 51% improvement with four anchors and a 52 % improvement with eight anchors. The algorithm processes input data consisting of estimated distances between the tag and each individual anchor. This methodology is adaptable to various Internet of Things (IoT) modulation techniques, and can also be implemented with Ultra Wide Band (UWB)ormillimeter-wave (mmWave) technologies. Future works can expand the current two-dimensional (2D) model to support three-dimensional (3D) positioning.