Guaranteeing Practical Convergence in Algorithms for Sensor and Source Localization

This paper considers localization of a source or a sensor from distance measurements. We argue that linear algorithms proposed for this purpose are susceptible to poor noise performance. Instead given a set of sensors/anchors of known positions and measured distances of the source/sensor to be localized from them we propose a potentially non-convex weighted cost function whose global minimum estimates the location of the source/sensor one seeks. The contribution of this paper is to provide nontrivial ellipsoidal and polytopic regions surrounding these sensors/anchors of known positions, such that if the object to be localized is in this region, localization occurs by globally exponentially convergent gradient descent in the noise free case. Exponential convergence in the noise free case represents practical convergence as it ensures graceful performance degradation in the presence of noise. These results guide the deployment of sensors/anchors so that small subsets can be made responsi...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Baris Fidan, Soura Dasgupta, Brian D. O. Anderson
• Keywords: Gradient Descent, Noise Free Case, Non-convex Weighted Cost, TSP 2008