Minkowski timespace has the capability to overcome the limited accuracy of L2-norm based range-free localization methods. This paper proposes the concept of Minkowski triangulation uncertainty (MTU) in wireless sensor networks (WSNs) for localization of unknown target. To set up a localization framework, triangulation uncertainty parameter is defined using Lemma 3.1. A two-stage estimation algorithm is then presented: countLocalized and countAnchor. countLocalized computes the number of localized sensor nodes by leveraging the uncertainty strategy based upon indeterminate independent measurement. countAnchor designates the anchor nodes to triangulate the unknown target by formulating a convex hull model. The convex hull is the Minkowski sum of the actual and projected positions of the two vector node positions. The proposed MTU technique establishes that the number of triangulations formed by Minkowski method is inclusive of the triangulations formed by conventional L2-norm range of sensor nodes in a WSN. Measurement strategies such as angle, distance and positioning error are compared in the simulation. The said technique links Minkowski space to localization by ensuring efficiency in large target areas and number of nodes in manifolds. Results confirm that the MTU technique is better than the existing models by at least 12%, 50%, 5.5% and 24% in terms of localization ratio, localization error, neighbour anchor nodes and network connectivity, respectively.
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Prateek, Arya, R. Range free localization technique under erroneous estimation in wireless sensor networks. J Supercomput (2021). https://doi.org/10.1007/s11227-021-04075-x
- Error estimation
- Localization uncertainty
- Minkowski distance
- Wireless sensor networks