|
Self localization is a term used to describe the ability of a network to automatically determine the location of its nodes, given little or no external information. Self localization is an enabling technology for many future capabilities; specifically those that rely on a large number of sensors that self organize to form a coherent system. Most prior work in this area focuses on centralized computation with stationary nodes and synchronized clocks. We report on preliminary results for a setting that is more general in three ways. First, nodes in the network are moving. This implies the pair-wise distances between nodes are not fixed and therefore an iterative tracking procedure is needed to estimate the time varying node positions. Second, we do not assume synchronization between clocks on different nodes. In fact, we allow the clocks to have both an unknown offset and to be running at differing rates (i.e., a drift). Third, our method is decentralized, so there is no need for a single entity withfaccess to all measurements. In this setup, each node in the network is responsible for estimating its state.
The method is based on repeated pair-wise communication between nodes. We focus on two types of observables in this paper. First, we use the time between when a message was sent from one node and when it was received by another node. In the case of synchronized clocks and stationary nodes, this observable provides information about the distance between the nodes. In the more general case with non-synchronized clocks, this observable is coupled to the clock offsets and drifts as well as the distance between nodes. Second, we use the Doppler stretch observed by the receiving node. In the case of synchronized clocks, this observable provides information about the line of sight velocity between the nodes. In the case of non-synchronized clocks, this observable is coupled to the clock drift as well as the line of sight velocity. We develop a sophisticated mathematical representation that allows all of these effects to be accounted for simultaneously.
We approach the problem from a Bayesian viewpoint, where measurements are accumulated over time and used to form a probability density on the state, conditioned on the measurements. What results is a recursive filtering (or tracking) algorithm that optimally merges the measurements. We show by simulation and illustrative data collections that our method provides an efficient decentralized method for determining the location of a collection of moving nodes.
|
