Finding the physical location of a specific network node is a prototypical task for navigation inside a wireless network. In this paper, we consider in depth the implications of wireless communication as a measurement input of gradient-based taxis algorithms. We discuss how gradients can be measured and determine the errors of this estimation. We then introduce a gradient-based taxis algorithm as an example of a family of gradient-based, convergent algorithms and discuss its convergence in the context of network robotics. We also conduct an exemplary experiment to show how to overcome some of the specific problems related to network robotics. Finally, we show how to adapt this framework to more complex objectives.
The network community has developed some algorithms similar to the gradient-based taxis algorithm discussed here. There exist for example algorithms to calculate relative bearing from gradients @cite_1 . These algorithms employ, in contrast to the finite differences used here, principal component analysis to estimate gradients. Furthermore, gradients can be used to localize network nodes by fitting a local model to the measured signal strength data @cite_17 . This and similar algorithms need precise position information acquired for example via GPS measurements or using laser range finders @cite_18 . The most straightforward linear model was explored successfully in @cite_13 @cite_12 .
@cite_18 @cite_1 @cite_13 @cite_12 @cite_17
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We present a method for using real world mobility traces to identify tractable theoretical models for the study of distributed algorithms in mobile networks. We validate the method by deriving a vehicular ad hoc network model from a large corpus of position data generated by Boston-area taxicabs. Unlike previous work, our model does not assume global connectivity or eventual stability; it instead assumes only that some subset of processes are connected through transient paths (e.g., paths that exist over time). We use this model to study the problem of prioritized gossip, in which processes attempt to disseminate messages of different priority. Specifically, we present CabChat, a distributed prioritized gossip algorithm that leverages an interesting connection to the classic Tower of Hanoi problem to schedule the broadcast of packets of different priorities. Whereas previous studies of gossip leverage strong connectivity or stabilization assumptions to prove the time complexity of global termination, in our model, with its weak assumptions, we instead analyze CabChat with respect to its ability to deliver a high proportion of high priority messages over the transient paths that happen to exist in a given execution. We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the 'gradient' component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of pixel images in about 0.4 s using a single graphics processing unit (GPU). We consider the problem of node positioning in ad hoc networks. We propose a distributed, infrastructure-free positioning algorithm that does not rely on GPS (Global Positioning System). Instead, the algorithm uses the distances between the nodes to build a relative coordinate system in which the node positions are computed in two dimensions. Despite the distance measurement errors and the motion of the nodes, the algorithm provides sufficient location information and accuracy to support basic network functions. Examples of applications where this algorithm can be used include Location Aided Routing [10] and Geodesic Packet Forwarding [2]. Another example are sensor networks, where mobility is less of a problem. The main contribution of this work is to define and compute relative positions of the nodes in an ad hoc network without using GPS. We further explain how the proposed approach can be applied to wide area ad hoc networks. Global Navigation Satellite Systems (GNSS) can be used for navigation purposes in vehicular environments. However, the limited accuracy of GNSS makes it unsuitable for applications such as vehicle collision avoidance. Improving the positioning accuracy in vehicular networks, Cooperative Positioning (CP) algorithms have emerged. CP algorithms are based on data communication among vehicles and estimation of the distance between the nodes of the network. Among the variety of radio ranging techniques, Received Signal Strength (RSS) is very popular due to its simplicity and lower cost compared to other methods like Time of Arrival (TOA), and Time Difference of Arrival (TDOA). The main drawback of RSS- based ranging is its inaccuracy, which mostly originates from the uncertainty of the path loss exponent. Without knowing the environment path loss exponent, which is a time-varying parameter in the mobile networks, RSS is effectively useless for distance estimation. There are many approaches and techniques proposed in the literature for dynamic estimation of the path loss exponent within a certain environment. Most of these methods are not functional for mobile applications or their efficiency decreases dramatically with increasing mobility of the nodes. In this paper, we propose a method for dynamic estimation of the path loss exponent and distance based on the Doppler Effect and RSS. Since this method is fundamentally based on the Doppler Effect, it can be implemented within networks with mobile nodes. The higher the mobility of the nodes, the better performance of the proposed technique. This contribution is important because vehicles will be equipped with Dedicated Short Range Communication (DSRC) in the near future.