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.
A taxis algorithm from the same family as the algorithm introduced here was presented in @cite_2 for general abstract taxis. This algorithm is based on RDSA known from the stochastic approximation literature @cite_4 @cite_3 . RDSA uses a very efficient but rather unintuitive formulation of the gradient estimation. The authors discuss the noise characteristics of the physical model only very briefly and fail to mention motor noise at all. As discussed later, small scale fading is especially problematic and can violate some of the convergence conditions if not dealt with correctly (see sec:SmallScaleFading ). Because of that we discuss the physical characteristics of wireless communication and the robot in detail in the next sections.
@cite_4 @cite_3 @cite_2
2607406448 2143859410 1965193428 2584174354
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 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 new stochastic first-order algorithm for solving sparse regression problems. In each iteration, our algorithm utilizes a stochastic oracle of the subgradient of the objective function. Our algorithm is based on a stochastic version of the estimate sequence technique introduced by Nesterov (Introductory lectures on convex optimization: a basic course, Kluwer, Amsterdam, 2003). The convergence rate of our algorithm depends continuously on the noise level of the gradient. In particular, in the limiting case of noiseless gradient, the convergence rate of our algorithm is the same as that of optimal deterministic gradient algorithms. We also establish some large deviation properties of our algorithm. Unlike existing stochastic gradient methods with optimal convergence rates, our algorithm has the advantage of readily enforcing sparsity at all iterations, which is a critical property for applications of sparse regressions. In big cities, taxi service is imbalanced. In some areas, passengers wait too long for a taxi, while in others, many taxis roam without passengers. Knowledge of where a taxi will become available can help us solve the taxi demand imbalance problem. In this paper, we employ a holistic approach to predict taxi demand at high spatial resolution. We showcase our techniques using two real-world data sets, yellow cabs and Uber trips in New York City, and perform an evaluation over 9,940 building blocks in Manhattan. Our approach consists of two key steps. First, we use entropy and the temporal correlation of human mobility to measure the demand uncertainty at the building block level. Second, to identify which predictive algorithm can approach the theoretical maximum predictability, we implement and compare three predictors: the Markov predictor (a probability-based predictive algorithm), the Lempel-Ziv-Welch predictor (a sequence-based predictive algorithm), and the Neural Network predictor (a predictive algorithm that uses machine learning). The results show that predictability varies by building block and, on average, the theoretical maximum predictability can be as high as 83 . The performance of the predictors also vary: the Neural Network predictor provides better accuracy for blocks with low predictability, and the Markov predictor provides better accuracy for blocks with high predictability. In blocks with high maximum predictability, the Markov predictor is able to predict the taxi demand with an 89 accuracy, 11 better than the Neural Network predictor, while requiring only 0.03 computation time. These findings indicate that the maximum predictability can be a good metric for selecting prediction algorithms.