4,955 research outputs found

    Optimal Estimation via Nonanticipative Rate Distortion Function and Applications to Time-Varying Gauss-Markov Processes

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    In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject to a mean square error fidelity constraint. We show that such filters are equivalent to the design of an optimal \texttt{\{encoder, channel, decoder\}}, which ensures that the error satisfies {a} fidelity constraint. Moreover, we derive a universal lower bound on the mean square error of any estimator of time-varying multidimensional Gauss-Markov processes in terms of conditional mutual information. Unlike classical Kalman filters, the filter developed is characterized by a reverse-waterfilling algorithm, which ensures {that} the fidelity constraint is satisfied. The theoretical results are demonstrated via illustrative examples.Comment: 35 pages, 6 figures, submitted for publication in SIAM Journal on Control and Optimization (SICON

    Average Consensus in the Presence of Delays and Dynamically Changing Directed Graph Topologies

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    Classical approaches for asymptotic convergence to the global average in a distributed fashion typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practical settings due to varying delays that might affect transmissions at different times, as well as possible changes in the underlying interconnection topology (e.g., due to component mobility). In this work, we propose protocols to overcome these limitations. We first consider a fixed interconnection topology (captured by a - possibly directed - graph) and propose a discrete-time protocol that can reach asymptotic average consensus in a distributed fashion, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its outgoing links (i.e., the number of components to which it sends information). We subsequently extend the protocol to also handle changes in the underlying interconnection topology and describe a variety of rather loose conditions under which the modified protocol allows the components to reach asymptotic average consensus. The proposed algorithms are illustrated via examples.Comment: 37 page

    A data augmentation methodology for training machine/deep learning gait recognition algorithms

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    There are several confounding factors that can reduce the accuracy of gait recognition systems. These factors can reduce the distinctiveness, or alter the features used to characterise gait; they include variations in clothing, lighting, pose and environment, such as the walking surface. Full invariance to all confounding factors is challenging in the absence of high-quality labelled training data. We introduce a simulation-based methodology and a subject-specific dataset which can be used for generating synthetic video frames and sequences for data augmentation. With this methodology, we generated a multi-modal dataset. In addition, we supply simulation files that provide the ability to simultaneously sample from several confounding variables. The basis of the data is real motion capture data of subjects walking and running on a treadmill at different speeds. Results from gait recognition experiments suggest that information about the identity of subjects is retained within synthetically generated examples. The dataset and methodology allow studies into fully-invariant identity recognition spanning a far greater number of observation conditions than would otherwise be possible
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