10,363 research outputs found

    Kalman Filtering with Unknown Noise Covariances

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    Since it is often difficult to identify the noise covariances for a Kalman filter, they are commonly considered design variables. If so, we can as well try to choose them so that the corresponding Kalman filter has some nice form. In this paper, we introduce a one-parameter subfamily of Kalman filters with the property that the covariance parameters cancel in the expression for the Kalman gain. We provide a simple criterion which guarantees that the implicitly defined process covariance matrix is positive definite

    Directional antennas for wireless sensor networks

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    Directional antennas provide angle-of-arrival information, which can be used for localization and routing algorithms in wireless sensor networks. We briefly describe three classical, major types of antennas: 1) the Adcock-pair antenna, 2) the pseudo-Doppler antenna, and 3) the electronically switched parasitic element antenna. We have found the last type to be the most suitable for wireless sensor networks, and we present here the early design details and beam pattern measurements of a prototype antenna for the 2.4-GHz ISM band, the SPIDA: SICS Parasitic Interference Directional Antenna

    On the transition of Charlier polynomials to the Hermite function

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    It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which is still presented in its classical form in modern reference works, is valid if and only if a certain parameter is integer. In this light, it is surprising that a much more powerful transition exists from Charlier polynomials to the Hermite function, valid for any real value of the parameter. This greatly strengthens the asymptotic connections between Charlier polynomials and special functions, with applications for instance in queueing theory. It is shown in this paper that the convergence is uniform in bounded intervals, and a sharp rate bound is proved. It is also shown that there is a transition of derivatives of Charlier polynomials to the derivative of the Hermite function, again with a sharp rate bound. Finally, it is proved that zeros of Charlier polynomials converge to zeros of the Hermite function. While rigorous, the proofs use only elementary techniques.Comment: 29 pages, 3 figures; compared to v2, proof of transition for Charlier polynomial derivatives added; change in title to "transition" from "convergence

    A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains

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    A spectral method for identifying lumping in large Markov chains is presented. Identification of meta stable states is treated as a special case. The method is based on spectral analysis of a self-adjoint matrix that is a function of the original transition matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.Comment: 10 pages, 7 figure

    Some Notes on Parallel Quantum Computation

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    We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth, while circuits composed of both cannot. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we exhibit a simple quantum circuit related to it that we believe cannot be parallelized to less than linear depth, and therefore might be used to prove that QNC < QP