Optimal linear smoothing : Continuous data case

In this paper, Rauch-Tung-Striebel(RTS) optimal smoothing algorithm is applied to improving off-line satellite attitude determination accuracy. The measurements are first processed by the forward filter, and then, a separate backward smoothing pass is used for obtaining the smoothing solution. The performances between RTS and extended Kalman filter(EKF) in gyro/star-sensor integrated system are compared. RTS smoother exhibits better accuracy and robustness than EKF under the situation of lower sensors precision, different length of data and larger initial attitude error. The results verify the effectiveness and practicability of RTS smoothing algorithm in satellite attitude determination.

In this paper we consider the transmission of stored video from a server to a client for medical applications such as, Telemonitoring, to optimize medical quality of service (m-QoS) and to examine how the client buffer space can be used efficiently and effectively towards reducing the rate variability of the compressed variable bit rate (VBR) video. Three basic results are presented. First, we show how to obtain the greatest possible reduction in rate variability when sending stored video to client with a given buffer size. Second, how to reduce high peak data rate of compressed VBR video when a patient is moving/walking very fast in hospital. Third, we evaluate the impact of optimal smoothing algorithm on the network parameters such as, peak-to-mean ratio, standard deviation, delay, jitter, average delay and average jitter to optimize the m-QoS. To resolve these all problems we used optimal smoothing algorithm and show its performance over a set of long MPEG-4 encoded video traces. Simulation results show that m-QoS is optimized by minimizing network metrics.

This paper studies the smoothing algorithms in Distributed Interactive Simulation. Two smoothing algorithms, straight line and cubic spline, are analyzed. A dead-reckoned test flight trajectory is used as the test platform. The Multinomial Logit Models method is used to rate the smoothness. The RMS and maximum errors are used to measure the accuracy. The conclusions are: (1) smoothing algorithm can significantly improve the visual smoothness; (2) smoothing process increases error; (3) linear smoothing algorithm is recommended for most applications, (4) more smoothing steps can improve the visual smoothness; however, it can also increase errors.

Application of ARIMA-RTS optimal smoothing algorithm in gas well production prediction

A closed-form optimal nonlinear smoothing algorithm is derived for estimation of signal that is indirectly observed through a discrete time point process (DTPP). A finite-state Markov signal influences the rate of the point process. The smoothers obtained are simple, recursive, and finite dimensional. An illustrative example of the derived estimation scheme is presented.

An efficient spatial smoothing algorithm for filtering data while preserving spatial detail is obtained using the system (impulse response) function of the sensor. In contrast to the normal procedure for determining the filter coefficients for an arbitrary system function, this technique does not involve the use of Fourier transforms. The algorithm results in optimal smoothing within the constraints of retaining good vertical detail after only three or four iterations. A refinement of this procedure involving higher-order filter functions produced the equivalent operation in a single pass. The spatial filtering coefficients are obtained analytically for the frequently applicable Gaussian system function. The efficiency of this procedure is illustrated by filtering simulation, logs, and spectral data. For real-time smoothing of nuclear log data, a filter length of five times the vertical resolution is required. >

Grassmannian quantization codebooks play a central role in a number of limited feedback schemes for single and multi-user MIMO communication systems. In practice, it is often desirable that these codebooks possess additional properties that facilitate their implementation, beyond the provision of good quantization performance. Although some good codebooks exist, their design tends to be a rather intricate task. The goal of this paper is to suggest a flexible approach to the design of Grassmannian codebooks based on smooth optimization algorithms for the Grassmannian manifold and the use of smooth penalty functions to obtain additional desirable properties. As one example, rank-2 codebooks with a nested structure and elements from a discrete alphabet are designed. In some numerical comparisons, codebooks designed using the proposed approach have better Fubini-Study distance properties than some existing codebooks, and provide tangible performance gains when applied to a simple MIMO downlink scenario with zero-forcing beamforming, PU <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> RC, and block diagonalization signalling. Furthermore, the proposed approach yields codebooks that attain desirable additional properties without incurring a substantial degradation in performance.

Several recursive methods are available for the estimation of linear time-varying process models from sampled input/output records. During convergence from poor initial estimates, they give no clear picture of the time variation. A remedy is to base the estimate at every point in time on the whole record, by use of optimal smoothing techniques originally developed for state estimation. Optimal smoothing algorithms are reviewed and their computational requirements and stability in an identification context are examined. The most attractive are tested on synthetic records and on hydrological records. It is concluded that they are feasible and effective. Examples are given of features revealed by optimal smoothing, but not by the usual identification techniques.

Optimal smoothing for spherical Gauss–Markov Random Fields with application to weather data estimation

Sequential algorithms for filtering, fixed-interval, fixed-point and fixed-lag smoothing are developed for a class of linear distributed-parameter systems. The class of systems concerned is that involving noisy measurement data which are obtained from a finite number subdomain in the spatial domain, i.e. pointwise sensor. The basic tools of the development are the Wiener-Hopf equation, innovation theory and the fundamental value theory for the differential operator. The fixed-lag smoother obtained is new. Finally, for the numerical solution, the expansion method of eigen-functions in L2(D) and L2(D × D) is asserted, and it is shown that the results obtained here are general forms, which contain the results of the finite state space reported earlier.

Smoothing algorithms of various kinds have been around for several decades. However, some basic issues regarding the dynamical structure and the minimal dimension of the steady-state algorithm are still poorly understood. In this paper, we derive a realization of minimal dimension of the optimal smoother for a signal admitting a state-space description of dimension n. It is shown that the dimension of the smoothing algorithm can vary from n to 2n, depending on the zero structure of the signal model. The dynamics (pole structure) of the steady-state smoother is also characterized explicitly and is related to the zero structure of the model. We use several recent ideas from stochastic realization theory. In particular, a minimal Markovian representation of the smoother is derived, which requires solving a nonsymmetric Wiener-Hopf factorization problem. In this way, the smoother is naturally expressed as the cascade of a whitening filter and a linear filter of least possible dimension, whose state space is a minimal Markovian subspace containing the smoothed estimate x/spl I.cap/. This, among other aspects, affords a very simple calculation of the error covariance matrix of the smoother. A reduced-order two-filter implementation of the type due to Mayne (1966) and Fraser (1967) is obtained by solving a Riccati equation of reduced dimension, which is in general smaller than the dimension of the Riccati equations considered in the literature.

SUMMARY For the sequential estimation of the size of a finite population, the maximum likelihood estimator is a commonly used estimator but has no explicit expression. In this paper, it is shown that the maximum likelihood estimator is inadmissible. An estimator which is simple in form and dominates the maximum likelihood estimator asymptotically is proposed. To study the optimality property of the estimator for the stopping rule SB from a decision theoretical approach, we investigate the admissibility of the estimator under a general weighted squared error loss function. Although the maximum likelihood estimator and its risk have no closed form expression, the estimator will be shown to be inadmissible by means of a general theorem that we establish later as Theorem 2-1. In this paper, we only consider the simple capture-capture model discussed by Samuel (1968). More complex and realistic capture-recapture models have been developed subsequently (Pollack & Otto, 1983; Pickands & Raghavachari, 1987; Bonett, Woodward & Bentler, 1987; Cormack, 1989; Huggins, 1989). We conjecture that many of the

In this paper we consider the Bayesian inference of the unknown parameters of the progressively censored competing risks data, when the lifetime distributions are Weibull. It is assumed that the latent cause of failures have independent Weibull distributions with the common shape parameter, but different scale parameters. In this article, it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameters have Beta-Dirichlet priors. When the common shape parameter is known, the Bayes estimates of the scale parameters have closed form expressions, but when the common shape parameter is unknown, the Bayes estimates do not have explicit expressions. In this case we propose to use MCMC samples to compute the Bayes estimates and highest posterior density (HPD) credible intervals. Monte Carlo simulations are performed to investigate the performances of the estimators. Two data sets are analyzed for illustration. Finally we provide a methodology to compare two different censoring schemes and thus find the optimum Bayesian censoring scheme.

A least squares smoothing (LSS) approach is presented for the blind estimation of single-input multiple-output finite impulse response systems. By exploiting the isomorphic relation between the input and output subspaces, this geometrical approach identifies the channel from the least squares smoothing error of the channel output. Based on this approach, an adaptive least squares smoothing (A-LSS) algorithm is proposed. Compared with subspace and linear prediction-based algorithms, A-LSS gains an advantage for its high convergence rate, adaptivity to both channel order and channel parameter variation, low complexity with no matrix operations, and modular structure suitable for VLSI implementation.

Studies the performance of a statistical multiplexer, to which messages composed of a variable number of fixed-length packets arrive at the rate of one packet per slot (train arrivals), resulting in a correlated packet arrival stream. The distribution of the message lengths is general. The system is analyzed by using an infinite-dimensional state description and a generating-functions approach. An explicit expression is obtained for the probability generating function (pgf) of the queue length and the packet delay. Also, closed-form expressions are derived for the mean and the tail distribution of the queue length and the packet delay. The mean message waiting time is obtained as well. The buffer behavior with train arrivals is compared to that with batch arrivals, where all the packets of a message enter the buffer during the same slot. By means of some numerical examples, the impact of the message-length distribution on the multiplexer performance is investigated.