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ERROR ANALYSIS OF OPTIMAL filtering ALGORITHM FOR COLORED NOISE

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1970年第4期AC15卷 452-+页

作者： FUJITA, S FUKAO, T Department of Electrical Engineering Tokyo Institute of Technology Japan

algorithms are developed for the error analysis of the optimal filtering solution for colored noise. The types of error sources considered are those both in the imprecise specification of the model and in the improper choice of the noise statistics. The matrix differential equations have been derived permitting the calculation of the actual error covariance and the additional error due to the preceding error sources. For a case where only the error source based on the incorrect choice of the noise statistics is present, a conservative design criterion has also been established, which makes it possible to prescribe the performance of the filter for colored noise. A simple example demonstrates the utility of these results.

关键词： Error analysis filtering algorithms Colored noise RLC circuits Upper bound Frequency Statistical analysis Noise measurement White noise Admittance

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OPTIMAL filtering IN STOCHASTIC DISCRETE-TIME-SYSTEMS WITH UNKNOWN INPUTS

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1994年第12期39卷 2461-2464页

作者： BORISOV, AV PANKOV, AR Department of Applied Mathematics Moscow Aviation Institute State Technical University Moscow Russia

In this note we derive a recursive filtering algorithm for the linear discrete-time dynamic system with indeterminate-stochastic inputs. The algorithm is based on the minimax-optimal method of parameter estimation in the linear regression model with parameters of two different types: unknown and stochastic with partially known characteristics.

关键词： Stochastic systems Stochastic processes Covariance matrix filtering algorithms Linear regression Vectors Minimax techniques Symmetric matrices Parameter estimation State estimation

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FAST, RECURSIVE-LEAST-SQUARES TRANSVERSAL FILTERS FOR ADAPTIVE filtering

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IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING 1984年第2期32卷 304-337页

作者： CIOFFI, JM KAILATH, T STANFORD UNIV INFORMAT SYST LAB STANFORD CA 94305 USA

Fast transversal filter (FTF) implementations of recursive-least-squares (RLS) adaptive-filtering algorithms are presented in this paper. Substantial improvements in transient behavior in comparison to stochastic-gradient or LMS adaptive algorithms are efficiently achieved by the presented algorithms. The true, not approximate, solution of the RLS problem is always obtained by the FTF algorithms even during the critical initialization period (first N iterations) of the adaptive filter. This true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic-gradient algorithms (factor of 1.6 to 3.5, depending upon application). Additionally, the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing, fast-RLS algorithms, such as the fast Kalman algorithms of Morf, Ljung, and Falconer (1976) and the fast ladder (lattice) algorithms of Morf and Lee (1977-1981). They are further shown to attain (steady-state unnormalized), or improve upon (first N initialization steps), the very low computational requirements of the efficient RLS solutions of Carayannis, Manolakis, and Kalouptsidis (1983). Finally, several efficient procedures are presented by which to ensure the numerical Stability of the transversal-filter algorithms, including the incorporation of soft-constraints into the performance criteria, internal bounding and rescuing procedures, and dynamic-range-increasing, square-root (normalized) variations of the transversal filters.

关键词： Transversal filters Adaptive filters Lattices Resonance light scattering Least squares approximation Adaptive algorithm Information systems Laboratories Switches filtering algorithms

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RECURSIVE filtering ALGORITHM FOR A 2-DIMENSIONAL SYSTEM

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1979年第1期24卷 130-132页

作者： KATAYAMA, T KOSAKA, M HITACHI LTD SYST DEV LABHITACHIJAPAN

An approximate two-dimensional recursive filtering algorithm that parallels the one-dimensional Kalman filter is presented for a causal system considered by Habibi [1]. A numerical result is also shown.

关键词： filtering algorithms Kalman filters Controllability Observability White noise Digital filters Pattern recognition Polynomials Two dimensional displays

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A FAST ALGORITHM FOR TWO-DIMENSIONAL MEDIAN filtering

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS 1987年第11期34卷 1364-1374页

作者： AHMAD, MO SUNDARARAJAN, D Department of Electrical and Computer Engineering Concordia University Montreal QUE Canada

The median of a set of numbers is a number which partitions the given set, excluding that number, into two subsets with an equal number of elements such that the number is greater than or equal to the elements in one subset and less than or equal to in the other. In image processing, in order to compute the running median, the window is moved from one neighborhood to the next. In this paper, a fast two-dimensional median filtering algorithm is proposed. The algorithm is designed in such a way that in order to find the median of a window, the results obtained during the partitioning of the previous window are used. Test results obtained by running the algorithm on VAX 11/780 are presented and its performance is compared with the Huang's histogram algorithm for median filtering. It is shown that the proposed algorithm's execution time is faster and is independent of the number of bits used to represent the data values. The novel features in the algorithm design that contribute to fast execution are also presented.

关键词： filtering algorithms Partitioning algorithms Histograms Image processing Algorithm design and analysis Testing Pixel Sorting Iterative algorithms Iterative methods

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Adaptive Data filtering of Inertial Sensors with Variable Bandwidth

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SENSORS 2015年第2期15卷 3282-3298页

作者： Alam, Mushfiqul Rohac, Jan Czech Tech Univ Fac Elect Engn Dept Measurement Tech 2 Prague 16627 Czech Republic

MEMS (micro-electro-mechanical system)-based inertial sensors, i.e., accelerometers and angular rate sensors, are commonly used as a cost-effective solution for the purposes of navigation in a broad spectrum of terrestrial and aerospace applications. These tri-axial inertial sensors form an inertial measurement unit (IMU), which is a core unit of navigation systems. Even if MEMS sensors have an advantage in their size, cost, weight and power consumption, they suffer from bias instability, noisy output and insufficient resolution. Furthermore, the sensor's behavior can be significantly affected by strong vibration when it operates in harsh environments. All of these constitute conditions require treatment through data processing. As long as the navigation solution is primarily based on using only inertial data, this paper proposes a novel concept in adaptive data pre-processing by using a variable bandwidth filtering. This approach utilizes sinusoidal estimation to continuously adapt the filtering bandwidth of the accelerometer's data in order to reduce the effects of vibration and sensor noise before attitude estimation is processed. Low frequency vibration generally limits the conditions under which the accelerometers can be used to aid the attitude estimation process, which is primarily based on angular rate data and, thus, decreases its accuracy. In contrast, the proposed pre-processing technique enables using accelerometers as an aiding source by effective data smoothing, even when they are affected by low frequency vibration. Verification of the proposed concept is performed on simulation and real-flight data obtained on an ultra-light aircraft. The results of both types of experiments confirm the suitability of the concept for inertial data pre-processing.

关键词： inertial navigation attitude control filtering algorithms adaptive signal processing accelerometers

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filtering AND SMOOTHING FOR LINEAR DISCRETE-TIME DISTRIBUTED PARAMETER-SYSTEMS BASED ON WIENER-HOPF THEORY WITH APPLICATION TO ESTIMATION OF AIR-POLLUTION

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS 1981年第12期11卷 785-801页

作者： OMATU, S SEINFELD, JH Department of Chemical Engineering California Institute of Technology Pasadena CA USA Department of Information Science and Systems Engineering University of Tokushima Tokushima Japan

Optimal filtering and smoothing algorithms for linear discrete-time distributed parameter systems are derived by a unified approach based on the Wiener-Hopf theory. The Wiener-Hopf equation for the estimation problems is derived using the least-squares estimation error criterion. Using the basic equation, three types of the optimal smoothing estimators are derived, namely, fixed-point, fixed-interval, and fixed-lag smoothers. Finally, the results obtained are applied to estimation of atmospheric sulfur dioxide concentrations in the Tokushima prefecture of Japan.

关键词： filtering theory Nonlinear filters Smoothing methods Distributed parameter systems Air pollution Gaussian processes filtering algorithms Equations Chemical engineering Chemical technology

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LINEAR filtering IN PRESENCE OF TIME-VARYING BIAS

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1972年第6期AC17卷 828-&页

作者： TACKER, EC LEE, CC Department of Electrical and chemical Engineering Louisiana State University Baton Rouge LA USA Department of Electrical Engineering Louisiana State University Baton Rouge LA USA

The problem of estimating the state of a linear system subjected to a time-varying bias with sample paths generated from \dot{b} = F^{\astr}b is considered, and an optimal filtering algorithm is derived. It is shown that the structure of the optimal estimator is the same as that determined earlier by Friedland for constant bias disturbances, and that the algorithm possesses the same computational advantages over the augmented Kalman-Bucy filter.

关键词： Maximum likelihood detection State estimation Filters Covariance matrix Partitioning algorithms Equations Least squares methods Time varying systems filtering algorithms Lead

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PARALLEL filtering ALGORITHM FOR LINEAR-SYSTEMS WITH UNKNOWN TIME-VARYING NOISE STATISTICS

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1974年第5期AC19卷 552-556页

作者： ALSPACH, DL UNIV CALIF SAN DIEGODEPT APPL MECH & ENGN SCILA JOLLACA

The problem of estimating the state of a linear dynamic system driven by additive Gaussian noise with unknown time varying statistics is considered. Estimates of the state of the system are obtained which are based on all past observations of the system. These observations are linear functions of the state contaminated by additive white Gaussian noise. A previously developed algorithm designed for use in the case of stationary noise is modified to allow estimation of an unknown Kalman gain and thus the system state in the presence of unknown time varying noise statistics. The algorithm is inherently parallel in nature and if implemented in a computer with parallel processing capability should only be slightly slower than the stationary Kalman filtering algorithm with known noise statistics.

关键词： filtering algorithms Linear systems Time varying systems Statistics State estimation Kalman filters Additive noise Gaussian noise Additive white noise Algorithm design and analysis

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OPTIMAL SELF-TUNING filtering, PREDICTION, AND SMOOTHING FOR DISCRETE MULTIVARIABLE PROCESSES

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1984年第2期29卷 128-137页

作者： MOIR, TJ GRIMBLE, MJ UNIV STRATHCLYDE DEPT ELECT ENGNGLASGOW G1 1XWSCOTLAND SHEFFIELD CITY POLYTECH DEPT ELECT & ELECT ENGNSHEFFIELD S1 1WBS YORKSHIREENGLAND

An algorithm is proposed for self-tuning optimal fixed-lag smoothing or filtering for linear discrete-time multivariable processes. A z -transfer function solution to the discrete multivariable estimation problem is first presented. This solution involves spectral factorization of polynomial matrices and assumes knowledge of the process parameters and the noise statistics. The assumption is then made that the signal-generating process and noise statistics are unknown. The problem is reformulated so that the model is in an innovations signal form, and implicit self-tuning estimation algorithms are proposed. The parameters of the innovation model of the process can be estimated using an extended Kalman filter or, alternatively, extended recursive least squares. These estimated parameters are used directly in the calculation of the predicted, smoothed, or filtered estimates. The approach is an attempt to generalize the work of Hagander and Wittenmark.

关键词： Smoothing methods Statistics Technological innovation filtering algorithms Nonlinear filters Polynomials Signal processing Recursive estimation Least squares approximation Parameter estimation

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