Combined problem of filtering and optimization with cross-correlated noise
Linear stochastic continuous feedback system with white noise and control input, investigating combined problem of filtering and optimal control
Boland, J. S., III↗
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Optimum homomorphic filters.
Optimum homomorphic filter analysis based on cascade representation
LINEAR SYSTEM↗
Methods of sequential estimation for determining initial data in numerical weather prediction
Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.
Cohn, S. E.↗
An airborne study of boundary layer heat and moisture fluxes for project FIFE
A summary of work accomplished during the first International Satellite Cloud Climatology Project (ISLSCP) Field Experiment is presented. The Wyoming King Air participated in Intensive Field Campaigns (IFCs) 3 and 4 in 1987, which were committed to a combination of airborne sensible and latent heat flux measurements and soil moisture mappings, with the University of Kansas' X-band side-looking airborne radar (SLAR). A total of 9 flux missions were flown in 1987 using several different flight designs. A critical decision in the first round of aircraft flux analyses, agreed to by all the flux aircraft investigators, was to pass the aircraft data through a high-pass filter prior to the eddy-correlation flux calculations. Several conclusions were drawn from this study: (1) boundary layer (BL) profiles of heat fluxes were usually linear; (2) high-pass filtering applied to the aircraft data did not add to the disagreement between the profile; (3) undersampling at high frequencies could have accounted for as much as a 15 percent underestimate of surface fluxes; (4) disagreement between the aircraft and surface latent heat fluxes changed signs between summer and fall; (5) magnitude and sign of disagreement between aircraft and surface heat fluxes varied systematically with BL depth or height of aircraft profile; and (6) Bowen ratios from both detrended and filtered aircraft data agreed with surface values better for moist, summer cases than for dry cases.
Kelly, Robert D.↗
Non-Migrating Tides, with Zonally Symmetric Component, Generated in the Mesosphere
For comparison with measurements from the TIMED satellite and coordinated ground based observations, we discuss results from our Numerical Spectral Model (NSM) that incorporates the Doppler Spread Parameterization (Hines, 1997) for small-scale gravity waves (GWs). The NSM extends from the ground into the thermosphere and describes the major dynamical features of the atmosphere including the wave driven equatorial oscillations (QBO and SAO), and the seasonal variations of tides and planetary waves. With emphasis on the non-migrating tides, having periods of 24 and 12 hours, we discuss our modeling results that account for the classical migrating solar excitation sources only. As reported earlier, the NSM reproduces the observed seasonal variations and in particular the large equinoctial maxima in the amplitude of the migrating diurnal tide at altitudes around 90 km. Filtering of the tide by the zonal circulation and GW momentum deposition was identified as the cause. The GWs were also shown to produce a strong non-linear interaction between the diurnal and semi-diurnal tides. Confined largely to the mesosphere, the NSM produces through dynamical interactions a relatively large contribution of non-migrating tides. A striking feature is seen in the diurnal and semi-diurnal oscillations of the zonal mean (m = 0). Eastward propagating tides are also generated for zonal wave numbers m = 1 to 4. When the NSM is run without GWs, the amplitudes for the non-migrating tides, including m = 0, are generally small. Planetary wave interaction and non-linear coupling that involves the filtering of GWs and related height integration of dynamical features are discussed as possible mechanisms for generating these non-migrating tides in the NSM. As is the case for the solar migrating tides, the non-migrating tides reveal persistent seasonal variations. Under the influence of the QBO and SAO, interannual variations are produced.
Mayr, H. G.↗
Optimal control of linear systems with time- delay and observation noise
Optimal control generated by Kalman filter and least mean-squared predictor for linear systems with time delay
Kleinman, D. L.↗
Algorithms for linear-systems control
Control-theory design package aids design of linear-quadratic-Gaussian (LOG) controllers and optimal filters. It is applicable to systems that can be modeled by linear time-invariant differential or difference equations.
Armstrong, E. S.↗
Attitude determination and calibration using a recursive maximum likelihood-based adaptive Kalman filter
An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.
Kelly, D. A.↗
Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Miller, Brad A.↗
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Miller, Bard A.↗
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Miller, Brad A.↗
Nonlinear modeling and estimation of slew induced structural deformations
A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformation are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.
Dwyer, T. A. W., III↗
Bilinear modeling and state estimation of slew-induced deformations of a flexible multibody system
A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformations are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.
Dwyer, Thomas A. W., III↗
Integrated adaptive filtering and design for control experiments of flexible structures
A novel method is presented of identifying a state space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relations between the state space model and the finite difference model for linear stochastic systems derived through projection filters. It is proven that least squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. Experimental example is used to illustrate the feasibility of the method.
Huang, Jen-Kuang↗
Time-domain technique for optimal design of digital-filter equalizers.
A technique is presented for the design of frequency-sampling and transversal digital filters from specified unit-impulse responses. The multiplier coefficients for the digital filter are specified by the use of a linear-programming algorithm. Examples include the design of digital filters to generate intersymbol-free pulses for data transmission over ideal bandlimited channels and to equalize data transmission channels that have known unit-impulse responses.
Burlage, D. W.↗
Least squares restoration of multi-channel images
In this paper, a least squares filter for the restoration of multichannel imagery is presented. The restoration filter is based on a linear, space-invariant imaging model and makes use of an iterative matrix inversion algorithm. The restoration utilizes both within-channel (spatial) and cross-channel information as constraints. Experiments using color images (three-channel imagery with red, green, and blue components) were performed to evaluate the filter's performance and to compare it with other monochrome and multichannel filters.
Chin, Roland T.↗
Benchmarking a Soil Moisture Data Assimilation System for Agricultural Drought Monitoring
Despite considerable interest in the application of land surface data assimilation systems (LDAS) for agricultural drought applications, relatively little is known about the large-scale performance of such systems and, thus, the optimal methodological approach for implementing them. To address this need, this paper evaluates an LDAS for agricultural drought monitoring by benchmarking individual components of the system (i.e., a satellite soil moisture retrieval algorithm, a soil water balance model and a sequential data assimilation filter) against a series of linear models which perform the same function (i.e., have the same basic inputoutput structure) as the full system component. Benchmarking is based on the calculation of the lagged rank cross-correlation between the normalized difference vegetation index (NDVI) and soil moisture estimates acquired for various components of the system. Lagged soil moistureNDVI correlations obtained using individual LDAS components versus their linear analogs reveal the degree to which non-linearities andor complexities contained within each component actually contribute to the performance of the LDAS system as a whole. Here, a particular system based on surface soil moisture retrievals from the Land Parameter Retrieval Model (LPRM), a two-layer Palmer soil water balance model and an Ensemble Kalman filter (EnKF) is benchmarked. Results suggest significant room for improvement in each component of the system.
soil moisture↗
Applications of charge-coupled device transversal filters to communication
The paper discusses the computational power of state-of-the-art charged-coupled device (CCD) transversal filters in communications applications. Some of the performance limitations of CCD transversal filters are discussed, with attention given to time delay and bandwidth, imperfect charge transfer efficiency, weighting coefficient error, noise, and linearity. The application of CCD transversal filters to matched filtering, spectral filtering, and Fourier analysis is examined. Techniques for making programmable transversal filters are briefly outlined.
Buss, D. D.↗