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At least 127 records · Page 7

Application of analytical redundancy management to Shuttle crafts

The study involves the bank of filters approach to analytical redundancy management since this is amenable to microelectronic implementation. Attention is given to a study of the UD factorized filter to determine if it gives more accurate estimates than the standard Kalman filter when data processing word size is reduced. It is reported that, as the word size is reduced, the effect of modeling error dominates the filter performance of the two filters. However, the UD filter is shown to maintain a slight advantage in tracking performance. It is concluded that because of the UD filter's stability in the serial processing mode, it remains the leading candidate for microelectronic implementation.

Montgomery, R. C.↗

Algorithms for isolating worst case systematic data errors

Two separate algorithms are derived for testing filter sensitivity to systematic data errors. One algorithm provides the absolute minimum Euclidean norm data error for a given estimate component error. The second algorithm can be used to find the minimum norm data error which can be generated by restricted degree Legendre polynomials. A specific very long baseline interferometry (VLBI) baseline estimation is analyzed with the algorithm. It is found that the local vertical is the most sensitive component to error in the data space. The efficiency of a data error sequence linear in elevation angle is within 7% that of the absolute worst case sequence. Elevation angle dependent errors are explored and the special case of a mismodeled troposphere is treated.

Curkendall, D. W.↗

A method for obtaining practical flutter-suppression control laws using results of optimal control theory

The results of optimal control theory are used to synthesize a feedback filter. The feedback filter is used to force the output of the filtered frequency response to match that of a desired optimal frequency response over a finite frequency range. This matching is accomplished by employing a nonlinear programing algorithm to search for the coefficients of the feedback filter that minimize the error between the optimal frequency response and the filtered frequency response. The method is applied to the synthesis of an active flutter-suppression control law for an aeroelastic wind-tunnel model. It is shown that the resulting control law suppresses flutter over a wide range of subsonic Mach numbers. This is a promising method for synthesizing practical control laws using the results of optimal control theory.

Newson, J. R.↗

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqui↗

Interpolation of a surface from sets of discrete height data of different statistical characteristics

This paper presents and analyzes a method for the interpolation of a unique surface from two sets of independent digital height data of differing statistical characteristics. This method is based on linear prediction and thus relies on the concepts of auto- and cross-covariance functions. The linear prediction algorithm for two sets of digital height measurements is first derived and then evaluated using the method of moving averages and bilinear interpolation for comparison. It is found that the overall root mean square interpolation errors of linear prediction are similar to those from moving averages and bilinear interpolation. This accuracy performance, together with the well known potential for controlled filtering of measuring errors and good-behavior in areas of poor control, makes linear prediction a versatile and general method for interpolating a unique surface from two sets of digital height data, with applications in photogrammetric mapping, remote sensing, and other fields.

Leberl, F.↗

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqiu↗

Optical systolic solutions of linear algebraic equations

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

Neuman, C. P.↗

Use of Whatman-41 filters in air quality sampling networks (with applications to elemental analysis)

The operation of a 16-site parallel high volume air sampling network with glass fiber filters on one unit and Whatman-41 filters on the other is reported. The network data and data from several other experiments indicate that (1) Sampler-to-sampler and filter-to-filter variabilities are small; (2) hygroscopic affinity of Whatman-41 filters need not introduce errors; and (3) suspended particulate samples from glass fiber filters averaged slightly, but not statistically significantly, higher than from Whatman-41-filters. The results obtained demonstrate the practicability of Whatman-41 filters for air quality monitoring and elemental analysis.

Neustadter, H. E.↗

Shuttle entry trajectory reconstruction using inflight accelerometer and gyro measurements

An error analysis has been made of a Shuttle postflight entry trajectory reconstruction process to obtain trajectory state estimation errors and to assess the impact of these errors on Shuttle aerodynamic force coefficient extraction. In this analysis, the entry trajectory is assumed to be reconstructed via numerical integration of onboard accelerometer and gyro measurements and constrained to satisfy ground-based radio tracking. The trajectory state estimation errors are calculated using a Kalman-Schmidt sequential filter assuming various measurement error models and combinations of ground-based tracking. The resultant trajectory estimation errors are analyzed in a simplified perturbation process to establish the accuracy to which postflight aerodynamic force coefficients can be determined. Results are presented which show that the principal error sources affecting the trajectory reconstruction and thus the force coefficient extraction, assuming perfect atmospheric density knowledge, are the accelerometer and gyro resolution, acceleration-sensitive gyro drifts, and the alignment uncertainties associated with integration on the Shuttle.

Compton, H. R.↗

Searching Circuit For A Servoloop

Feedback error voltage forced into range of stability. Circuit connected in series with error-voltage line of feedback loop. When loop operates normally in stable region, searching circuit does not disturb operation, and error-voltage output of loop filter is control voltage. When servo unlocks and error-voltage output of loop filter wanders into unstable range, searching circuit forces control voltage to sweep through stable region repeatedly until lock recovered. Consists of two halves identical except polarities of some parts in each half opposite of corresponding parts in other half.

Sigman, E. H.↗

Parallel Processing of Broad-Band PPM Signals

A parallel-processing algorithm and a hardware architecture to implement the algorithm have been devised for timeslot synchronization in the reception of pulse-position-modulated (PPM) optical or radio signals. As in the cases of some prior algorithms and architectures for parallel, discrete-time, digital processing of signals other than PPM, an incoming broadband signal is divided into multiple parallel narrower-band signals by means of sub-sampling and filtering. The number of parallel streams is chosen so that the frequency content of the narrower-band signals is low enough to enable processing by relatively-low speed complementary metal oxide semiconductor (CMOS) electronic circuitry. The algorithm and architecture are intended to satisfy requirements for time-varying time-slot synchronization and post-detection filtering, with correction of timing errors independent of estimation of timing errors. They are also intended to afford flexibility for dynamic reconfiguration and upgrading. The architecture is implemented in a reconfigurable CMOS processor in the form of a field-programmable gate array. The algorithm and its hardware implementation incorporate three separate time-varying filter banks for three distinct functions: correction of sub-sample timing errors, post-detection filtering, and post-detection estimation of timing errors. The design of the filter bank for correction of timing errors, the method of estimating timing errors, and the design of a feedback-loop filter are governed by a host of parameters, the most critical one, with regard to processing very broadband signals with CMOS hardware, being the number of parallel streams (equivalently, the rate-reduction parameter).

Gray, Andrew↗

Altimetry, Orbits and Tides

The nature of the orbit error and its effect on the sea surface heights calculated with satellite altimetry are explained. The elementary concepts of celestial mechanics required to follow a general discussion of the problem are included. Consideration of errors in the orbits of satellites with precisely repeating ground tracks (SEASAT, TOPEX, ERS-1, POSEIDON, amongst past and future altimeter satellites) are detailed. The theoretical conclusions are illustrated with the numerical results of computer simulations. The nature of the errors in this type of orbits is such that this error can be filtered out by using height differences along repeating (overlapping) passes. This makes them particularly valuable for the study and monitoring of changes in the sea surface, such as tides. Elements of tidal theory, showing how these principles can be combined with those pertinent to the orbit error to make direct maps of the tides using altimetry are presented.

Colombo, O. L.↗

Sea surface topography fields of the tropical Pacific from data assimilation

Time series of maps of monthly tropical Pacific dynamic topography anomalies from 1979 through 1985 were constructed by means of assimilation of the tide gauge and expendable bathythermograph (XBT) data into a linear model driven by observed winds. Estimates of error statistics were calculated and compared to actual differences between hindcasts and observations. Four experiements were performed as follows: one with no assimilation, one with assimiation of sea level anomaly data from eight selected island tide gauge stations, one with assimilation of dynamic height anomalies derived from XBT data, and one with both XBT and tide gauge data assimilated. Data from seven additional tide gauge stations were withheld from the assimilation process and used for verification in all four experiements. Statistical objective maps based on data alone were also constructed for comparison purposes. The dynamic response of the model without assimilation was, in general, weaker than the observed response. Assimilation resulted in enhanced signal amplitude in all three assimilation experiments. With few exceptions the error estimated generated by the Kalman filter appeared quite reasonable. Since the error processes cannot be assumed to be white or stationary, we could find no straightforward way to test the formal statistical hypothesis that the time series of differences between the filter ouput and the actual observations were drawn from a population with statistics given by the Kalman filter estimaes. We found that the best filter we could devise was still short of the goal of producing a white innovation sequence. Extensive changes in the assumed error statistics make only marginal differences. The same is true for long time and space scale behavior of different models with richer physics and finer resolution. Better data assimilation results will probably require relaxation of the assumptions of stationarity and serial independence of the errors. Formation of such detailed noise models will require longer time series, with the attendant problems of matching very different data sets.

Miller, Robert N.↗

A theoretical analysis of the round-off propagation in different Kalman filter implementations

A theoretical analysis is made of the error propagation due to numerical round-off for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter and the Chandrasekhar square root filter. From these error models, new insights about the applicability of the different filters and their sensitivity to round-off, is obtained. It is shown that the CKF may become completely unreliable when the original plant is unstable, and that this is easily circumvented by a number of techniques. The square root filters, often quoted to possess a conditioning or sensitivity that is the square root of that of the CKF, are shown to possess this property only for the computation of the covariance of the filtered signal and not for the computation of the Kalman gain or the filtered estimate. Finally, the Chandrasekhar filter is shown to be numerically unstable.

Verhaegen, M.↗

The Atacama Cosmology Telescope: A Measurement of the Thermal Sunyaev-Zel'dovich Effect Using the Skewness of the CMB Temperature Distribution

We present a detection of the unnormalized skewness (T(sup ~)(sup 2)(n(circumflex)) induced by the thermal Sunyaev-Zel'dovich (tSZ) effect in filtered Atacama Cosmology Telescope (ACT) 148 GHz cosmic microwave background temperature maps. Contamination due to infrared and radio sources is minimized by template subtraction of resolved sources and by constructing a mask using outlying values in the 218 GHz (tSZ-null) ACT maps. We measure (T(sup ~)(sup 3) (n(circumflex)) = -31 plus or minus 6 micro-K(sup 3) (measurement error only) or plus or minus 14 micro-K(sup 3) (including cosmic variance error) in the filtered ACT data, a 5sigma detection. We show that the skewness is a sensitive probe of sigma(sub 8), and use analytic calculations and tSZ simulations to obtain cosmological constraints from this measurement. From this signal alone we infer a value of sigma(sub 8) = 0.78 sup +0.03 sub -0.04 (68% C.L.) sup +0.05 sub -0.16. Our results demonstrate that measurements of nonGaussianity can be a useful method for characterizing the tSZ effect and extracting the underlying cosmological information.

Wilson, Michael J.↗

Compressed/reconstructed test images for CRAF/Cassini

A set of compressed, then reconstructed, test images submitted to the Comet Rendezvous Asteroid Flyby (CRAF)/Cassini project is presented as part of its evaluation of near lossless high compression algorithms for representing image data. A total of seven test image files were provided by the project. The seven test images were compressed, then reconstructed with high quality (root mean square error of approximately one or two gray levels on an 8 bit gray scale), using discrete cosine transforms or Hadamard transforms and efficient entropy coders. The resulting compression ratios varied from about 2:1 to about 10:1, depending on the activity or randomness in the source image. This was accomplished without any special effort to optimize the quantizer or to introduce special postprocessing to filter the reconstruction errors. A more complete set of measurements, showing the relative performance of the compression algorithms over a wide range of compression ratios and reconstruction errors, shows that additional compression is possible at a small sacrifice in fidelity.

Dolinar, S.↗

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

VanZwieten, Tannen↗

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Sedlak, Joseph E.↗