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Geometric and probabilistic models for subpixel accuracy are developed. The geometric models bound the error in offset estimation using the pixels in an observed digital straight line. One probabilistic model bounds the estimate of error offset for continuous images. The other model bounds the error for discrete images given that one is in the correct pixel.
The use of Redundant Asynchronous Multiprocessor System to achieve ultrareliable Fault Tolerant Control Systems shows great promise. The development has been hampered by the inability to determine whether differences in the outputs of redundant CPU's are due to failures or to accrued error built up by slight differences in CPU clock intervals. This study derives an analytical dynamic model of the difference between redundant CPU's due to differences in their clock intervals and uses this model with on-line parameter identification to idenitify the differences in the clock intervals. The ability of this methodology to accurately track errors due to asynchronisity generate an error signal with the effect of asynchronisity removed and this signal may be used to detect and isolate actual system failures.
The use of extra collecting horns in the focal plane of an antenna as a means of determining the Direction of Arrival (DOA) of the signal impinging on it, provided it is within the antenna beam, is considered. Our analysis yields a relatively simple algorithm to extract the DOA from the horns' outputs. An algorithm which, in effect, measures the thermal noise of the horns' signals and determines its effect on the uncertainty of the extracted DOA parameters is developed. Both algorithms were implemented in software and tested in simulated data. Based on these tests, it is concluded that this is a viable approach to the DOA determination. Though the results obtained are of general applicability, the particular motivation for the present work is their application to the pointing of a mechanically deformed antenna. It is anticipated that the pointing algorithm developed for a deformed antenna could be obtained as a small perturbation of the algorithm developed for an undeformed antenna. In this context, it should be pointed out that, with a deformed antenna, the array of horns and its associated circuitry constitute the main part of the deformation-compensation system. In this case, the pointing system proposed may be viewed as an additional task carried out by the deformation-compensation hardware.
Department of Mathematical Sciences, University of Alberta, Edmonton, Canada This paper describes the fundamental theory of the ensemble canonical correlation (ECC) algorithm for the seasonal climate forecasting. The algorithm is a statistical regression sch eme based on maximal correlation between the predictor and predictand. The prediction error is estimated by a spectral method using the basis of empirical orthogonal functions. The ECC algorithm treats the predictors and predictands as continuous fields and is an improvement from the traditional canonical correlation prediction. The improvements include the use of area-factor, estimation of prediction error, and the optimal ensemble of multiple forecasts. The ECC is applied to the seasonal forecasting over various parts of the world. The example presented here is for the North America precipitation. The predictor is the sea surface temperature (SST) from different ocean basins. The Climate Prediction Center's reconstructed SST (1951-1999) is used as the predictor's historical data. The optimally interpolated global monthly precipitation is used as the predictand?s historical data. Our forecast experiments show that the ECC algorithm renders very high skill and the optimal ensemble is very important to the high value.
In a series of papers Hung pioneered the development of shearography, an optical NDE technique that detects gradients of surface displacements. Its utility for qualitative flaw characterization has been demonstrated, and while there is a need for using shearography in NDE for quantitative analysis, a large amount of the research has concentrated on the qualitative evaluation of structures and materials. The purpose of this paper is to begin building upon a foundation for the newly emerging quantitative shearography. We begin the analysis by considering the approximations leading to the governing shearography equation.
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In a parameter study of satellite orbits, sampling errors of area-time averaged rain rate due to temporal sampling by satellites were estimated. The sampling characteristics were studied by accounting for the varying visiting intervals and varying fractions of averaging area on each visit as a function of the latitude of the grid box for a range of satellite orbital parameters. The sampling errors were estimated by a simple model based on the first-order Markov process of the time series of area averaged rain rates. For a satellite of nominal Tropical Rainfall Measuring Mission (Thiele, 1987) carrying an ideal scanning microwave radiometer for precipitation measurements, it is found that sampling error would be about 8 to 12 pct of estimated monthly mean rates over a grid box of 5 X 5 degrees. It is suggested that an observation system based on a low inclination satellite combined with a sunsynchronous satellite simultaneously might be the best candidate for making precipitation measurements from space.
The Laser Atmospheric Wind Sounder (LAWS) study phase has resulted in a preliminary error budget and an estimate of the instrument performance. This paper will present the line-of-sight (LOS) Velocity Measurement Error Budget, the instrument Boresight Error Budget, and the predicted signal-to-noise ratio (SNR) performance. The measurement requirements and a preliminary design for the LAWS instrument are presented in a companion paper.
Precision attitude determination for recent and planned space missions typically includes quaternion star trackers (ST) and a three-axis inertial reference unit (IRU). Sensor selection is based on estimates of knowledge accuracy attainable from a Kalman filter (KF), which provides the optimal solution for the case of linear dynamics with measurement and process errors characterized by random Gaussian noise with white spectrum. Non-Gaussian systematic errors in quaternion STs are often quite large and have an unpredictable time-varying nature, particularly when used in non-inertial pointing applications. Two filtering methods are proposed to reduce the attitude estimation error resulting from ST systematic errors, 1) extended Kalman filter (EKF) augmented with Markov states, 2) Unscented Kalman filter (UKF) with a periodic measurement model. Realistic assessments of the attitude estimation performance gains are demonstrated with both simulation and flight telemetry data from the Lunar Reconnaissance Orbiter.
Passive and active microwave rain sensors onboard earth-orbiting satellites estimate monthly rainfall from the instantaneous rain statistics collected during satellite overpasses. It is well known that climate-scale rain estimates from meteorological satellites incur sampling errors resulting from the process of discrete temporal sampling and statistical averaging. Sampling and retrieval errors ultimately become entangled in the estimation of the mean monthly rain rate. The sampling component of the error budget effectively introduces statistical noise into climate-scale rain estimates that obscure the error component associated with the instantaneous rain retrieval. Estimating the accuracy of the retrievals on monthly scales therefore necessitates a decomposition of the total error budget into sampling and retrieval error quantities. This paper presents results from a statistical evaluation of the sampling and retrieval errors for five different space-borne rain sensors on board nine orbiting satellites. Using an error decomposition methodology developed by one of the authors, sampling and retrieval errors were estimated at 0.25 resolution within 150 km of ground-based weather radars located at Kwajalein, Marshall Islands and Melbourne, Florida. Error and bias statistics were calculated according to the land, ocean and coast classifications of the surface terrain mask developed for the Goddard Profiling (GPROF) rain algorithm. Variations in the comparative error statistics are attributed to various factors related to differences in the swath geometry of each rain sensor, the orbital and instrument characteristics of the satellite and the regional climatology. The most significant result from this study found that each of the satellites incurred negative longterm oceanic retrieval biases of 10 to 30%.
Taylor series truncation effects on estimation of error parameters in reliability testing
A methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. Theoretical Kalman filter estimation error bias and variance values are derived at steady-state operating conditions, and the tuner selection routine is applied to minimize these values. The new methodology yields an improvement in on-line engine performance estimation accuracy.
A 1-year field program was conducted at South Pole Station in 1992 to measure the downward infrared radiance spectrum at a resolution of 1/ cm over the spectral range 550-1667 cm-'. The atmosphere over the Antarctic Plateau is the coldest and driest on Earth, where in winter, surface temperatures average about -60 C, the total column water vapor is as low as 300 pm of precipitable water, and the clear-sky downward longwave flux is usually less than 80 W/sq m. Three clear-sky test cases are selected, one each for summer, winter, and spring, for which high- quality radiance data are available.as well as ancillary data to construct model atmospheres from radiosondes, ozonesondes, and other measurements. The model atmospheres are used in conjunction with the line-by-line radiative transfer model (LBLRTM) to compare model calculations with the spectral radiance measurements. The high-resolution calculations of LBLRTM (approx. = 0.001/ cm) are matched to the lower-resolution measurements (1/ cm) by adjusting their spectral resolution and by applying a correction for the finite field of view of the interferometer. In summer the uncertainties in temperature and water vapor profiles dominate the radiance error in the LBLRTM calculations. In winter the uncertainty in viewing zenith angle becomes important as well as the choice of atmospheric levels in the strong near-surface temperature inversion. The spectral radiance calculated for each of the three test cases generally agrees with that measured, to within twice the total estimated radiance error, thus validating LBLRTM to this level of accuracy for Antarctic conditions. However, the discrepancy exceeds twice the estimated error in the gaps between spectral lines in the region 1250-1500/ cm, where emission is dominated by the foreign-broadened water vapor continuum.
State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range 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.