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A constant direction of the Riccati equation associated with a class of singular discrete-time optimization problems is defined. The set of constant directions is completely characterized using a control viewpoint. Constant directions are used to reduce the computational complexity of the optimal system. Application to optimal filtering in colored noise is given.
This paper discusses means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data. The commonly used analytical predictors of accuracy are compared from both statistical and simplified geometric standpoints. Emphasizing practical considerations, such as modeling error, the accuracy predictions are evaluated with real and simulated data. Improved computations of the Cramer-Rao bound to correct large discrepancies caused by colored noise and modeling error are presented. This corrected Cramer-Rao bound is the best available analytical predictor of accuracy. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.
Means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data are discussed. The most commonly used analytical predictors of accuracy are derived and compared from both statistical and simplified geometrics standpoints. The accuracy predictions are evaluated with real and simulated data, with an emphasis on practical considerations, such as modeling error. Improved computations of the Cramer-Rao bound to correct large discrepancies due to colored noise and modeling error are presented. The corrected Cramer-Rao bound is shown to be the best available analytical predictor of accuracy, and several practical examples of the use of the Cramer-Rao bound are given. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.
Chi and Mendel (1984) analyzed the performance of minimum-variance deconvolution (MVD). In this correspondence, a further analysis of the performance of the MVD filter is presented. It is shown that the MVD filter performs like an inverse filter and a whitening filter as SNR goes to infinity, and like a matched filter as SNR goes to zero. The estimation error of the MVD filter is colored noise, but it becomes white when SNR goes to zero. This analysis also conects the error power-spectral density of the MVD filter with the spectrum of the causal-prediction error filter.
The fidelity and resolution of the traditional Wiener restorations given in the prevalent digital processing literature can be significantly improved when the transformations between the continuous and discrete representations in image gathering and display are accounted for. However, the visual quality of these improved restorations also is more sensitive to the defects caused by aliasing artifacts, colored noise, and ringing near sharp edges. In this paper, these visual defects are characterized, and methods for suppressing them are presented. It is demonstrated how the visual quality of fidelity-maximized images can be improved when (1) the image-gathering system is specifically designed to enhance the performance of the image-restoration algorithm, and (2) the Wiener filter is combined with interactive Gaussian smoothing, synthetic high edge enhancement, and nonlinear tone-scale transformation. The nonlinear transformation is used primarily to enhance the spatial details that are often obscurred when the normally wide dynamic range of natural radiance fields is compressed into the relatively narrow dynamic range of film and other displays.
Results are reported from a stochastic analysis of a 5-day time series of the geomagnetic AE index during an active period. The original data, the power spectrum, and the autocorrelation function are shown, and the steps in the analysis are described in detail. It is found that the autocorrelation time scale is about 50 min, giving a correlation dimension (for the construction of a time series of m-dimensional vectors) of 2.4. This result is consistent with either colored-noise or deterministic-chaos magnetosphere models, indicating the need for further investigation.
Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.
This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.
Estimation subroutine package comprises fast, efficient, and simple least-squares data-processing algorithms for use in orbit determination and related analyses. Very reliable and general algorithms have been documented. Package contains collection of streamlined subroutines that can be used to solve large variety of parameter-estimation and filtering problems. Special routines are included for problems with colored process noise and covariance (factor) mapping.
Much of the work that the Space Shuttle will perform requires a capability to rendezvous with other orbiting objects. The formulation and design philosophy behind the Space Shuttle Orbiter rendezvous navigation system are the subjects of this paper. The current rendezvous navigation design incorporates a Kalman filter to estimate the relative position and velocity. The filter is augmented with state elements for the estimation of colored measurement noise and acceleration modeling errors. Several measurement types are available to the filter: a manual optical sighting device, an automatic optical tracking instrument, and a rendezvous radar which provides range and range rate measurements as well as the line of sight direction. The filter also includes a technique for detecting highly improbable measurements and excluding them from Kalman processing.
We have simulated full-sky maps of the cosmic microwave background (CMB) anisotropy expected from cold dark matter (CDM) models at 0.5 deg and 1.0 deg angular resolution. Statistical properties of the maps are presented as a function of sky coverage, angular resolution, and instrument noise, and the implications of these results for observability of the Doppler peak are discussed. The rms fluctuations in a map are not a particularly robust probe of the existence of a Doppler peak; however, a full correlation analysis can provide reasonable sensitivity. We find that sensitivity to the Doppler peak depends primarily on the fraction of sky covered, and only secondarily on the angular resolution and noise level. Color plates of the simulated maps are presented to illustrate the anisotropies.
Software was developed for a Fujitsu HOAP-2 humanoid robot to demonstrate that such "human form" robots can be used to perform useful tasks in an unknown environment; specifically, that they can operate with or in the place of humans to carry out construction operations necessary for space exploration, such as building or maintaining planetary surface habitats for humans. This paper describes the autonomous vision and hand-eye coordination software that enables the HOAP-2 to locate and manipulate objects. Simple vision and pattern detection algorithms including color filtering, noise filtering, image segmentation, orientation filters, and a feedback controlled tracking system enable the robot to locate marked building materials in the workspace. Experimentally determined spatial mappings associate locations in the visual field with the arm joint angles and trajectories necessary to reach these locations, allowing the robot to reach for and manipulate the building materials. These capabilities, when combined with locomotion capabilities, enable the robot to operate autonomously in an unknown workspace.
The MODIS instruments on Terra and Aqua were designed to allow the measurement of chlorophyll fluorescence effects over ocean. The retrieval algorithm is based on the difference between the water-leaving radiances at 667nm and 678nm. The water-leaving radiances at these wavelengths are usually very low relative to the top- of-atmosphere radiances. The high radiometric accuracy needed to retrieve the small fluorescence signal lead to a dual gain design for the 667 and 678nm bands. This paper discusses the benefits obtained from this design choice and provides justification for the use of only one set of gains for global processing of ocean color products. Noise characteristics of the two bands and their related products are compared to other products of bands from 412nm to 2130nm. The impact of polarization on the two bands is discussed. In addition, the impact of stray light on the two bands is compared to other MODIS bands.
The MODIS instruments on Terra and Aqua were designed to allow the measurement of chlorophyll fluorescence effects over ocean. The retrieval algorithm is based on the difference between the water-leaving radiances at 667nm and 678nm. The water-leaving radiances at these wavelengths are usually very low relative to the top-of-atmosphere radiances. The high radiometric accuracy needed to retrieve the small fluorescence signal lead to a dual gain design for the 667 and 678nm bands. This paper discusses the benefits obtained from this design choice and provides justification for the use of only one set of gains for global processing of ocean color products. Noise characteristics of the two bands and their related products are compared to other products of bands from 412nm to 2130nm. The impact of polarization on the two bands is discussed. In addition, the impact of stray light on the two bands is compared to other MODIS bands.
Accurate electronic-noise simulation is essential for low-energy physics in liquid-argon TPCs. More realistic noise modeling allows us to better tune reconstruction algorithms and more reliably assess and optimize signal-detection thresholds. We present a data-driven noise simulation framework developed for the ICEBERG test stand for DUNE that generates synthetic noise waveforms that reproduce both (i) the measured per-channel magnitude of the Fast Fourier Transform (FFT) and (ii) frequency-dependent channel-to-channel correlations observed in ICEBERG noise data. Using a dedicated noise-only dataset, we build a compact noise model containing per-channel FFT-magnitude targets together with a small set of band-wise cross-wire color matrices. White noise is generated in the frequency domain by drawing circular-symmetric complex Gaussian coefficients with random phases and scaling them to match the measured FFT-magnitude targets, and cross-wire correlations are subsequently imposed using the stored color matrices. The model and algorithm were integrated into the LArSoft + Wire-Cell Toolkit simulation chain and validated by comparing waveform structure, frequency-domain spectra, and band-limited correlation matrices from simulated noise and ICEBERG data. This approach can be extended to other LArTPC operating conditions.
Images with signal-dependent noise present challenges beyond those of images with additive white or colored signal-independent noise in terms of designing the optimal 4-f correlation filter that maximizes correlation-peak signal-to-noise ratio, or combinations of correlation-peak metrics. Determining the proper design becomes more difficult when the filter is to be implemented on a constrained-modulation spatial light modulator device. The design issues involved for updatable optical filters for images with signal-dependent film-grain noise and speckle noise are examined. It is shown that although design of the optimal linear filter in the Fourier domain is impossible for images with signal-dependent noise, proper nonlinear preprocessing of the images allows the application of previously developed design rules for optimal filters to be implemented on constrained-modulation devices. Thus the nonlinear preprocessing becomes necessary for correlation in optical systems with current spatial light modulator technology. These results are illustrated with computer simulations of images with signal-dependent noise correlated with binary-phase-only filters and ternary-phase-amplitude filters.
This Annual Report illustrates the work carried out during the last grant-year activity on the Test of the Equivalence Principle in an Einstein Elevator. The activity focused on the following main topics: (1) analysis and conceptual design of a detector configuration suitable for the flight tests; (2) development of techniques for extracting a small signal from data strings with colored and white noise; (3) design of the mechanism that spins and releases the instrument package inside the cryostat; and (4) experimental activity carried out by our non-US partners (a summary is shown in this report). The analysis and conceptual design of the flight-detector (point 1) was focused on studying the response of the differential accelerometer during free fall, in the presence of errors and precession dynamics, for various detector's configurations. The goal was to devise a detector configuration in which an Equivalence Principle violation (EPV) signal at the sensitivity threshold level can be successfully measured and resolved out of a much stronger dynamics-related noise and gravity gradient. A detailed analysis and comprehensive simulation effort led us to a detector's design that can accomplish that goal successfully.
The Multiscale Retinex With Color Restoration (MSRCR) is a non-linear image enhancement algorithm that provides simultaneous dynamic range compression, color constancy and rendition. The overall impact is to brighten up areas of poor contrast/lightness but not at the expense of saturating areas of good contrast/brightness. The downside is that with the poor signal-to-noise ratio that most image acquisition devices have in dark regions, noise can also be greatly enhanced thus affecting overall image quality. In this paper, we will discuss the impact of the MSRCR on the overall quality of an enhanced image as a function of the strength of shadows in an image, and as a function of the root-mean-square (RMS) signal-to-noise (SNR) ratio of the image.