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NASA NTRS1986

Space infrared telescope pointing control system. Infrared telescope tracking in the presence of target motion

The use of charge-coupled-devices, or CCD's, has been documented by a number of sources as an effective means of providing a measurement of spacecraft attitude with respect to the stars. A method exists of defocussing and interpolation of the resulting shape of a star image over a small subsection of a large CCD array. This yields an increase in the accuracy of the device by better than an order of magnitude over the case when the star image is focussed upon a single CCD pixel. This research examines the effect that image motion has upon the overall precision of this star sensor when applied to an orbiting infrared observatory. While CCD's collect energy within the visible spectrum of light, the targets of scientific interest may well have no appreciable visible emissions. Image motion has the effect of smearing the image of the star in the direction of motion during a particular sampling interval. The presence of image motion is incorporated into a Kalman filter for the system, and it is shown that the addition of a gyro command term is adequate to compensate for the effect of image motion in the measurement. The updated gyro model is included in this analysis, but has natural frequencies faster than the projected star tracker sample rate for dim stars. The system state equations are reduced by modelling gyro drift as a white noise process. There exists a tradeoff in selected star tracker sample time between the CCD, which has improved noise characteristics as sample time increases, and the gyro, which will potentially drift further between long attitude updates. A sample time which minimizes pointing estimation error exists for the random drift gyro model as well as for a random walk gyro model.

Powell, J. D.↗

NASA NTRS1972

A generalized method for the identification of aircraft stability and control derivatives from flight test data.

This paper discusses the application of a generalized identification method for flight test data analysis. The method is based on the maximum likelihood (ML) criterion and includes output error and equation error methods as special cases. Both the linear and nonlinear models with and without process noise are considered. The flight test data from lateral maneuvers of HL-10 and M2/F3 lifting bodies are processed to determine the lateral stability and control derivatives, instrumentation accuracies and biases. A comparison is made between the results of the output error method and the generalized ML method for M2/F3 data containing gusts. It is shown that better fits to time histories are obtained by using the generalized ML method.

Mehra, R. K.↗

DOE OSTI2025

Model validation and error attribution for a drifting qubit

Qubit performance is often reported in terms of a variety of single-value metrics, each providing a facet of the underlying noise mechanism limiting performance. However, the value of these metrics may drift over long timescales, and reporting a single number for qubit performance fails to account for the low-frequency noise processes that give rise to this drift. Here, in this work, we demonstrate how we can use the distribution of these values to validate or invalidate candidate noise models. We focus on the case of randomized benchmarking (RB), where typically a single error rate is reported but this error rate can drift over time when multiple passes of RB are performed. We show that using a statistical test as simple as the Kolmogorov-Smirnov statistic on the distribution of RB error rates can be used to rule out noise models, assuming the experiment is performed over a long enough time interval to capture relevant low frequency noise. With confidence in a noise model, we show how care must be exercised when performing error attribution using the distribution of drifting RB error rate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1992

Supersonic acoustic source mechanisms for free jets of various geometries

The aeroacoustic performance of several generic nozzle geometries was tested to evaluate the potential benefits of using non-round jet exit geometries to reduce noise from combat military aircraft. Both the aerodynamics and far field acoustics of several M(sub d) = 1.5 and 2.0 round, elliptic, and rectangular nozzles, including an augmented deflector exhaust nozzle (ADEN), were studied to assess noise emission. The nozzles were operated to jet total temperatures, T(sub 0) = 1160 degree R, and the data scaled to constant thrust. The data were propagated to 1500 ft. and corrected to perceived noise level. The aerodynamic results of the study show that the non-round nozzle geometries mix much faster with the surrounding medium than does an equivalent round nozzle plume. Both the ADEN and elliptic nozzles provide significant reduction of noise, 6 to 7 PNdB, along the major axis direction with little expected impact on nozzle performance. Shock noise processes are eliminated for elliptic nozzles, but are still significant with rectangular nozzles. Comparison of measurements to theoretical predictions of noise using the quasi-linear instability wave model demonstrates good qualitative agreement.

Seiner, John M.↗

NASA NTRS2002

Causes of Long-Term Drought in the United States Great Plains

The United States Great Plains (USGP) experienced a number of multi-year droughts during the last century, most notably the droughts of the 1930s and 1950s. This study examines the causes of such droughts using ensembles of long term (1930-1999) simulations carried out with the NASA Seasonal-to-Interannual Prediction Project (NSIPP-1) atmospheric general circulation model (AGCM) forced with observed sea surface temperatures (SSTs). The results show that the model produces long-term (multi-year) variations in the USGP precipitation that are similar to those observed. A correlative analysis suggests that the ensemble mean low frequency (time scales longer than about 6 years) rainfall variations in the USGP are linked to a pan-Pacific pattern of SST variability that is the leading empirical orthogonal function (EOF) in the low frequency SST data. The link between the SST and the Great Plains precipitation is confirmed in idealized AGCM simulations, in which the model is forced by the 2 polarities of the pan-Pacific SST pattern. The idealized simulations further show that it is primarily the tropical part of the SST anomalies that influence the USGP. As such, the USGP tend to have above normal precipitation when the tropical Pacific SSTs are above normal, while there is a tendency for drought when the tropical SSTs are cold. The upper tropospheric response to the pan-Pacific SST EOF shows a global-scale pattern with a strong wave response in the Pacific and a substantial zonally-symmetric component in which USGP pluvial (drought) conditions are associated with reduced (enhanced) heights throughout the extra-tropics. The potential predictability of rainfall in the USGP associated with SSTs is rather modest, with on average about 1/3 of the total low frequency rainfall variance forced by SST anomalies. Further idealized experiments with climatological SST, suggest that the remaining low frequency variance in the USGP precipitation is the result of interactions with soil moisture. In particular, simulations with soil moisture feedback show a six-fold increase in the variance in annual USGP precipitation compared with simulations in which the soil feedback is excluded. In addition to increasing variance, the interactions with the soil introduce year-to-year memory in the hydrological cycle that is consistent with a red noise process, in which the low frequencies in the deep soil are the result of integrating a net forcing (precipitation-evaporation-runoff) that is white noise on interannual time scales. As such, the role of low frequency SST variability is to introduce a bias to the net forcing on the soil moisture that drives the random process preferentially to either wet or dry conditions.

Schubert, Siegfried D.↗

NASA NTRS1996

Variance Analysis of Unevenly Spaced Time Series Data

We have investigated the effect of uneven data spacing on the computation of delta (sub chi)(gamma). Evenly spaced simulated data sets were generated for noise processes ranging from white phase modulation (PM) to random walk frequency modulation (FM). Delta(sub chi)(gamma) was then calculated for each noise type. Data were subsequently removed from each simulated data set using typical two-way satellite time and frequency transfer (TWSTFT) data patterns to create two unevenly spaced sets with average intervals of 2.8 and 3.6 days. Delta(sub chi)(gamma) was then calculated for each sparse data set using two different approaches. First the missing data points were replaced by linear interpolation and delta (sub chi)(gamma) calculated from this now full data set. The second approach ignored the fact that the data were unevenly spaced and calculated delta(sub chi)(gamma) as if the data were equally spaced with average spacing of 2.8 or 3.6 days. Both approaches have advantages and disadvantages, and techniques are presented for correcting errors caused by uneven data spacing in typical TWSTFT data sets.

Hackman, Christine↗

NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗

NASA NTRS1975

Design of optimal partial state feedback controllers for linear systems in stochastic environments

The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.

Joshi, S. M.↗

NASA NTRS1974

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.

Joshi, S. M.↗

DOE OSTI2023

Reliable Devices Yield Stable Quantum Computations

Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence the circuit outcomes. Here we address how temporal and spatial variations in noise relate device reliability to quantum computing stability. First, our approach quantifies the differences in statistical distributions of characterization metrics collected at different times and locations using Hellinger distance. We then validate an analytical bound that relates this distance directly to the stability of a computed expectation value. Our demonstration uses numerical simulations with models informed by the washington superconducting transmon device. We find that the stability metric is consistently bounded from above by the corresponding Hellinger distance, which can be cast as a specified tolerance level. These results underscore the significance of reliable quantum computing devices and the impact for stable quantum computation.

Dasgupta, Samudra↗

NASA NTRS1993

A multi-variance analysis in the time domain

Recently a new technique for characterizing the noise processes affecting oscillators was introduced. This technique minimizes the difference between the estimates of several different variances and their values as predicted by the standard power law model of noise. The method outlined makes two significant advancements: it uses exclusively time domain variances so that deterministic parameters such as linear frequency drift may be estimated, and it correctly fits the estimates using the chi-square distribution. These changes permit a more accurate fitting at long time intervals where there is the least information. This technique was applied to both simulated and real data with excellent results.

Walter, Todd↗

NASA NTRS1988

Advanced Receiver tracking of Voyager 2 near solar conjunction

The Advanced Receiver (ARX) was used to track the Voyager 2 spacecraft at low Sun-Earth-Probe (SEP) angles near solar conjunction in December of 1987. The received carrier signal exhibited strong fluctuations in both phase and amplitude. The ARX used spectral estimation and mathematical modeling of the phase and receiver noise processes to set an optimum carrier tracking bandwidth. This minimized the mean square phase error in tracking carrier phase and thus minimized the loss in the telemetry signal-to-noise ratio due to the carrier loop. Recovered symbol SNRs and errors in decoded engineering data for the ARX are compared with those for the current Block 3 telemetry stream. Optimum bandwidths are plotted against SEP angle. Measurements of the power spectral density of the solar phase and amplitude fluctuations are also given.

Brown, D. H.↗

NASA NTRS1980

Location and propagation of shock associated noise from supersonic jets

Shock associated noise from unheated supersonic jets is investigated through acoustic measurements in both the near and far fields. The peak Helmholtz number of broadband shock noise is found to be independent of nozzle pressure ratio when based on the length of the shock cells and the ambient speed of sound. This indicates that the acoustic wavelengths generated in the shock noise process are limited in size by the shock cell spacing. Excellent agreement between power spectral densities measured at various far-field angles is obtained at and above the peak shock noise frequency when source convection effects are included. Results show a directivity of broadband shock noise pointed in the upstream direction, with omnidirectionality being approached only at high pressure ratios. The relative importance of shock noise with respect to jet mixing noise is found to be maximum near the pressure ratio at which a Mach disc begins to form in the jet. Near-field measurements point to the downstream shock cells as the region where the dominant shock noise eminates from the jet.

Norum, T. D.↗

NASA NTRS1989

Bilinear modeling and nonlinear estimation

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Dwyer, Thomas A. W., III↗

NASA NTRS1996

Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation

The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.

Hutsell, Steven T.↗

DOE OSTI2021

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

42 ENGINEERING↗

NASA NTRS1997

Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise

Magnetometers and gyroscopes have been shown to provide very accurate attitudes for a variety of spacecraft. These results have been obtained, however, using a batch-least-squares algorithm and long periods of data. For use in onboard applications, attitudes are best determined using sequential estimators such as the Kalman filter. When a filter is used to determine attitudes using magnetometer and gyroscope data for input, the resulting accuracy is limited by both the sensor accuracies and errors inherent in the Earth magnetic field model. The Kalman filter accounts for the random component by modeling the magnetometer and gyroscope errors as white noise processes. However, even when these tuning parameters are physically realistic, the rate biases (included in the state vector) have been found to show systematic oscillations. These are attributed to the field model errors. If the gyroscope noise is sufficiently small, the tuned filter 'memory' will be long compared to the orbital period. In this case, the variations in the rate bias induced by field model errors are substantially reduced. Mistuning the filter to have a short memory time leads to strongly oscillating rate biases and increased attitude errors. To reduce the effect of the magnetic field model errors, these errors are estimated within the filter and used to correct the reference model. An exponentially-correlated noise model is used to represent the filter estimate of the systematic error. Results from several test cases using in-flight data from the Compton Gamma Ray Observatory are presented. These tests emphasize magnetometer errors, but the method is generally applicable to any sensor subject to a combination of random and systematic noise.

Sedlak, J.↗

NASA NTRS1987

Adaptive control and noise suppression by a variable-gain gradient algorithm

An adaptive control system based on normalized LMS filters is investigated. The finite impulse response of the nonparametric controller is adaptively estimated using a given reference model. Specifically, the following issues are addressed: The stability of the closed loop system is analyzed and heuristically established. Next, the adaptation process is studied for piecewise constant plant parameters. It is shown that by introducing a variable-gain in the gradient algorithm, a substantial reduction in the LMS adaptation rate can be achieved. Finally, process noise at the plant output generally causes a biased estimate of the controller. By introducing a noise suppression scheme, this bias can be substantially reduced and the response of the adapted system becomes very close to that of the reference model. Extensive computer simulations validate these and demonstrate assertions that the system can rapidly adapt to random jumps in plant parameters.

Merhav, S. J.↗