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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
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.↗
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.↗
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.↗
NASA NTRS1986

Formulation and implementation of a practical algorithm for non-stationary adaptive state estimation

Background information on the Kalman filter is given first. A discussion of the filter parameters and their a priori determination follows. The discussion points out the need for adaptive determination of the process noise statistics. The filter innovations are presented as a means for developing the adaptive criteria. The criteria center around the estimation of the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of a locally stationary random process is presented. The definition of a local stationarity is presented. Local stationarity allows for the separation of the process statistics into a stationary component and a time-varying component. The separation method is discussed. A method for estimating the stationary and time-varying components is presented. As an example of its application to real problems, the algorithm is applied to the problem to the problem of reentry trajectory estimation for the Space Shuttle. Both the adaptive algorithm and the steady-state Kalman filter are applied to the problem. The results of the reconstructions are presented. The adaptive algorithm exhibits superior performance.

Whitemore, S. A.↗
NASA NTRS1990

Random field estimation approach to robot dynamics

The difference equations of Kalman filtering and smoothing recursively factor and invert the covariance of the output of a linear state-space system driven by a white-noise process. Here it is shown that similar recursive techniques factor and invert the inertia matrix of a multibody robot system. The random field models are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. They are easier to describe than the models based on classical mechanics, which typically require extensive derivation and manipulation of equations of motion for complex mechanical systems. With the spatially random models, more primitive locally specified computations result in a global collective system behavior equivalent to that obtained with deterministic models. The primary goal of applying random field estimation is to provide a concise analytical foundation for solving robot control and motion planning problems.

Rodriguez, Guillermo↗
NASA NTRS1987

Fixed lag smoothers for carrier phase and frequency tracking

The application of fixed lag smoothing algorithms are presented for the problem of estimation of the phase and frequency of a sinusoidal carrier received in the presence of process noise and additive observation noise. A suboptimal structure consists of a phase-locked loop (PLL) followed by a post loop correction to the phase and frequency estimates. When the PLL is operating under a high signal-to-noise ratio, the phase detector is approximately linear, and the smoother equations then correspond to the optimal linear equations for an equivalent linear signal model. The performance of such a smoother can be predicted by the linear filtering theory. However, if the PLL is operating near the threshold region of the signal to noise ratio, the phase detector cannot be assumed to be linear. Then the actual performance of the smoother can significantly differ from that predicted by linear filtering theory. Both the theoretical and simulated performance of such smoothers derived on the basis of various models for the phase of frequency processes are presented.

Kumar, R.↗
NASA NTRS1987

Optimum filters and smoothers design for carrier phase and frequency tracking

The report presents the application of fixed lag smoothing algorithms to the problem of estimation of the phase and frequency of a sinusoidal carrier received in the presence of process noise and additive observation noise. A suboptimal structure consists of a phase-locked loop (PLL) followed by post-loop correction to the phase and frequency estimates. When the PLL is operating under high signal-to-noise ratio, the phase detector is approximately linear, and the smoother equations then correspond to the optimal linear equations for an equivalent linear signal model. The performance of such a smoother can be predicted by linear filtering theory. However, if the PLL is operating near the threshold region of the signal-to-noise ratio, the phase detector cannot be assumed to be linear. Then the actual performance of the smoother can significantly differ from that predicted by linear theory. In this report we present both the theoretical and simulated performance of such smoothers derived on the basis of various models for the phase and frequency processes.

Kumar, Rajendra↗
NASA NTRS1990

Neuromorphic learning of continuous-valued mappings from noise-corrupted data. Application to real-time adaptive control

The ability of feed-forward neural network architectures to learn continuous valued mappings in the presence of noise was demonstrated in relation to parameter identification and real-time adaptive control applications. An error function was introduced to help optimize parameter values such as number of training iterations, observation time, sampling rate, and scaling of the control signal. The learning performance depended essentially on the degree of embodiment of the control law in the training data set and on the degree of uniformity of the probability distribution function of the data that are presented to the net during sequence. When a control law was corrupted by noise, the fluctuations of the training data biased the probability distribution function of the training data sequence. Only if the noise contamination is minimized and the degree of embodiment of the control law is maximized, can a neural net develop a good representation of the mapping and be used as a neurocontroller. A multilayer net was trained with back-error-propagation to control a cart-pole system for linear and nonlinear control laws in the presence of data processing noise and measurement noise. The neurocontroller exhibited noise-filtering properties and was found to operate more smoothly than the teacher in the presence of measurement noise.

Troudet, Terry↗
NASA NTRS1991

Measuring earth orientation with the Global Positioning System

A globally distributed network of high-precision receivers which obtain data from the full Global Positioning System (GPS) configuration of 18 or more satellites may soon become an efficient and economical method for the rapid determination of short-term variations in earth orientation. A covariance analysis has been performed to evaluate the errors associated with GPS monitoring of earth orientation. Earth orientation parameters were modeled either as constants over observing windows of various lengths, or as stochastic process-noise variables. The sensitivity of earth orientation estimates to systematic errors in selected model parameters was also examined. GPS measurements appear to be highly competitive with those from other techniques, and have the potential to generate nearly continuous centimeter-level earth orientation information to aid both spacecraft navigation and the study of high-frequency earth orientation-related processes.

Freedman, Adam P.↗
NASA NTRS1990

Model reduction by weighted Component Cost Analysis

Component Cost Analysis considers any given system driven by a white noise process as an interconnection of different components, and assigns a metric called 'component cost' to each component. These component costs measure the contribution of each component to a predefined quadratic cost function. A reduced-order model of the given system may be obtained by deleting those components that have the smallest component costs. The theory of Component Cost Analysis is extended to include finite-bandwidth colored noises. The results also apply when actuators have dynamics of their own. Closed-form analytical expressions of component costs are also derived for a mechanical system described by its modal data. This is very useful to compute the modal costs of very high order systems. A numerical example for MINIMAST system is presented.

Kim, Jae H.↗