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Algorithm rapidly estimates frequency of sinusoidal signal corrupted by zero-mean, additive, white Gaussian noise. Incorporates differential mathematical model of signal, cyclic sampling of signal, and least-squares best-estimate criterion. Adapts to changing signal frequency. Amount of computation required to obtain estimate increases only linearly with number of successive measurements processed.
In mobilesat applications, frequency offset on the received signal must be estimated and removed prior to further modem processing. A straightforward method of estimating the carrier frequency offset is to raise the received MPSK signal to the M-th power, and then estimate the location of the peak spectral component. An analysis of the lower signal to noise threshold of this method is carried out for BPSK signals. Predicted thresholds are compared to simulation results. It is shown how the method can be extended to pi/M MPSK signals. A real-time implementation of frequency offset estimation for the Australian mobile satellite system is described.
The paper presents a frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which is called a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.
This paper presents a frequency-domain estimator that can identify both a parametrized nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.
The accuracy of a rapid method which estimates the frequency response function from stereoscopic dynamic data is computed. It is shown that reversal of the order of the operations of coordinate transformation and Fourier transformation, which provides a significant increase in computational speed, introduces error. A portion of the error, proportional to the perturbation components normal to the camera focal planes, cannot be eliminated. The remaining error may be eliminated by proper scaling of frequency data prior to coordinate transformation. Methods are developed for least squares estimation of the full 3x3 frequency response matrix for a three dimensional structure.
Conceptual two-stage software scheme serves as prototype of multistage scheme for digital estimation of phase, frequency, and rate of change of frequency ("Doppler rate") of possibly phase-modulated received sinusoidal signal in communication system in which transmitter and/or receiver traveling rapidly, accelerating, and/or jerking severely. Each additional stage of multistage scheme provides increasingly refined estimate of frequency and phase of signal. Conceived for use in estimating parameters of signals from spacecraft and high dynamic GPS signal parameters, also applicable, to terrestrial stationary/mobile (e.g., cellular radio) and land-mobile/satellite communication systems.
Three analytical problems in estimating the frequency at which commercial airline flights will encounter high cabin ozone levels are formulated and solved: namely, estimating flight-segment mean levels, estimating maximum-per-flight levels, and estimating the maximum average level over a specified flight interval. For each problem, solution procedures are given for different levels of input information - from complete cabin ozone data, which provides a direct solution, to limited ozone information, such as ambient ozone means and standard deviations, with which several assumptions are necessary to obtain the required estimates. Each procedure is illustrated by an example case calculation that uses simultaneous cabin and ambient ozone data obtained by the NASA Global Atmospheric Sampling Program. Critical assumptions are discussed and evaluated, and the several solutions for each problem are compared. Example calculations are also performed to illustrate how variations in lattitude, altitude, season, retention ratio, flight duration, and cabin ozone limits affect the estimated probabilities.
A real-time method for estimating time-varying aircraft frequency responses from input and output measurements was demonstrated. The Bat-4 subscale airplane was used with NASA Langley Research Center's AirSTAR unmanned aerial flight test facility to conduct flight tests and collect data for dynamic modeling. Orthogonal phase-optimized multisine inputs, summed with pilot stick and pedal inputs, were used to excite the responses. The aircraft was tested in its normal configuration and with emulated failures, which included a stuck left ruddervator and an increased command path latency. No prior knowledge of a dynamic model was used or available for the estimation. The longitudinal short period dynamics were investigated in this work. Time-varying frequency responses and stability margins were tracked well using a 20 second sliding window of data, as compared to a post-flight analysis using output error parameter estimation and a low-order equivalent system model. This method could be used in a real-time fault detection system, or for other applications of dynamic modeling such as real-time verification of stability margins during envelope expansion tests.
A robust identification method was developed for use in an adaptive control system. The type of estimator is called the robust estimator, since it is robust to the effects of both unmodeled dynamics and an unmeasurable disturbance. The development of the robust estimator was motivated by a need to provide guarantees in the identification part of an adaptive controller. To enable the design of a robust control system, a nominal model as well as a frequency-domain bounding function on the modeling uncertainty associated with this nominal model must be provided. Two estimation methods are presented for finding parameter estimates, and, hence, a nominal model. One of these methods is based on the well developed field of time-domain parameter estimation. In a second method of finding parameter estimates, a type of weighted least-squares fitting to a frequency-domain estimated model is used. The frequency-domain estimator is shown to perform better, in general, than the time-domain parameter estimator. In addition, a methodology for finding a frequency-domain bounding function on the disturbance is used to compute a frequency-domain bounding function on the additive modeling error due to the effects of the disturbance and the use of finite-length data. The performance of the robust estimator in both open-loop and closed-loop situations is examined through the use of simulations.
Methods developed at NASA for efficiently estimating multiple-input multiple-output frequency responses of various aircraft control loops are discussed. These methods use simultaneous orthogonal multisine excitations and ratios of input-output Fourier transform data that can be computed in real time. An example is given to demonstrate some of the methods using flight test data for the X-56A airplane.
The algorithms for the equation error and output error methods, the two basic procedures for the extraction of aircraft parameters from flight data, are formulated in the frequency domain. The output error method includes the maximum likelihood estimation technique. This is further extended to those cases where the measured data is in the form of frequency response curves and the model of an aircraft includes elastic degrees of freedom and unsteady aerodynamics. Then the generalized maximum likelihood method, which can be applied to the identification of an aircraft subjected to external disturbances, is introduced. Next, all estimation methods mentioned are discussed with emphasis on advantages of the frequency domain analysis. The paper concludes with an example using real flight data.
A Global Positioning System (GPS) receiver having a number of channels, receives an aggregate of pseudorange code time division modulated signals. The aggregate is converted to baseband and then to digital form for separate processing in the separate channels. A fast fourier transform processor computes the signal energy as a function of Doppler frequency for each correlation lag, and a range and frequency estimator computes estimates of pseudorange, and frequency. Raw estimates from all channels are used to estimate receiver position, velocity, clock offset and clock rate offset in a conventional navigation and control unit, and based on the unit that computes smoothed estimates for the next measurement interval.
This paper discusses the use of an adaptive system to stabilize a multi-tank launch vehicle with sloshable fuel. The adaptive system utilizes a sensor to measure the fluid slosh angle, a recursive-least-squares estimator to estimate the natural frequency of the sloshing fuel, and a linear filter which stabilizes the unstable fuel slosh using the frequency estimate. Single-input and multiinput estimators were investigated. The time-varying complexity of the slosh control loop keeps the system persistently excited through flight, even though the attitude is controlled by a conventional PID controller. For the first portion of flight, the adaptive system maintains stability. A modification is proposed for latter portions of flight. The approach requires no tank baffles or partitions.
The performance of the NASTRAN CQUAD4 membrane and plate element in the analysis of undamped natural vibration modes of thin fiber reinforced composite plates was evaluated. The element provides natural frequency estimates that are comparable in accuracy to alternative formulations, and, in most cases, deviate by less than 10 percent from experimentally measured frequencies. The predictions lie within roughly equal accuracy bounds for the two material types treated (GFRP and CFRP), and for the ply layups considered (unidirectional, cross-ply, and angle-ply). Effective elastic lamina moduli had to be adjusted for fiber volume fraction to attain this level of frequency. The lumped mass option provides more accurate frequencies than the consistent mass option. This evaluation concerned only plates with L/t ratios on the order of 100 to 150. Since the CQUAD4 utilizes first-order corrections for transverse laminate shear stiffness, the element should provide useful frequency estimates for plate-like structures with lower L/t. For plates with L/t below 20, consideration should be given to idealizing with 3-D solid elements. Based on the observation that natural frequencies and mode shapes are predicted with acceptable engineering accuracy, it is concluded that CQUAD4 should be a useful and accurate element for transient shock and steady state vibration analysis of naval ship
A new high dynamic global positioning system (GPS) receiver is presented and its performance characterized by analysis, simulation, and demonstration. The demonstration receiver is a breadboard model capable of tracking a single simulated satellite signal in pseudorange and range rate. Pseudorange and range rate estimates are made once every 20 ms, using a maximum likelihood estimator, and are tracked by means of a third-order fading memory filter in a feedback configuration. The receiver tracks pseudorange with rms errors of under 1 m when subjected to simulated 50 g, 40 g/s circular trajectories. The tracking threshold is approximately 28 dB-Hz, which provides 12 dB margin relative to the minimum specified signal strength, assuming 3.5 dB system noise figure and 0 dBi antenna gain.
We have investigated the improvement in the signal-to-noise ratio for a coherent Doppler lidar through the use of a multi-element heterodyne detector array. Such an array enables the spatial summation of atmospheric refractive turbulence induced speckles, and time varying target speckles. Our recent experiments have shown that the non-coherent summation of the lidar signals from a heterodyne detector array can enhance the heterodyne mixing efficiency and thus the signal-to-noise ratio. In this paper, we expand this work to include the coherent summation of array signals. The digitized heterodyne signals were stored in a personal computer. Fast Fourier transforms were performed on both the non-coherent and coherent summations of the detector array signals. It was found that the coherent summation greatly enhanced the accuracy in the Doppler frequency estimate. A theoretical analysis was performed and indicated good agreement with experimental results. We have also applied these results to the more general lidar applications including atmospheric wind sensing, and have found that in most lidar applications the Doppler frequency estimate is increased through the use of the heterodyne detector array.
A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.
A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.