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Results are presented of a procedure for estimating stability and control parameters from flight data, by using maximum likelihood methods employing an interactive computer system, which was established at the NASA Langley Research Center. Problems encountered are discussed.
Specific test requirements related to the wind tunnel testing of the XV-15 advanced tilt rotor research aircraft were determined. The following analytical tools were developed: (1) digital simulation of the XV-15, incorporating a simplified tunnel support model, control system loop, measurement lags, gust disturbances, and sensor noise, (2) specialization of existing data analysis programs to the high order XV-15 dynamical model (transfer function program, a time series analysis program, an advanced maximum likelihood parameter identification program), (3) several auxiliary programs to provide estimates of damping from transfer functions as well as calculations of model decomposition of system response. The following results were discussed: (1) modelling of the aircraft, instrumentation, and controls, (2) results of the rotor/cantilever wing model and coupled wing, (3) examples of data prediction with system identification techniques, and (4) detailed conclusions and recommendations.
This study was performed to determine if Landsat data could be used to improve the accuracy of the estimation of cotton acreage. A linear classification algorithm and a maximum likelihood algorithm were used for computer classification of the area, and the classification was compared with ground truth. The classification accuracy for some fields was greater than 90 percent; however, the overall accuracy was 71 percent for cotton and 56 percent for soybeans. The results of this research indicate that computer analysis of Landsat data has potential for improving upon the methods presently being used to determine cotton acreage; however, additional experiments and refinements are needed before the method can be used operationally.
A square root formulation is presented for the discrete combined state parameter estimation problem with linear plant dynamics, Gaussian random disturbances, and constant but uncertain parameters. The estimator is a combination of the classical Kalman filter and a maximum likelihood algorithm which maximizes the parameter log-likelihood function using a first order search routine.
This paper considers the parameter identification problem of general discrete-time, nonlinear, multiple-input/multiple-output dynamic systems with Gaussian-white distributed measurement errors. Knowledge of the system parameterization is assumed to be known. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems. It is shown that if the vector of true parameters is locally CML identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the CML estimation sequence will converge to the true parameters.
The research being conducted pertains to the determination of the stability and control derivatives of the F/A-18 High Alpha Research Vehicle (HARV) from flight data using the Maximum Likelihood Method. The document outlines the approach used in the parameter estimation (PID) process and briefly describes the mathematical modeling of the F/A-18 HARV and the maneuvers designed to generate a sufficient data base for the PID research.
Accurate and reliable bathymetric data are needed for a wide diversity of marine research and management applications. Satellite-derived bathymetry represents a time saving method to map large shallow waters of remote regions compared to the current costly in situ measurement techniques. This study aims to create very high-resolution (VHR) bathymetry and habitat mapping in Mayotte island waters (Indian Ocean) by fusing 0.5 m Pleiades-1 passive multispectral imagery and active ICESat-2 LiDAR bathymetry. ICESat-2 georeferenced photons were filtered to remove noise and corrected for water column refraction. The bathymetric point clouds were validated using the French naval hydrographic and oceanographic service Litto3D® dataset and then used to calibrate the multispectral image to produce a digital depth model (DDM). The latter enabled the creation of a digital albedo model used to classify benthic habitats. ICESat-2 provided bathymetry down to 15 m depth with a vertical accuracy of bathymetry estimates reaching 0.89 m. The benthic habitats map produced using the maximum likelihood supervised classification provided an overall accuracy of 96.62%. This study successfully produced a VHR DDM solely from satellite data. Digital models of higher accuracy were further discussed in the light of the recent and near-future launch of higher spectral and spatial resolution satellites.
A classical method for reconstructing atmospheric turbulence from onboard measurements of airdata and inertial sensors was improved and implemented for real-time computation. The reconstructed turbulence measurements were then included in a system identification analysis to estimate nondimensional stability and control derivatives in a longitudinal short period model using the maximum likelihood equation-error method in the frequency domain with Fourier-transform data. Flight test results using a subscale transport-type airplane showed that the power spectra for the reconstructed vertical gusts resembled the von Kármán turbulence model. Flight data in moderate and severe turbulence exhibited a decorrelation of the modeling data that increased the accuracy of parameter estimation results using the reconstructed turbulence. In particular, pitch rate and angle-of-attack rate derivatives could both be identified from flight data about straight and level flight without special maneuvers or prior information.
This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.
The lateral aerodynamic characteristics of the X-31 were determined at angles of attack ranging from 20 to 45 deg. Estimates of the lateral stability and control parameters were obtained by applying two parameter estimation techniques, linear regression, and the extended Kalman filter to flight test data. An attempt to apply maximum likelihood to extract parameters from the flight data was also made but failed for the reasons presented. An overview of the System Identification process is given. The overview includes a listing of the more important properties of all three estimation techniques that were applied to the data. A comparison is given of results obtained from flight test data and wind tunnel data for four important lateral parameters. Finally, future research to be conducted in this area is discussed.
A procedure for estimating noise statistics as well as system model parameters, based on a maximum likelihood criterion, has been successfully applied to a number of aircraft parameter-identification problems. In the present investigation, an a posteriori criterion is examined for use in such an application, when it is desired to model process noise. The criteria lead to identical results when there is no process noise.
We investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.
The results of applying a modified stepwise regression algorithm and a maximum likelihood algorithm to flight data from a twin-engine commuter-class icing research aircraft are presented. The results are in the form of body-axis stability and control derivatives related to the short-period, longitudinal motion of the aircraft. Data were analyzed for the baseline (uniced) and for the airplane with an artificial glaze ice shape attached to the leading edge of the horizontal tail. The results are discussed as to the accuracy of the derivative estimates and the difference between the derivative values found for the baseline and the iced airplane. Additional comparisons were made between the maximum likelihood results and the modified stepwise regression results with causes for any discrepancies postulated.
Viterbi decoding tests were carried out at DSS 62, Madrid, Spain. Results of bit error rate, burst statistics, and estimation of signal-to-noise ratio are presented.
A report is given to supplement the progress report of June 17, 1977. In that progress report gamma, lognormal, and Rayleigh probability density functions were fitted to the times between lightning flashes in the storms of 9/12/75, 8/26/75, and 7/13/76 by the maximum likelihood method. The goodness of fit is checked by the Kolmogoroff-Smirnoff test. Plots of the estimated densities along with normalized histograms are included to provide a visual check on the goodness of fit. The lognormal densities are the most peaked and have the highest tails. This results in the best fit to the normalized histogram in most cases. The Rayleigh densities have too broad and rounded peaks to give good fits. In addition, they have the lowest tails. The gamma densities fall inbetween and give the best fit in a few cases.
The Delta Classifier defined as an agricultural crop classification scheme employing a temporal trend procedure is applied to more than 100 different Landsat data sets collected during the 1974-1975 growing season throughout the major wheat-producing regions of the United States. The classification approach stresses examination of temporal trends of the Landsat mean vectors of crops in the absence of corresponding ground truth information. It is shown that the resulting classifications compare favorably to ground truth estimates for wheat proportion in those cases where ground truth is available, and that the temporal trend procedure yields estimates of the wheat proportion that are comparable to the best results from maximum likelihood classification with photointerpreter-defined training fields.
Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) series, have been observing severe convection at 15–60-minute intervals for over 40 years. When properly assessed, such a data record can be valuable in efforts of estimating severe storm risk throughout the diurnal cycle based on automated detection of patterns consistently found atop severe storms. Furthermore, environmental conditions favorable for severe weather are well-known and are thought to be represented well by modern reanalysis products. Promoting resilience against such hazards on local and global scales is a chief goal the NASA Disasters program, which seeks to encourage use of satellite observations to mitigate risk. For instance, hail is the costliest severe weather hazard across the globe in terms of insured loss, but reporting inconsistencies for hail events globally make it difficult to develop models that can quantify the risk. Satellite observation and model reanalysis taken together have the potential to, with reasonable skill and specificity, characterize environmental conditions that are favorable for hazardous weather, and thereby enable creation of hazard climatologie. Such climatologies are particularly useful over regions without extensive radar networks or storm reporting. By mapping the multivariate combination of observed cloud features and reanalysis environmental parameters/indices to United States Next Generation Weather Radar (NEXRAD) radar-estimated Maximum Expected Size of Hail (MESH) by way of a deep neural network (DNN), estimates of likelihood for potentially severe hail can be produced. Such estimates are of greater complexity and efficiency than could be performed with previous multivariate or logistic regression analyses for observed points within convective systems. Statistical distributions of convective parameters from satellite and reanalysis are shown to highlight non-severe/severe class separation for well-known hailstorm predictors, e.g., overshooting cloud top characteristics, deep-layer wind shear, mid-level stability, helicity, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN, which can efficiently produce a quantitative hail risk metric with better than 70% detection rate and under 30% false alarms. These hail classifications can then be aggregated across the satellite record to yield a hazard climatology for hail frequency and severity – knowledge of which is of particular interest to those who manage risk (e.g., insurers) and are seeking opportunities to identify hail-prone regions, particularly in developing nations. This NASA study uses satellite observations and model parameters in a DNN to perform climatological hailstorm analysis in support of catastrophe model development, with the hope of promoting risk resilience particularly in regions without adequate weather radar coverage.
By analyzing the motions of a thruster-controlled spacecraft, it is possible to provide on-line (1) thruster fault detection and isolation (FDI), and (2) vehicle mass- and thruster-property identification (ID). Technologies developed recently at NASA Ames have significantly improved the speed and accuracy of these ID and FDI capabilities, making them feasible for application to a broad class of spacecraft. Since these technologies use existing sensors, the improved system robustness and performance that comes with the thruster fault tolerance and system ID can be achieved through a software-only implementation. This contrasts with the added cost, mass, and hardware complexity commonly required by FDI. Originally developed in partnership with NASA - Johnson Space Center to provide thruster FDI capability for the X-38 during re-entry, these technologies are most recently being applied to the MIT SPHERES experimental spacecraft to fly on the International Space Station in 2004. The model-based FDI uses a maximum-likelihood calculation at its core, while the ID is based upon recursive least squares estimation. Flight test results from the SPHERES implementation, as flown aboard the NASA KC-1 35A 0-g simulator aircraft in November 2003 are presented.