Results for “error vector” — Page 12

NASA NTRS1999

Improved Stratospheric Temperature Retrievals for Climate Reanalysis

The Data Assimilation Office (DAO) is embarking on plans to generate a twenty year reanalysis data set of climatic atmospheric variables. One of the focus points will be in the evaluation of the dynamics of the stratosphere. The Stratospheric Sounding Unit (SSU), flown as part of the TIROS Operational Vertical Sounder (TOVS), is one of the primary stratospheric temperature sensors flown consistently throughout the reanalysis period. Seven unique sensors made the measurements over time, with individual instrument characteristics that need to be addressed. The stratospheric temperatures being assimilated across satellite platforms will profoundly impact the reanalysis dynamical fields. To attempt to quantify aspects of instrument and retrieval bias we are carefully collecting and analyzing all available information on the sensors, their instrument anomalies, forward model errors and retrieval biases. For the retrieval of stratospheric temperatures, we adapted the minimum variance approach of Jazwinski (1970) and Rodgers (1976) and applied it to the SSU soundings. In our algorithm, the state vector contains an initial guess of temperature from a model six hour forecast provided by the Goddard EOS Data Assimilation System (GEOS/DAS). This is combined with an a priori covariance matrix, a forward model parameterization, and specifications of instrument noise characteristics. A quasi-Newtonian iteration is used to obtain convergence of the retrieved state to the measurement vector. This algorithm also enables us to analyze and address the systematic errors associated with the unique characteristics of the cell pressures on the individual SSU instruments and the resolving power of the instruments to vertical gradients in the stratosphere. The preliminary results of the improved retrievals and their assimilation as well as baseline calculations of bias and rms error between the NESDIS operational product and col-located ground measurements will be presented.

Rokke, L.↗

NASA NTRS2010

A Systematic Approach for Model-Based Aircraft Engine Performance Estimation

A requirement for effective aircraft engine performance estimation is the ability to account for engine degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. This paper presents a linear point design methodology for minimizing the degradation-induced error in model-based aircraft engine performance estimation applications. The technique specifically focuses on the underdetermined estimation problem, where there are more unknown health parameters than available sensor measurements. A condition for Kalman filter-based estimation is that the number of health parameters estimated cannot exceed the number of sensed measurements. In this paper, the estimated health parameter vector will be replaced by a reduced order tuner vector whose dimension is equivalent to the sensed measurement vector. The reduced order tuner vector is systematically selected to minimize the theoretical mean squared estimation error of a maximum a posteriori estimator formulation. This paper derives theoretical estimation errors at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the estimation accuracy achieved through conventional maximum a posteriori and Kalman filter estimation approaches. Maximum a posteriori estimation results demonstrate that reduced order tuning parameter vectors can be found that approximate the accuracy of estimating all health parameters directly. Kalman filter estimation results based on the same reduced order tuning parameter vectors demonstrate that significantly improved estimation accuracy can be achieved over the conventional approach of selecting a subset of health parameters to serve as the tuner vector. However, additional development is necessary to fully extend the methodology to Kalman filter-based estimation applications.

Simon, Donald L.↗

NASA NTRS1980

Adaptation and optimization of a line-by-line radiative transfer program for the STAR-100 (STARSMART)

A program to calculate upwelling infrared radiation was modified to operate efficiently on the STAR-100. The modified software processes specific test cases significantly faster than the initial STAR-100 code. For example, a midlatitude summer atmospheric model is executed in less than 2% of the time originally required on the STAR-100. Furthermore, the optimized program performs extra operations to save the calculated absorption coefficients. Some of the advantages and pitfalls of virtual memory and vector processing are discussed along with strategies used to avoid loss of accuracy and computing power. Results from the vectorized code, in terms of speed, cost, and relative error with respect to serial code solutions are encouraging.

Rarig, P. L.↗

NASA NTRS1989

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Lin, Tsung-Chieh↗

NASA NTRS1991

Neural-Network Simulator

F77NNS (FORTRAN 77 Neural Network Simulator) computer program simulates popular back-error-propagation neural network. Designed to take advantage of vectorization when used on computers having this capability, also used on any computer equipped with ANSI-77 FORTRAN Compiler. Problems involving matching of patterns or mathematical modeling of systems fit class of problems F77NNS designed to solve. Program has restart capability so neural network solved in stages suitable to user's resources and desires. Enables user to customize patterns of connections between layers of network. Size of neural network F77NNS applied to limited only by amount of random-access memory available to user.

Mitchell, Paul H.↗

NASA NTRS1990

A method of determining attitude from magnetometer data only

Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress.

Natanson, G. A.↗

NASA NTRS1991

Optimization of lateral-directional dynamics for an aircraft operating at high angle of attack

In this paper, the control laws for the lateral-directional dynamics of a supermaneuverable aircraft is analyzed with a view to reducing the levels of lateral acceleration and sideslip, which are encountered during aggressive rolling maneuvers at high angles of attack. The analysis uses a linearized model of the lateral-directional dynamics and thus H-free-flow techniques can be applied. It is shown that trade-offs exist between simultaneously minimizing lateral acceleration measured at the pilot's station, ny(p), minimizing sideslip and minimizing tracking errors between the roll-rate about the velocity vector and its command. The paper concludes that a significant reduction in ny(p) is only attainable by compromising the roll-rate performance.

Snell, S. A.↗

NASA NTRS1995

The effect of sensor sheltering and averaging techniques on wind measurements at the Shuttle Landing Facility

This document presents results of a field study of the effect of sheltering of wind sensors by nearby foliage on the validity of wind measurements at the Space Shuttle Landing Facility (SLF). Standard measurements are made at one second intervals from 30-feet (9.1-m) towers located 500 feet (152 m) from the SLF centerline. The centerline winds are not exactly the same as those measured by the towers. A companion study, Merceret (1995), quantifies the differences as a function of statistics of the observed winds and distance between the measurements and points of interest. This work examines the effect of nearby foliage on the accuracy of the measurements made by any one sensor, and the effects of averaging on interpretation of the measurements. The field program used logarithmically spaced portable wind towers to measure wind speed and direction over a range of conditions as a function of distance from the obstructing foliage. Appropriate statistics were computed. The results suggest that accurate measurements require foliage be cut back to OFCM standards. Analysis of averaging techniques showed that there is no significant difference between vector and scalar averages. Longer averaging periods reduce measurement error but do not otherwise change the measurement in reasonably steady flow regimes. In rapidly changing conditions, shorter averaging periods may be required to capture trends.

Merceret, Francis J.↗

NASA NTRS2005

An Error Analysis of the Phased Array Antenna Pointing Algorithm for STARS Flight Demonstration No. 2

STARS is a multicenter NASA project to determine the feasibility of using space-based assets, such as the Tracking and Data Relay Satellite System (TDRSS) and Global Positioning System (GPS), to increase flexibility (e.g. increase the number of possible launch locations and manage simultaneous operations) and to reduce operational costs by decreasing the need for ground-based range assets and infrastructure. The STARS project includes two major systems: the Range Safety and Range User systems. The latter system uses broadband communications (125 kbps to 500 kbps) for voice, video, and vehicle/payload data. Flight Demonstration #1 revealed the need to increase the data rate of the Range User system. During Flight Demo #2, a Ku-band antenna will generate a higher data rate and will be designed with an embedded pointing algorithm to guarantee that the antenna is pointed directly at TDRS. This algorithm will utilize the onboard position and attitude data to point the antenna to TDRS within a 2-degree full-angle beamwidth. This report investigates how errors in aircraft position and attitude, along with errors in satellite position, propagate into the overall pointing vector.

Carney, Michael P.↗

NASA NTRS2013

CFD Extraction Tool for TecPlot From DPLR Solutions

This invention is a TecPlot macro of a computer program in the TecPlot programming language that processes data from DPLR solutions in TecPlot format. DPLR (Data-Parallel Line Relaxation) is a NASA computational fluid dynamics (CFD) code, and TecPlot is a commercial CFD post-processing tool. The Tec- Plot data is in SI units (same as DPLR output). The invention converts the SI units into British units. The macro modifies the TecPlot data with unit conversions, and adds some extra calculations. After unit conversions, the macro cuts a slice, and adds vectors on the current plot for output format. The macro can also process surface solutions. Existing solutions use manual conversion and superposition. The conversion is complicated because it must be applied to a range of inter-related scalars and vectors to describe a 2D or 3D flow field. It processes the CFD solution to create superposition/comparison of scalars and vectors. The existing manual solution is cumbersome, open to errors, slow, and cannot be inserted into an automated process. This invention is quick and easy to use, and can be inserted into an automated data-processing algorithm.

Norman, David↗

NASA NTRS1991

Accuracy and speed in computing the Chebyshev collocation derivative

We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

Don, Wai-Sun↗

NASA NTRS1979

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Jezewski, D. J.↗

NASA NTRS1980

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Vezewski, D. J.↗

NASA NTRS2012

Application of an Optimal Tuner Selection Approach for On-Board Self-Tuning Engine Models

An enhanced design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented in this paper. It specific-ally addresses the under-determined estimation problem, in which there are more unknown parameters than available sensor measurements. This work builds upon an existing technique for systematically selecting a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. While the existing technique was optimized for open-loop engine operation at a fixed design point, in this paper an alternative formulation is presented that enables the technique to be optimized for an engine operating under closed-loop control throughout the flight envelope. The theoretical Kalman filter mean squared estimation error at a steady-state closed-loop operating point is derived, and the tuner selection approach applied to minimize this error is discussed. A technique for constructing a globally optimal tuning parameter vector, which enables full-envelope application of the technology, is also presented, along with design steps for adjusting the dynamic response of the Kalman filter state estimates. Results from the application of the technique to linear and nonlinear aircraft engine simulations are presented and compared to the conventional approach of tuner selection. The new methodology is shown to yield a significant improvement in on-line Kalman filter estimation accuracy.

Simon, Donald L.↗

NASA NTRS1990

Compensating user position for GPS ephemeris error

A method for canceling the effect of GPS ephemeris error on user position is proposed. In this method, the baseline vectors from the reference stations to the user are estimated without adjusting the GPS ephemeris. The user position is computed by adjustment using differenced data from the user and each station separately and averaging the results with weights inversely proportional to the lengths of the baselines. Alternatively, the differenced data can be averaged in a similar manner before the user position is estimated. The averaging procedure cancels most of the ephemeris error because the error is proportional to the length of the baseline. A numerical simulation is performed to demonstrate and evaluate the method. Two reference stations with perfectly known locations are assumed to be placed several hundred kilometers apart. A user receiver with a poorly known location is located between the stations. The user positions are first estimated separately using data from the user and each station and then averaged. The averaging reduces the error by about one order of magnitude.

Wu, J. T.↗

NASA NTRS1974

On differentiating the probability of error in multipopular feature selection

A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities.

Peters, B. C.↗

NASA NTRSDate not supplied

Effects of Communication Modality on Pilot-Controller Coordination during a Simulated m:N Operation

The last decade or so has seen growing interest in new control paradigms and concepts of operation for uncrewed aircraft systems (UAS) in which multiple aircraft are piloted remotely by a single or relatively small number of people. Referred to as “one-to-many” and “many-to- many” (alternatively, “multi-operator, multi-vehicle”)—and frequently expressed as the corresponding ratios, 1:N and m:N—such novel configurations of aircraft and the people who manage them are seen as critical to the path to future operations involving UAS. Examples of industry domains interested in these control paradigms are small package delivery services utilizing small UAS and passenger-carrying, short-range “Urban Air Mobility” (UAM) operations. Stakeholders in such operations have identified communication and coordination of flight activity with air traffic controllers (ATC) as a barrier to operations. In contrast to present-day flight operations, in which a pilot communicates with one ATC on one radio frequency for one aircraft, multi-vehicle operations potentially entail a significant increase in pilot task load for management of comms. New concepts, such as UAS Service Suppliers (USSs) and Providers of Services to UAM (PSUs), have been proposed to address the known bottleneck for Air Traffic Management (ATM) presented by multi-vehicle operations. While progress has been steadily made over years developing USSs and PSUs, it is generally expected that initial UAM operations will rely on traditional voice-over-radio communication with ATC for purposes of ATM. The current study was a human-in-the-loop simulation that had participants, each possessing a Private Pilot License, act as the ground-based pilot-in- command for multiple vehicles in a hypothetical UAM service in the San Francisco Bay Area. The experiment utilized a 2-by-3, within-subjects design in which the pilot’s Vehicle Load (4 vs. 12) and Comm System (Voice, Datalink, and a Hybrid) were manipulated. The task given to pilots was to use the Comm System to coordinate flight activity for all aircraft with appropriate controllers, having to obtain departure and arrival clearances at “vertiport” facilities and transition clearances for any intermediate airspaces along the route. Pilots were additionally responsible for compliance with vectoring instructions issued by ATC. Subjective workload questionnaires (NASA-TLX) were administered following each experimental trial. Screen recordings of the pilot’s Ground Control Station (GCS) and audio recordings of trials were subsequently coded to obtain performance metrics: response times and error rates. Presented in this paper are results related to pilot responses to vectoring instructions issued by ATC. Workload was found to be significantly higher in the 12-Vehicle condition compared to the 4-Vehicle condition, nearly maxing out the NASA-TLX overall workload scale. There was no significant difference made by the Comm System on workload ratings. Pilots’ response times to communications were fastest in the Voice condition, although overall “service time” for compliance was shorter in Datalink and Hybrid conditions in most cases. Errors by pilots were frequent in both Vehicle Load conditions, most perniciously when using the Voice system. The results of this study suggest tradeoffs in advantages and disadvantages of the three comm systems. Recommendations for communication system design are provided taking the tradeoffs into account.

Garrett G Sadler↗

NASA NTRSDate not supplied

Effects of Communication Modality on Pilot-Controller Coordination during a Simulated m:N Operation

The last decade or so has seen growing interest in new control paradigms and concepts of operation for uncrewed aircraft systems (UAS) in which multiple aircraft are piloted remotely by a single or relatively small number of people. Referred to as “one-to-many” and “many-to- many” (alternatively, “multi-operator, multi-vehicle”)—and frequently expressed as the corresponding ratios, 1:N and m:N—such novel configurations of aircraft and the people who manage them are seen as critical to the path to future operations involving UAS. Examples of industry domains interested in these control paradigms are small package delivery services utilizing small UAS and passenger-carrying, short-range “Urban Air Mobility” (UAM) operations. Stakeholders in such operations have identified communication and coordination of flight activity with air traffic controllers (ATC) as a barrier to operations. In contrast to present-day flight operations, in which a pilot communicates with one ATC on one radio frequency for one aircraft, multi-vehicle operations potentially entail a significant increase in pilot task load for management of comms. New concepts, such as UAS Service Suppliers (USSs) and Providers of Services to UAM (PSUs), have been proposed to address the known bottleneck for Air Traffic Management (ATM) presented by multi-vehicle operations. While progress has been steadily made over years developing USSs and PSUs, it is generally expected that initial UAM operations will rely on traditional voice-over-radio communication with ATC for purposes of ATM. The current study was a human-in-the-loop simulation that had participants, each possessing a Private Pilot License, act as the ground-based pilot-in- command for multiple vehicles in a hypothetical UAM service in the San Francisco Bay Area. The experiment utilized a 2-by-3, within-subjects design in which the pilot’s Vehicle Load (4 vs. 12) and Comm System (Voice, Datalink, and a Hybrid) were manipulated. The task given to pilots was to use the Comm System to coordinate flight activity for all aircraft with appropriate controllers, having to obtain departure and arrival clearances at “vertiport” facilities and transition clearances for any intermediate airspaces along the route. Pilots were additionally responsible for compliance with vectoring instructions issued by ATC. Subjective workload questionnaires (NASA-TLX) were administered following each experimental trial. Screen recordings of the pilot’s Ground Control Station (GCS) and audio recordings of trials were subsequently coded to obtain performance metrics: response times and error rates. Presented in this paper are results related to pilot responses to vectoring instructions issued by ATC. Workload was found to be significantly higher in the 12-Vehicle condition compared to the 4-Vehicle condition, nearly maxing out the NASA-TLX overall workload scale. There was no significant difference made by the Comm System on workload ratings. Pilots’ response times to communications were fastest in the Voice condition, although overall “service time” for compliance was shorter in Datalink and Hybrid conditions in most cases. Errors by pilots were frequent in both Vehicle Load conditions, most perniciously when using the Voice system. The results of this study suggest tradeoffs in advantages and disadvantages of the three comm systems. Recommendations for communication system design are provided taking the tradeoffs into account.

urban air mobility↗