Results for “error vector” — Page 13

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↗

NASA NTRS2011

Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation

An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce 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. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.

Simon, Donald L.↗

NASA NTRS2011

Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter

Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.

Keppenne, Christian↗

NASA NTRS1979

Nonresonance rotation of Venus

Radar observations accumulated over the past 14 yr are used to make a precise estimate of the spin vector of Venus. The results obtained show that the spin vector of Venus may be adequately described in the standard 1950.0 coordinate system by a period of 243.01 + or - 0.03 days (retrograde) and a north pole direction corresponding to alpha = 272.8 + or - 0.5 deg and delta = 67.2 + or - 0.3 deg; the quoted errors represent estimates of 70% confidence intervals. The angular separations between the spin vector and those vectors representing the unit normals to the invariable plane of the solar system and the orbital plane of Venus are found to be 0.5 deg and 2.6 deg, respectively. It is concluded that Venus is not rotating with a resonance spin period relative to the orbit of earth and that the spin of Venus may be in a generalized Cassini state.

Shapiro, I. I.↗

NASA NTRS1966

Maximum a posteriori interval estimation.

Maximum a posteriori /MAP/ interval estimation for state vector of random process, solving fixed delay filtering and deriving error matrix

RANDOM PROCESS↗

NASA NTRS1978

Vector space methods of photometric analysis - Applications to O stars and interstellar reddening

A multivariate vector-space formulation of photometry is developed which accounts for error propagation. An analysis of uvby and H-beta photometry of O stars is presented, with attention given to observational errors, reddening, general uvby photometry, early stars, and models of O stars. The number of observable parameters in O-star continua is investigated, the way these quantities compare with model-atmosphere predictions is considered, and an interstellar reddening law is derived. It is suggested that photospheric expansion affects the formation of the continuum in at least some O stars.

Massa, D.↗

NASA NTRS1985

The Use of a Laser Doppler Velocimeter in a Standard Flammability Tube

The use of the Laser Doppler Velocimeter, (LDV), to measure the flow associated with the passage of a flame through a standard flammability limit tube (SFLT) was studied. Four major results are presented: (1) it is shown that by using standard ray tracing calculations, the displacement of the LDV volume and the fringe rotation within the experimental error of measurement can be predicted; (2) the flow velocity vector field associated with passage of an upward propagating flame in an SFLT is determined; (3) it is determined that the use of a light interruption technique to track particles is not feasible; and (4) it is shown that a 25 mW laser is adequate for LDV measurements in the Shuttle or Spacelab.

Strehlow, R. A.↗

NASA NTRS1985

Two locations, two times, and the element set

A robust analytical formulation is developed to apply classical initial orbital determination to artificial satellites whose locations are uncertain to about 1 cu km and separated in time by no more than 30 min. An analytical simplification reduces Gauss's method, iteration on the semilatus rectum, iteration on the true anomaly, and the Lambert-Euler technique, to the solution of a single equation in one unknown, instead of the usual coupled triplet of three equations in three unknowns. The method is demonstrated for all common artificial satellite orbits over a variety of time intervals between the two location vectors, and for a varied set of position and distance errors.

Taff, L. G.↗

NASA NTRS1989

A multidomain spectral collocation method for the Stokes problem

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

Landriani, G. Sacchi↗