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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

On the error in crop acreage estimation using satellite (LANDSAT) data

The problem of crop acreage estimation using satellite data is discussed. Bias and variance of a crop proportion estimate in an area segment obtained from the classification of its multispectral sensor data are derived as functions of the means, variances, and covariance of error rates. The linear discriminant analysis and the class proportion estimation for the two class case are extended to include a third class of measurement units, where these units are mixed on ground. Special attention is given to the investigation of mislabeling in training samples and its effect on crop proportion estimation. It is shown that the bias and variance of the estimate of a specific crop acreage proportion increase as the disparity in mislabeling rates between two classes increases. Some interaction is shown to take place, causing the bias and the variance to decrease at first and then to increase, as the mixed unit class varies in size from 0 to 50 percent of the total area segment.

Chhikara, R.↗
NASA NTRS1982

Gain optimization with nonlinear controls

An algorithm has been developed for the analysis and design of controls for nonlinear systems. The technical approach is to use statistical linearization to model the nonlinear dynamics of a system. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this report is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general however and numerical computation requires only that the specific nonlinearity be considered in the analysis.

Slater, G. L.↗
NASA NTRS2006

Nonlinear consider covariance analysis using a sigma-point filter formulation

The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.

covariance↗
NASA NTRS1972

Stability analysis of Riccati covariance equations of Kalman filter.

The present paper takes the basic mathematical approach to analyze the stability of Riccati equations. First, a simple stability criterion like that of the linear constant coefficient system is sought for the nonlinear constant Riccati Equation. Then, a complete analysis on the limiting covariance P follows. The analysis is focussed on the main theorem. Finally, the computational aspects of the Riccati equations are analyzed with examples. The application of this analysis is to provide a simple stability criterion for the Kalman filter computation to test and predict filter convergence and thus modify filter parameters accordingly.

Teng, L.↗
NASA NTRS1984

Gain optimization with non-linear controls

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Slater, G. L.↗
NASA NTRS2017

Precomputing Process Noise Covariance for Onboard Sequential Filters

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

onboard↗
NASA NTRS1992

Linear analysis of opto-mechanical systems

A general framework is presented for the matrix-form, linear optical model analysis of controlled optomechanical systems; the models are conjoined with linear models of structures and controls to compute system performance as a function of optics, structures, and control parameters. Covariance analysis, optimization, and estimation/simulation are used. Attention is given to a tolerancing example for the Hubble Space Telescope's Wide Field and Planetary Camera, which involves the creation of a linear model of residual pupil shear.

Redding, David C.↗
NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗
NASA NTRS1971

Extensions of the space trajectories error analysis programs

A generalized covariance analysis technique which permits the study of the sensitivity of linear estimation algorithms to errors in a priori statistics has been developed and programed. Several sample cases are presented to illustrate the use of this technique. Modifications to the Simulated Trajectories Error Analysis Program (STEAP) to enable targeting a multiprobe mission of the Planetary Explorer type are discussed. The logic for the mini-probe targeting is presented. Finally, the initial phases of the conversion of the Viking mission Lander Trajectory Reconstruction (LTR) program for use on Venus missions is discussed. An integrator instability problem is discussed and a solution proposed.

Adams, G. L.↗
NASA NTRS1969

Sensitivity aspects of linear digital control systems.

Linear computer-controlled closed loop systems sensitivity analysis, deriving estimation error incremental covariance to demonstrate quality deterioration under perturbed initial conditions, parameters, etc

Christie, L. A.↗
NASA NTRS1975

Users manual for flight control design programs

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

Nalbandian, J. Y.↗
NASA NTRS2018

Assessment and Verification of SLS Block 1-B Exploration Upper Stage State and Stage Disposal Performance

One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.

Patrick, Sean↗
NASA NTRS1990

True covariance simulation of the EUVE (extreme ultra violet explorer) update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the onboard computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the order of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1990

True covariance simulation of the EUVE update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the real behavior of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1989

True covariance simulation of the EUVE update filter

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, Itzhack Y.↗
NASA NTRSDate not supplied

Reduced Dimensionality Analysis of TEMPO Ozone Profile Retrievals Using the Compact Phase Space (CPSR) Algorithm

TEMPO ozone (O 3 ) profile retrievals are expected to have fidelity in the troposphere due the sensitivities of the associated averaging kernels. However, those averaging kernels are severely rank deficiency meaning that a visual inspection of the vertical structure of the averaging kernel profile sensitivities is misleading due linear dependencies in the profile. The Compact Phase Space Retrieval (CPSR) algorithm use singular value decompositions of the averaging kernels and the ‘compressed’ retrieval solution error covariance to project the transformed averaging kernels into a space that removes the linear dependencies and accounts for the solution error uncertainties. In this oral presentation and poster, we apply the CPSR dimensional reduction analysis to TEMPO and TROPOMI O 3 profile retrievals for 13:45 UTC March 29, 2024 to study the phase space characteristics of the transformed averaging kernels as a function of latitude for North America. Our results show that TEMPO generally has more phase space vertical structure in the troposphere than TROPOMI. TEMPO has four to five dominant modes, and TROPOMI has five to six dominant modes. That means that dimensional reduction can reduce the TEMPO resource requirements by ~77% and the TROPOMI requirements by ~81%. Finally, we found that after removing linear dependences and after accounting for solution uncertainties TEMPO still has sensitivities throughout the troposphere.

TEMPO↗