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NASA NTRS2005

Generic Kalman Filter Software

The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on the basis of the aforementioned templates. The GKF software can be used to develop many different types of unfactorized Kalman filters. A developer can choose to implement either a linearized or an extended Kalman filter algorithm, without having to modify the GKF software. Control dynamics can be taken into account or neglected in the filter-dynamics model. Filter programs developed by use of the GKF software can be made to propagate equations of motion for linear or nonlinear dynamical systems that are deterministic or stochastic. In addition, filter programs can be made to operate in user-selectable "covariance analysis" and "propagation-only" modes that are useful in design and development stages.

Lisano, Michael E., II↗

DOE OSTI2024

From Data to Insights: A Covariate Analysis of the IARPA BRIAR Dataset for Multimodal Biometric Recognition Algorithms at Altitude and Range

This paper examines covariate effects on fused whole body biometrics performance in the IARPA BRIAR dataset, specifically focusing on UAV platforms, elevated positions, and distances up to 1000 meters. The dataset includes outdoor videos compared with indoor images and controlled gait recordings. Normalized raw fusion scores relate directly to predicted false accept rates (FAR), offering an intuitive means for interpreting model results. A linear model is developed to predict biometric algorithm scores, analyzing their performance to identify the most influential covariates on accuracy at altitude and range. Weather factors like temperature, wind speed, solar loading, and turbulence are also investigated in this analysis. The study found that resolution and camera distance best predicted accuracy and findings can guide future research and development efforts in long-range/elevated/UAV biometrics and support the creation of more reliable and robust systems for national security and other critical domains.

Bolme, David↗

NASA NTRS2003

Cranial diameter pulsations measured by non-invasive ultrasound decrease with tilt

INTRODUCTION: Intracranial pressure (ICP) may play a significant role in physiological responses to microgravity by contributing to the nausea associated with microgravity exposure. However, effects of altered gravity on ICP in astronauts have not been investigated, primarily due to the invasiveness of currently available techniques. We have developed an ultrasonic device that monitors changes in cranial diameter pulsation non-invasively so that we can evaluate ICP dynamics in astronauts during spaceflight. This study was designed to demonstrate the feasibility of our ultrasound technique under the physiological condition in which ICP dynamics are changed due to altered gravitational force. METHODS: Six healthy volunteers were placed at 60 degrees head-up, 30 degrees headup, supine, and 15 degrees head-down positions for 3 min at each angle. We measured arterial blood pressure (ABP) with a finger pressure cuff, and cranial diameter pulsation with a pulsed phase lock loop device (PPLL). RESULTS: Analysis of covariance demonstrated that amplitudes of cranial diameter pulsations were significantly altered with the angle of tilt (p < 0.001). The 95% confidence interval for linear regression coefficients of the cranial diameter pulsation amplitudes with tilt angle was 0.862 to 0.968. However, ABP amplitudes did not show this relationship. DISCUSSION: Our noninvasive ultrasonic technique reveals that the amplitude of cranial diameter pulsation decreases as a function of tilt angle, suggesting that ICP pulsation follows the same relationship. It is demonstrated that the PPLL device has a sufficient sensitivity to detect changes non-invasively in ICP pulsation caused by altered gravity.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS1982

Linear discriminant analysis with misallocation in training samples

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

Chhikara, R.↗

NASA NTRS2000

Stardust Navigation Covariance Analysis

The Stardust spacecraft was launched on February 7, 1999 aboard a Boeing Delta-II rocket. Mission participants include the National Aeronautics and Space Administration (NASA), the Jet Propulsion Laboratory (JPL), Lockheed Martin Astronautics (LMA) and the University of Washington. The primary objective of the mission is to collect in-situ samples of the coma of comet Wild-2 and return those samples to the Earth for analysis. Mission design and operational navigation for Stardust is performed by the Jet Propulsion Laboratory (JPL). This paper will describe the extensive JPL effort in support of the Stardust pre-launch analysis of the orbit determination component of the mission covariance study. A description of the mission and it's trajectory will be provided first, followed by a discussion of the covariance procedure and models. Predicted accuracy's will be examined as they relate to navigation delivery requirements for specific critical events during the mission. Stardust was launched into a heliocentric trajectory in early 1999. It will perform an Earth Gravity Assist (EGA) on January 15, 2001 to acquire an orbit for the eventual rendezvous with comet Wild-2. The spacecraft will fly through the coma (atmosphere) on the dayside of Wild-2 on January 2, 2004. At that time samples will be obtained using an aerogel collector. After the comet encounter Stardust will return to Earth when the Sample Return Capsule (SRC) will separate and land at the Utah Test Site (UTTR) on January 15, 2006. The spacecraft will however be deflected off into a heliocentric orbit. The mission is divided into three phases for the covariance analysis. They are 1) Launch to EGA, 2) EGA to Wild-2 encounter and 3) Wild-2 encounter to Earth reentry. Orbit determination assumptions for each phase are provided. These include estimated and consider parameters and their associated a-priori uncertainties. Major perturbations to the trajectory include 19 deterministic and statistical maneuvers planned for the mission. The spacecraft is three axis stabilized and has unbalanced thrusters for attitude control. Accelerations due to the attitude control system are treated stochastically. The tracking scenario for the study is patterned after the actual schedule employed during the different phases of the mission. Conventional X-band two-way Doppler and SRA range data was simulated and the standard accuracy for these data types was assumed throughout most of the mission. However, a deweighting scheme was used for the Doppler data during times of low Sun-Earth-Probe angles, especially in the case of the DSM. Optical data is assumed to be available starting at 50 days prior to the comet encounter. The optical data will be used to improve the ephemeris of Wild-2, which is considered crucial to properly target the comet flyby. Results of the covariance analysis are presented for all mission phases. Navigation capability will be discussed in terms of the uncertainty in the encounter B-Plane (B.R and B.T) and linearized time of flight. Delivery errors based on the final maneuver prior to the comet encounter will be presented. The most stringent navigation requirement is for the Earth reentry. The uncertainty in the flight path angle must be less than 0.02 degree (orbit determination and maneuver performance) to assure successful recovery of the SRC. Results presented show that this requirement can be met.

Menon, Premkumar R.↗

NASA NTRS1987

A covariance analysis algorithm for interconnected systems

A covariance analysis algorithm for propagation of signal statistics in arbitrarily interconnected nonlinear systems is presented which is applied to six-degree-of-freedom systems. The algorithm uses statistical linearization theory to linearize the nonlinear subsystems, and the resulting linearized subsystems are considered in the original interconnection framework for propagation of the signal statistics. Some nonlinearities commonly encountered in six-degree-of-freedom space-vehicle models are referred to in order to illustrate the limitations of this method, along with problems not encountered in standard deterministic simulation analysis. Moreover, the performance of the algorithm shall be numerically exhibited by comparing results using such techniques to Monte Carlo analysis results, both applied to a simple two-dimensional space-intercept problem.

Cheng, Victor H. L.↗

NASA NTRS2000

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Tippett, Michael K.↗

DOE OSTI2024

Water loss through evapotranspiration after precipitation events in bioenergy crops grown in similar climatic conditions

The relationship between precipitation and evapotranspiration (ET) is critical to understanding water cycle related dynamics in ecosystems, including crops. Existing studies of bioenergy crops have primarily focused on annual or seasonal ET rates, with less attention given to the immediate ET response following precipitation events. This study examines the variation in ET rates in the days subsequent to precipitation events across various bioenergy crops—corn, switchgrass, and prairies—utilizing 13 years (2010–2022) of growing season data. Meteorological and eddy covariance flux data were collected from seven eddy covariance flux towers as part of the GLBRC scale-up experiment at the Kellogg Biological Station Long Term Ecological Research sites. The analysis revealed that average ET peaked the day after precipitation and declined linearly over the following days, with a statistically significant relationship (p-value = 0.00027, R2 = 0.96). Neither the type of biofuel vegetation nor the historical land use significantly influenced ET post-precipitation events (p-values = 0.53 and 0.153, respectively). Key predictors of ET following precipitation events include shortwave radiation, season, day of the year, ambient temperature, vapor pressure deficit (VPD), long-wave radiation, precipitation amount, soil moisture, and annual variability. These findings enhance our comprehension of ET responses in bioenergy crop systems, with implications for water management in sustainable agriculture.

09 BIOMASS FUELS↗

NASA NTRS1976

Information and display requirements for independent landing monitors

The ways an Independent Landing Monitor (ILM) may be used to complement the automatic landing function were studied. In particular, a systematic procedure was devised to establish the information and display requirements of an ILM during the landing phase of the flight. Functionally, the ILM system is designed to aid the crew in assessing whether the total system (e.g., avionics, aircraft, ground navigation aids, external disturbances) performance is acceptable, and, in case of anomaly, to provide adequate information to the crew to select the least unsafe of the available alternatives. Economically, this concept raises the possibility of reducing the primary autoland system redundancy and associated equipment and maintenance costs. The required level of safety for the overall system would in these cases be maintained by upgrading the backup manual system capability via the ILM. A safety budget analysis was used to establish the reliability requirements for the ILM. These requirements were used as constraints in devising the fault detection scheme. Covariance propagation methods were used with a linearized system model to establish the time required to correct manually perturbed states due to the fault. Time-to-detect and time-to-correct requirements were combined to devise appropriate altitudes and strategies for fault recovery.

Karmarker, J. S.↗

NASA NTRS1975

Statistical analysis of trim maneuvers in low thrust interplanetary navigation

An analytical technique for the statistical analysis of a low thrust trim maneuver in interplanetary navigation has been developed. The maneuver is treated rigorously as a nonlinear function of the trajectory errors to be removed, and the corresponding nongaussian statistics are developed. The method determines the statistical properties of the maneuver direction and duration, as well as the final state dispersion covariance. The analytical technique is applied to the terminal maneuver in a 1980 Encke slow flyby mission and is found to yield accurate statistical results with much less effort than Monte Carlo simulation. The method permits consideration of a shorter terminal maneuver than does linear analysis, with a consequent improvement in delivery accuracy.

Rinker, G. C.↗

NASA NTRS1985

Systematic estimation of forecast and observation error covariances in four-dimensional data assimilation

A two-part algorithm is presented for reliably computing weather forecast model and observational error covariances during data assimilation. Data errors arise from instrumental inaccuracies and sub-grid scale variability, whereas forecast errors occur because of modeling errors and the propagation of previous analysis errors. A Kalman filter is defined as the primary algorithm for estimating the forecast and analysis error convariance matrices. A second algorithm is described for quantifying the noise covariance matrices of any degree to obtain accurate values for the observational error covariances. Numerical results are provided from a linearized one-dimensional shallow-water model. The results cover observational noise covariances, initial instrumental errors and erroneous model values.

Dee, D. P.↗

NASA NTRS2016

Optical Error Budgeting Using Linearized Ray-Trace Models

The Root-Sum-Squared, or “RSS” wavefront error model is a simple, scalar tool, commonly used for space telescope error budgeting. At the same time, much more detailed models, combining ray-trace and Fourier optics with optical alignments and wavefront controls, can provide accurate, high -resolution simulations for detailed system and subsystem design. This paper makes a connection between the two modeling approaches by deriving RSS model coefficients from ray-trace models, including the effects of wavefront controls, for computing system performance from component error statistics. It is shown that, properly constructed, the simple RSS error budget is a covariance analysis, and can be as accurate as high-resolution wavefront models for statistical wavefront error prediction. A notional segmented-aperture space telescope is used to illustrate this error modeling process.

Wavefront error↗

NASA NTRS1995

On-line estimation of error covariance parameters for atmospheric data assimilation

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

Dee, Dick P.↗

NASA NTRS1977

Analysis and application of minimum variance discrete linear system identification

An on-line minimum variance (MV) parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise (AMN). The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean-square convergent and mean-square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kotob, S.↗

NASA NTRS1975

Analysis and application of minimum variance discrete time system identification

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kaufman, H.↗

NASA NTRS1976

Analysis and application of minimum variance discrete time system identification

Kotob, S.↗

NASA NTRS2011

Superpixel-Augmented Endmember Detection for Hyperspectral Images

Superpixels are homogeneous image regions comprised of several contiguous pixels. They are produced by shattering the image into contiguous, homogeneous regions that each cover between 20 and 100 image pixels. The segmentation aims for a many-to-one mapping from superpixels to image features; each image feature could contain several superpixels, but each superpixel occupies no more than one image feature. This conservative segmentation is relatively easy to automate in a robust fashion. Superpixel processing is related to the more general idea of improving hyperspectral analysis through spatial constraints, which can recognize subtle features at or below the level of noise by exploiting the fact that their spectral signatures are found in neighboring pixels. Recent work has explored spatial constraints for endmember extraction, showing significant advantages over techniques that ignore pixels relative positions. Methods such as AMEE (automated morphological endmember extraction) express spatial influence using fixed isometric relationships a local square window or Euclidean distance in pixel coordinates. In other words, two pixels covariances are based on their spatial proximity, but are independent of their absolute location in the scene. These isometric spatial constraints are most appropriate when spectral variation is smooth and constant over the image. Superpixels are simple to implement, efficient to compute, and are empirically effective. They can be used as a preprocessing step with any desired endmember extraction technique. Superpixels also have a solid theoretical basis in the hyperspectral linear mixing model, making them a principled approach for improving endmember extraction. Unlike existing approaches, superpixels can accommodate non-isometric covariance between image pixels (characteristic of discrete image features separated by step discontinuities). These kinds of image features are common in natural scenes. Analysts can substitute superpixels for image pixels during endmember analysis that leverages the spatial contiguity of scene features to enhance subtle spectral features. Superpixels define populations of image pixels that are independent samples from each image feature, permitting robust estimation of spectral properties, and reducing measurement noise in proportion to the area of the superpixel. This permits improved endmember extraction, and enables automated search for novel and constituent minerals in very noisy, hyperspatial images. This innovation begins with a graph-based segmentation based on the work of Felzenszwalb et al., but then expands their approach to the hyperspectral image domain with a Euclidean distance metric. Then, the mean spectrum of each segment is computed, and the resulting data cloud is used as input into sequential maximum angle convex cone (SMACC) endmember extraction.

Thompson, David R.↗

NASA NTRS1976

Analysis and application of minimum variance discrete time system identification

An on-line minimum variance parameter identifier was developed which embodies both accuracy and computational efficiency. The new formulation resulted in a linear estimation problem with both additive and multiplicative noise. The resulting filter is shown to utilize both the covariance of the parameter vector itself and the covariance of the error in identification. It is proven that the identification filter is mean square covergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kotob, S.↗