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A Kalman filter has many properties that make it an attractive choice as a technique for combining Earth orientation measurements. It allows the full accuracy of the measurements to be used, whether the measurements are degenerate or are of full rank, are irregularly or regularly spaced in time, or are corrupted by systematic or other errors that can be described by stochastic models.
Methods to combine the diverse set of geodetic measurements of Earth orientation that are currently available, and to interpolate and extrapolate these data to generate an optimal estimate of Earth orientation, have been under development at JPL for a number of years. The strategy currently in use is a Kalman filtering scheme based on Earth orentation parameters and their excitation functions that incorporates stochastic models of the important physical processes and takes into account the variable form, quality, and temporal density of the data provided by diffent measurement services.
A comprehensive raindrop collision outcome regime diagram that delineates the physical conditions associated with the outcome regimes (i.e., bounce, coalescence, and different breakup types) of binary raindrop collisions is proposed. The proposed diagram builds on a theoretical regime diagram defined in the phase space of collision Weber numbers We and the drop diameter ratio p by including critical angle of impact considerations. In this study, the theoretical regime diagram is first evaluated against a comprehensive dataset for drop collision experiments representative of raindrop collisions in nature. Subsequently, the theoretical regime diagram is modified to explicitly describe the dominant regimes of raindrop interactions in (We, p) by delineating the physical conditions necessary for the occurrence of distinct types of collision-induced breakup (neck/filament, sheet, disk, and crown breakups) based on critical angle of impact consideration. Crown breakup is a subtype of disk breakup for lower collision kinetic energy that presents distinctive morphology. Finally, the experimental results are analyzed in the context of the comprehensive collision regime diagram, and conditional probabilities that can be used in the parameterization of breakup kernels in stochastic models of raindrop dynamics are provided.
Hurricane Sandy's track crossed the New Jersey coastline at an angle closer to perpendicular than any previous hurricane in the historic record, one of the factors contributing to recordsetting peak-water levels in parts of New Jersey and New York. To estimate the occurrence rate of Sandy-like tracks, we use a stochastic model built on historical hurricane data from the entire North Atlantic to generate a large sample of synthetic hurricanes. From this synthetic set we calculate that under long-term average climate conditions, a hurricane of Sandy's intensity or greater (category 1+) makes NJ landfall at an angle at least as close to perpendicular as Sandy's at an average annual rate of 0.0014 yr-1 (95% confidence range 0.0007 to 0.0023); i.e., a return period of 714 years (95% confidence range 435 to 1429).
A generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the Direct Simulation Monte Carlo (DSMC) solver SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer). The various mechanisms include adsorption, desorption, Eley-Rideal (ER), and several types of Langmuir-Hinshelwood (LH) mechanisms. The approach is to stochastically model the various competing reactions occurring on a set of active sites. Both gas-surface (e.g., adsorption, ER) and pure-surface (e.g., desorption) reaction mechanisms are incorporated, and the framework also includes catalytic or surface altering mechanisms involving the participation of the bulk-phase species (e.g., bulk carbon atoms). Marschall and MacLean developed a general formulation in which multiple phases and surface sites are used and a similar convention is adopted in the current work. Expressions for the microscopic parameters of reaction probabilities (for gas-surface reactions) and frequencies (for pure-surface reactions) that are required for DSMC are derived from the surface properties and macroscopic parameters such as rate constants, sticking coefficients, etc. The energy and angular distributions of the products are specified according to the reaction type and input parameters. This framework also presents physically consistent procedures to accurately compute the reaction probabilities and frequencies in the case of multiple reactions. The result is a modeling tool with a wide variety of surface reactions characterized via user-specified reaction rate constants, surface properties and parameters.
The integration of aircraft maneuver characteristics into an optimal taxiway scheduling solution is challenging due to the uncertainties that are intrinsic to ramp area aircraft trajectories. To address the challenge, we build a stochastic model of ramp area aircraft trajectories that is used to generate a probabilistic measure of conflict within the Charlotte Douglas International Airport (CLT) ramp area. Parameters of the conflict distributions are estimated and passed to a Mixed Integer Linear Program that solves for an optimal taxiway schedule constrained to be conflict free in the presence of trajectory uncertainties. Here we extend our previous research by accounting for departing and arriving aircraft whereas our prior formulation only accounted for departing aircraft.
This work describes a detector for the loss of control of a commercial transport in flight. The detector has a belief state defined by the latent variable stochastic modeling of a conditional variational autoencoder (CVAE) constructed with bidirectional recurrent layers. In 2000, the Boeing Company and the NASA Langley Research Center jointly developed a quantitative set of metrics for defining loss-of-control (LOC) for a commercial transport. We use the thresholds for these quantitative metrics to define a condition vector for training the CVAE. We demonstrate through experimentation that reconstruction probability is an accurate indicator that the vehicle has shifted to an LOC state. Second, we introduce a technique for inferring that the vehicle is experiencing a flight state change is approaching by measuring a shift in the sampling Gaussian distributions of the latent space. We provide an analysis of its applicability to flight data from a NASA generic commercial transport-type aircraft.
This work describes a detector for the loss of control condition of a commercial transport in flight. The detector has a belief state defined by the latent variable stochastic modeling of a conditional variational autoencoder (CVAE) constructed with bidirectional recurrent layers. In 2000, the Boeing Company and the NASA Langley Research Center jointly developed a quantitative set of metrics for defining loss-of-control (LOC) for a commercial transport. We use the thresholds for these quantitative metrics to define a condition vector for training the CVAE. First, we demonstrate through experimentation that reconstruction probability is an accurate indicator that the vehicle has shifted to an LOC state. Second, we introduce a technique for inferring that the vehicle is approaching a flight state change by measuring a shift in the sampling distributions of the CVAE latent space. The sampling distributions for flight observations that are approaching envelope limits are localized to external areas of the latent space. We provide an analysis of its applicability to flight data from NASA’s dynamically-scaled generic transport model (GTM) aircraft.
What You Will Learn: The focus is on payload imaging performance due to pointing motion. Some historical background on pointing performance analysis is given. The Optical Transfer Function (OTF) and Modulation Transfer Function (MTF) are defined. The imaging performance due to pointing motion is measured by image motion optical transfer functions (IM OTF). IM OTFs are defined for displacement, smear, and jitter motions, which are all rigorously defined. Deterministic and Statistical IM OTFs are briefly derived and graphically illustrated and compared. The IM OTFs are parameterized by pointing error metrics(PEM), which are means and covariances of displacement, smear, and jitter. Emphasis is on procedures and algorithms to evaluate the image motion optical transfer functions and pointing error metrics. Three procedures are covered, which depend on whether the pointing error data is from time-domain simulation, frequency-domain analysis, or stochastic modeling. A method to evaluate the relative contribution of disturbance sources and to identify the most significant contributors is presented. The presentation includes pertinent discussion of flexible structures and control-structure interaction. No single book can adequately cover this subject, so a book is not required for the course. A list of selected articles, reports, documents, and books is provided for reference and further study. Mathis kept to the minimum necessary to convey principles; lengthy derivations are left to the reference material. Graphics are used to illustrate concepts. As with any such learning endeavor, the knowledge gained will be retained and strengthened through actual practice.c©2019–2021 Mark E. Pittelkau— 5
Plan execution in unknown environments poses a number of challenges: uncertainty in domain modeling, stochasticity at execution time, and the presence of exogenous events. These challenges motivate an integrated approach to planning and execution that is able to respond intelligently to variation. We examine this problem in the context of the Europa Lander mission concept, and evaluate a planning and execution framework that responds to feedback and task failure using two techniques: flexible execution and replanning with plan optimization. We develop a theoretical framework to estimate gains from these techniques, and we compare these predictions to empirical results generated in simulation. These results indicate that an integrated approach to planning and execution leveraging flexible execution, replanning, and utility maximization shows significant promise for future tightly-constrained space missions that must address significant uncertainty.
Plan execution in unknown environments poses a number of challenges: uncertainty in domain modeling, stochasticity at execution time, and the presence of exogenous events. These challenges motivate an integrated approach to planning and execution that is able to respond intelligently to variation. We examine this problem in the context of the Europa Lander mission concept, and propose a planning and execution framework that responds to feedback and task failure using two techniques: flexible execution and replanning with plan optimization. We develop a theoretical framework to predict the value of each of these techniques, and we compare these predictions to empirical results generated in simulation. We demonstrate that an integrated approach to planning and execution that is grounded in flexible execution, replanning, and utility maximization will be an enabling technology for future tightly-constrained planetary surface missions.
Plan execution in unknown environments poses a number of challenges: uncertainty in domain modeling, stochasticity at execution time, and the presence of exogenous events. These challenges motivate an integrated approach to planning and execution that is able to respond intelligently to variation. We examine this problem in the context of the Europa Lander mission concept, and propose a planning and execution framework that responds to feedback and task failure using two techniques: flexible execution and replanning with plan optimization. We develop a theoretical framework to predict the value of each of these techniques, and we compare these predictions to empirical results generated in simulation. We demonstrate that an integrated approach to planning and execution that is grounded in flexible execution, replanning, and utility maximization will be an enabling technology for future tightly-constrained planetary surface missions.
The use of estimation techniques on stochastic models to solve control problems is an emerging paradigm that falls under the rubric of Active Inference (AI) and Control as Inference (CAI). In this work, we use probability propagation on factor graphs to show that various algorithms proposed in the literature can be seen as specific composition rules in a factor graph. We show how this unified approach, presented both in probability space and in log of the probability space, provides a very general framework that includes the Sum-product, the Max-product, Dynamic programming and mixed Reward/Entropy criteria-based algorithms. The framework also expands algorithmic design options that lead to new smoother or sharper policy distributions. We propose original recursions such as: a generalized Sum/Max-product algorithm, a Smooth Dynamic programming algorithm and a modified versions of the Reward/Entropy algorithm. The discussion is carried over with reference to a path planning problem where the recursions that arise from various cost functions, although they may appear similar in scope, bear noticeable differences. We provide a comprehensive table of composition rules and a comparison through simulations, first on a synthetic small grid with a single goal with obstacles, and then on a grid extrapolated from a real-world scene with multiple goals and a semantic map.
Hybrid Diagnosis Engine (HyDE) is a general framework for stochastic and hybrid model-based diagnosis that offers flexibility to the diagnosis application designer. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. Several alternative algorithms are available for the various steps in diagnostic reasoning. This approach is extensible, with support for the addition of new modeling paradigms as well as diagnostic reasoning algorithms for existing or new modeling paradigms. HyDE is a general framework for stochastic hybrid model-based diagnosis of discrete faults; that is, spontaneous changes in operating modes of components. HyDE combines ideas from consistency-based and stochastic approaches to model- based diagnosis using discrete and continuous models to create a flexible and extensible architecture for stochastic and hybrid diagnosis. HyDE supports the use of multiple paradigms and is extensible to support new paradigms. HyDE generates candidate diagnoses and checks them for consistency with the observations. It uses hybrid models built by the users and sensor data from the system to deduce the state of the system over time, including changes in state indicative of faults. At each time step when observations are available, HyDE checks each existing candidate for continued consistency with the new observations. If the candidate is consistent, it continues to remain in the candidate set. If it is not consistent, then the information about the inconsistency is used to generate successor candidates while discarding the candidate that was inconsistent. The models used by HyDE are similar to simulation models. They describe the expected behavior of the system under nominal and fault conditions. The model can be constructed in modular and hierarchical fashion by building component/subsystem models (which may themselves contain component/ subsystem models) and linking them through shared variables/parameters. The component model is expressed as operating modes of the component and conditions for transitions between these various modes. Faults are modeled as transitions whose conditions for transitions are unknown (and have to be inferred through the reasoning process). Finally, the behavior of the components is expressed as a set of variables/ parameters and relations governing the interaction between the variables. The hybrid nature of the systems being modeled is captured by a combination of the above transitional model and behavioral model. Stochasticity is captured as probabilities associated with transitions (indicating the likelihood of that transition being taken), as well as noise on the sensed variables.
A zonally averaged energy balance climate model is developed to generate zonal temperature variability through fluctuating meridional energy transports. Stochastic transport fluctuations are included in the model by multiplying the eddy diffusion coefficients by Gaussian random deviates. For a variability of eddy coefficients of 50 percent, the model is found to generate an interannual temperature variability of 0.03 K for the global temperature, and 0.04 and 0.05 K for the Northern and Southern Hemispheres, respectively. It is shown that the temperature variability level generated is linearly related to the transport variability level introduced. An increase in the level of model-generated temperature variability and a change in the shape of variance spectra of temperature anomaly time series are obtained by switching from the multiplicative noise model to an additive noise model. The results of these model studies are compared with a time series of central England temperatures as well as GCM generated climate variability.
Observational, semiempirical, and theoretical results are presented for individual cool giants and supergiants which show that stochastic stellar wind flows are an extremely important feature in these stars. It is shown that the status of the existing theoretical models is very uncertain, due to the fact that appropriate models must simultaneously take into account a broad variety of strongly coupled physical processes. The potentially important physical processes include global oscillation modes; convection; magnetic fields; the generation, propagation, and interaction of stochastic waves; three-dimensional radiative transfer effects; time-dependent hydrogen ionization; thermal bifurcation and instabilities; and nonequilibrium chemistry, particularly the formation and destruction of molecules and dust.
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.
The difficulty of how to test large systems, such as the one on board a NASA robotic remote explorer (RRE) vehicle, is fundamentally a search issue: the global state space representing all possible has yet to be solved, even after many decades of work. Randomized algorithms have been known to outperform their deterministic counterparts for search problems representing a wide range of applications. In the case study presented here, the LURCH randomized algorithm proved to be adequate to the task of testing a NASA RRE vehicle. LURCH found all the errors found by an earlier analysis of a more complete method (SPIN). Our empirical results are that LURCH can scale to much larger models than standard model checkers like SMV and SPIN. Further, the LURCH analysis was simpler than the SPIN analysis. The simplicity and scalability of LURCH are two compelling reasons for experimenting further with this tool.