Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sufficient statistics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

651 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

open quantum systems & decoherence↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗
NASA NTRS1996

On the Relationship Between Transit Velocity of Interplanetary Shocks and Solar Active Processes

Recently, it was reported that preferential relationships exist between the transit velocity V(sub T) of earthward-directed interplanetary shocks and solar active processes, in particular, eruptive filaments outside active regions (the size of the erupting filament L(sub f)) and solar flares (the value of the X-ray characteristic J). Unfortunately, statistical testing of the proposed associations was not accomplished, nor was the 'geo-effectiveness' of the events adequately described. Reported here are the results of a re-examination of the 21 eruptive filaments (SSC-EF events) and 26 X-ray flares (SSC-F events) that have been associated with storm sudden commencements (SSCs) at Earth. Simple statistical testing refutes the claim that a preferential relationship exists between V(sub T) and L(sub F), while it supports the claim that one exists between V(sub T) and J. More importantly, the inferred relationship between V(sub T) and J is found to be more complicated than previously thought. In particular, it now appears that SSC-F events may be separable into two groups, based on the value of J: a low-J group (J less than 56), in which V(sub T) varies directly with J, and a high-J group (J greater than 56), in which V(sub T) varies inversely with J. As a whole, high-J events are associated with shocks of higher average transit velocity than those of low-J events, and SSC-F events with shocks of higher average transit velocity than those of SSC-EF events. Further, high-J events tend to be of greater X-ray class ( greater than M3), longer duration (greater then 80 min), and are more likely to be associated with type II/IV radio emission (9 of 12) than low-J events. They also tend to occur in magnetically complex (gamma/delta configuration) active regions (10 of 12) that are large in area extent (area greater than 445 millionths of a solar hemisphere) on the day of flaring (9 of 12). Of the 9 solar proton events that affected the Earth's environment that were found to be associated with SSC-F events, six were high-J events. Concerning 'geo-effectiveness', there appears to be no preferential relationship between the value of the J-parameter and the most negative value of the Dst geomagnetic index Dst(min) following the SSC, which is found to usually occur at 6-14 h after SSC onset (18 of 26) and which ranged in value from -1 to -249 (having a median value of about -75). Of the 26 SSC-F events, only 14 can be associated with a Dst(min) less than or equal to -75, and of these only 7 were high-J events. Of the 14 storm-related events (i.e. Dst(min) less than or equal to -75), three have previously been identified as being either 'magnetic clouds' or 'bidirectional flows', both manifestations of earthward-directed coronal mass ejections (CMEs). Superposed epoch analyses of selected solar wind parameters and Dst during the interval of storm-related SSC-F events demonstrate that geoeffective SSC-F events tend to be associated with solar wind flows that are faster, greater in magnetic field strength, and have a rotating field which has a strong southward component shortly after SSC onset, in comparison to SSC-F events that do not have Dst(min) less than or equal to 75. Therefore, it is inferred that geoeffective SSC-F events are probably fast earthward-directed CMEs. Although no single parameter is found that can serve as a predictor of high-skill level for determining the geoeffectiveness of an SSC-F event prior to its occurrence at Earth, one finds that knowledge of the flare's hemispheric location and appearance or lack of appearance of a two-ribbon structure is sufficient to correctly predict the geoeffectiveness of 20 out of 25 of the SSC-F events (80%). Surprisingly, the association or lack of association of metric type II/IV radio emission as a characteristic for determining the geoeffectiveness of the SSC-F events proved unfruitful, as did, to a lesser extent, the duration of the X-ray emission.

Wilson, Robert M.↗