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NASA NTRS2021

Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering

Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. Although this problem has a long history, reliable algorithms for their estimation were scant, and necessary and sufficient conditions for identifiability of the covariances were in dispute until recently. Necessary and sufficient conditions for covariance estimation and a batch estimation algorithm were presented in our previous study. This paper presents stochastic gradient descent algorithms for noise covariance estimation in adaptive Kalman filters that are an order of magnitude faster than the batch method for similar or better root mean square error. More significantly, these algorithms are applicable to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. The computational efficiency of the new algorithms stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated stochastic gradient descent algorithms. The comparative evaluation of the proposed methods on a number of test cases demonstrates their computational efficiency and accuracy.

Adaptive Kalman filtering↗

NASA NTRSDate not supplied

Progress Towards a Common CERES Cloud Mask Algorithm for MODIS and VIIRS: Evaluation using CALIOP Data

For over two decades The Clouds and the Earth’s Radiant Energy System (CERES) project has endeavored to produce a long-term global climate data record for detecting changes in the Earth’s radiation budget and to improve understanding of how clouds contribute to those changes. CERES incorporates cloud information derived from passive narrowband satellite imaging radiometers, and over the course of the project different instruments have contributed to this effort, namely the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Visible Infrared Imaging Radiometer Suite (VIIRS).Cloud properties have been derived from MODIS on the Aqua satellite for CERES since 2002,and VIIRS on the NOAA-20 satellite launched in 2017 will continue the cloud record once Aqua-MODIS reaches the end of its operational lifetime. However, MODIS and VIIRS have different spectral capabilities and characteristics which complicates our ability to seamlessly transition the record from MODIS to VIIRS. This study evaluates some of the recent algorithm modifications incorporated by the CERES Cloud Working Group towards developing a unified cloud mask algorithm for MODIS and VIIRS that utilizes a set of spectral bands common to both instruments. Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products are used to evaluate MODIS and VIIRS regional cloud fraction estimates and identify areas where improvements can be made. The cloud mask algorithm relies on computed estimates of cloud-free top-of-atmosphere radiances to differentiate cloudy and cloud-free imager pixels. The unified cloud mask algorithm currently under development uses a reduced number of spectral bands common to both MODIS and VIIRS and so relies on the accuracy of these simulated cloud-free radiances more heavily than predecessor algorithms, i.e., the CERES Edition 4 cloud mask, which use as much spectral information as available on each imager with less consideration for cross-platform consistency. Our validation strategy using CALIOP data is also described. The CALIOP observations are critical for assessing cloud detection accuracies and for independently confirming cloud-free conditions which enables a more robust evaluation of the simulated cloud-free radiances for biases due to factors such as view angle and the spectral dependence of water vapor absorption. These effects are known to differ for the two satellite instruments. Comparisons of MODIS and VIIRS cloud fractions are presented in context with estimates from CALIOP and from the CERES Edition 4 cloud mask algorithm to gauge current progress in developing accurate and consistent MODIS and VIIRS cloud properties for CERES.

CERES↗

NASA NTRSDate not supplied

Formalization of the Bellman-Ford Algorithm for Airspace Applications

This paper describes the formal verification of one of the most well-known algorithms for finding the shortest path between all vertices in a directed graph, namely the Bellman-Ford algorithm. This formal verification, performed in the Prototype Verification System (PVS), is motivated by two applications in the aerospace domain which use the algorithm for path planning. The first is a pre-flight calculation that uses an adapted version of Bellman-Ford to find a route intended to maximize GNSS availability throughout the flight. The second is a more traditional application intended to find the shortest path between an autonomous aircraft's current position and a goal waypoint, while avoiding regions of space specified by geofences. A novel aspect of this formal verification effort is the inclusion of two distinct models of computation for the algorithm, one being a traditional serial computation, and the other being an explicitly parallel computation. The ability to use parallel computation in the Bellman-Ford algorithm is in fact why it was chosen over other traditionally more performant algorithms, especially for the GNSS application, where the size of the graph makes a purely serial computation infeasible.

formal verification↗

NASA NTRS2012

Cloud Screening and Quality Control Algorithm for Star Photometer Data: Assessment with Lidar Measurements and with All-sky Images

This paper presents the development and set up of a cloud screening and data quality control algorithm for a star photometer based on CCD camera as detector. These algorithms are necessary for passive remote sensing techniques to retrieve the columnar aerosol optical depth, delta Ae(lambda), and precipitable water vapor content, W, at nighttime. This cloud screening procedure consists of calculating moving averages of delta Ae() and W under different time-windows combined with a procedure for detecting outliers. Additionally, to avoid undesirable Ae(lambda) and W fluctuations caused by the atmospheric turbulence, the data are averaged on 30 min. The algorithm is applied to the star photometer deployed in the city of Granada (37.16 N, 3.60 W, 680 ma.s.l.; South-East of Spain) for the measurements acquired between March 2007 and September 2009. The algorithm is evaluated with correlative measurements registered by a lidar system and also with all-sky images obtained at the sunset and sunrise of the previous and following days. Promising results are obtained detecting cloud-affected data. Additionally, the cloud screening algorithm has been evaluated under different aerosol conditions including Saharan dust intrusion, biomass burning and pollution events.

data quality control algorithm↗

NASA NTRS2018

Comparison of First-Come First-Served and Optimization Based Scheduling Algorithms for Integrated Departure and Arrival Management

Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA) are investigating scheduling algorithms that will be a part of an integrated arrival and departure management system. Inha University, one of the Korean collaborators of KARI, developed an Extended First-Come First-Served (EFCFS) algorithm that is robust and efficient. However, since the EFCFS algorithm sequentially computes the schedule based on priority, the end results may not be optimal for system efficiency. The approach based on Mixed Integer Linear Programming (MILP) originally developed by NASA and modified by KARI is known to produce better schedules at the expense of computational cost. In this paper, the two different scheduling approaches are compared using common traffic scenarios and constraints at Incheon International Airport. Capabilities to apply weight class based wake turbulence runway separation minima and Miles-in-Trail (MIT) restrictions at selected meter fixes are added to the previously developed EFCFS scheduler. Based on historic data, 40 departures and 20 arrivals are chosen in a one-hour period and 100 scenarios were created by randomly assigning gate numbers, gate departure times, and runway landing times. With the current runway separation requirements, MILP resulted in about ten to twenty percent smaller average delays depending on the constraints. With artificially increased separation minima, the difference between MILP and EFCFS became more noticeable. However, the EFCFS was about ten times faster with smaller variations among different scenarios and constraints. The comparison suggests that the MILP-based algorithm has a small advantage at the current traffic level; however, has potential to be more effective in higher demand or severe weather situations. The EFCFS algorithm may be better suited for real-time applications or investigating larger scale scheduling problems.

air traffic optimization↗

NASA NTRS2020

Genetic Algorithm for Optimization of Neural Networks for Bayesian Inference of Model Uncertainty

The objective of this work was to develop a genetic optimization algorithm that can design a neural network capable of producing uncertainty estimates along with predictions. This algorithm is necessary because the inclusion of uncertainty modeling in a neural network greatly complicates the network’s design space, making the development of a converging model extremely difficult and time consuming. The genetic algorithm presented in this work uses a number of value ranges for various configurable neural network parameters to create a randomly generated population of network architectures. The initially generated population is then evolved over the course of several generations, with the best performing models breeding to produce novel network configurations. Mutations are randomly applied to the network designs to facilitate the development of adaptations beneficial to the task being performed. An experiment was conducted to validate the proposed algorithm, in which the genetic optimizer was tasked with producing a neural network capable of predicting the sound pressure level (SPL) resulting from jet-surface interaction (JSI) noise. The data used for this task was generated at the NASA Glenn Research Center in the Aero-Acoustic Propulsion Laboratory. Starting with an initial population size of 35 randomly generated networks, and evolved over the course of 10 generations, the genetic algorithm produced a design able to predict SPL as a result of JSI noise within 0.272 dB, on average.

Genetic algorithm↗

NASA NTRSDate not supplied

Verifying Autonomous Air Traffic Algorithms in the Presence of Sensor Error and Flight Perturbations

We offer a method to verify algorithms for air traffic control in the presence of sensor errors and flight perturbations. Since errors and perturbations are described by stochastic processes, verification by analytical methods is difficult. We turn to Monte Carlo simulation, but there are two major obstacles. Since air traffic algorithms are safety-critical, the algorithm must be established at a very high confidence level which requires an enormous number of trials. Another is that a simulation attempts to show that an algorithm correctly handles a hazard that might appear, but there is a lack of information about the frequency of occurrence of hazards in the airspace. This paper offers a solution to these and other obstacles. It recognizes there may be a number of algorithms that address different hazards, and the results of the different simulations must be combined to satisfy a global reliability requirement at a high confidence level. To demonstrate the feasibility of the approach, we apply it to an example, an initial effort in collision avoidance.

verification↗

NASA NTRSDate not supplied

Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST- CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses O ̃(n1/4) rounds of communication and O ̃(n9/4) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗

NASA NTRSDate not supplied

Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST- CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses O ̃(n 1/4 ) rounds of communication and O ̃(n 9/4 ) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗

NASA NTRS1972

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.

Roth, J. P.↗

NASA NTRS1975

Four-dimensional guidance algorithms for aircraft in an air traffic control environment

Theoretical development and computer implementation of three guidance algorithms are presented. From a small set of input parameters the algorithms generate the ground track, altitude profile, and speed profile required to implement an experimental 4-D guidance system. Given a sequence of waypoints that define a nominal flight path, the first algorithm generates a realistic, flyable ground track consisting of a sequence of straight line segments and circular arcs. Each circular turn is constrained by the minimum turning radius of the aircraft. The ground track and the specified waypoint altitudes are used as inputs to the second algorithm which generates the altitude profile. The altitude profile consists of piecewise constant flight path angle segments, each segment lying within specified upper and lower bounds. The third algorithm generates a feasible speed profile subject to constraints on the rate of change in speed, permissible speed ranges, and effects of wind. Flight path parameters are then combined into a chronological sequence to form the 4-D guidance vectors. These vectors can be used to drive the autopilot/autothrottle of the aircraft so that a 4-D flight path could be tracked completely automatically; or these vectors may be used to drive the flight director and other cockpit displays, thereby enabling the pilot to track a 4-D flight path manually.

Pecsvaradi, T.↗

NASA NTRS1976

An algorithm for propagating the square-root covariance matrix in triangular form

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Tapley, B. D.↗

NASA NTRS1978

A multilevel system of algorithms for detecting and isolating signals in a background of noise

Signal information is processed with the help of algorithms, and then on the basis of such processing, a part of the information is subjected to further processing with the help of more precise algorithms. Such a system of algorithms is studied, a comparative evaluation of a series of lower level algorithms is given, and the corresponding algorithms of higher level are characterized.

Gurin, L. S.↗

NASA NTRS1978

A fast D.F.T. algorithm using complex integer transforms

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

Reed, I. S.↗

NASA NTRS1978

Instrumental variables algorithm for modal parameter identification in flutter testing

The paper is concerned with the task of estimating modal parameters from system response measurement in aircraft flutter testing. A frequency-domain derivation of an instrumental-variables algorithm is presented for a linear time-invariant dynamic system of order n. Basically, this algorithm fits a set of poles and zeros to the measured transfer function. An illustrative example is provided regarding the application of the algorithm to aeroelasticity testing. It is shown that the algorithm can be implemented for on-line data reduction with a microcomputer-based analysis system. By using instrumental variables the sensitivity of the modal parameter estimates to noise in the system-response measurements is reduced greatly. The algorithm is expected to be a powerful and valuable tool for on-line estimation of modal parameters in flutter testing and should be useful in control system and structural dynamics tests.

Johnson, W.↗

NASA NTRS1979

A fast, conservative algorithm for solving the transonic full-potential equation

A fast, fully implicit approximate factorization (AF) algorithm designed to solve the conservative transonic full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., 'rotated differencing'), and thereby greatly enhances the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line overrelaxation algorithms.

Holst, T. L.↗

NASA NTRS1980

On the performance of explicit and implicit algorithms for transient thermal analysis

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite element models of the configurations are discribed. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system and a model of the space shuttle orbiter wing. Calculations were carried out using the SPAR finite element program, the MITAS lumped parameter program and a special purpose finite element program incorporating the GEAR algorithms. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff. Careful attention to modeling detail such as avoiding thin or short high-conducting elements can sometimes reduce the stiffness to the extent that explicit methods become advantageous.

Adelman, H. M.↗

NASA NTRS1981

Scaled Runge-Kutta algorithms for handling dense output

Low order Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step. The scaled Runge-Kutta methods are designed to be used with existing Runge-Kutta formulas, using the derivative evaluations of these defining algorithms as the core of the system. For a slight increase in computing time, the solution may be generated within the integration step, improving the efficiency of the Runge-Kutta algorithms, since the step length need no longer be severely reduced to coincide with the desired output point. Scaled Runge-Kutta algorithms are presented for orders 3 through 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem.

Horn, M. K.↗