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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.↗

NASA NTRS1978

Robustness and computational aspects of nonlinear stochastic estimators and regulators

Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the linear-quadratic Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have a 'separation-type' property.

Safonov, M. G.↗

NASA NTRS1977

Robustness and computational aspects of nonlinear stochastic estimators and regulators

Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the Linear-Quadratic-Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have 'separation-type' property.

Safonov, M. G.↗

NASA NTRS1980

Smoothing filters

The improvement of accuracy in using the smoothing filter instead of the Kalman filter is discussed. Factors of improvement for velocity errors of up to four are shown for position measurements. Smoothing equations are presented, and it is shown that smoothing equations for the smoothing filter appear to be stable.

Lear, W. H.↗

NASA NTRS1981

Application of maximum-entropy spectral estimation to deconvolution of XPS data

A comparison is made between maximum-entropy spectral estimation and traditional methods of deconvolution used in electron spectroscopy. The maximum-entropy method is found to have higher resolution-enhancement capabilities and, if the broadening function is known, can be used with no adjustable parameters with a high degree of reliability. The method and its use in practice are briefly described, and a criterion is given for choosing the optimal order for the prediction filter based on the prediction-error power sequence. The method is demonstrated on a test case and applied to X-ray photoelectron spectra.

Vasquez, R. P.↗

NASA NTRS1982

Terminal area automatic navigation, guidance, and control research using the Microwave Landing System (MLS). Part 2: RNAV/MLS transition problems for aircraft

The problems in navigation and guidance encountered by aircraft in the initial transition period in changing from distance measuring equipment, VORTAC, and barometric instruments to the more precise microwave landing system data type navaids in the terminal area are investigated. The effects of the resulting discontinuities on the estimates of position and velocity for both optimal (Kalman type navigation schemes) and fixed gain (complementary type) navigation filters, and the effects of the errors in cross track, track angle, and altitude on the guidance equation and control commands during the critical landing phase are discussed. A method is presented to remove the discontinuities from the navigation loop and to reconstruct an RNAV path designed to land the aircraft with minimal turns and altitude changes.

Pines, S.↗

NASA NTRS1982

Crustal interpretation of the MAGSAT data in the continental United States

The processing of MAGSAT scalar data to construct a crustal magnetic anomaly map over the continental U.S. involves removal of the reference field model, a path-by-path subtraction of a low order polynomial through a least-squares fit to reduce orbital offset errors, and a two dimensional spectral filtering to mitigate the spectral bias induced by the path-by-path orbital correction scheme. The resultant anomaly map shows reasonably good correlations with an aeromagnetic map derived from the project MAGNET. Prominent satellite magnetic anomalies are identified in terms of geological provinces and age boundaries. An inversion method was applied to MAGSAT data which produces both the Curie depth topography and laterally varying magnetic susceptibility of the crust. A contoured Curie depth map thus derived shows general agreements with a crustal thickness map based on seismic data.

Won, I. J.↗

NASA NTRS1988

Designing Digital Filters

Digital Filter Design program presents method to compare desired and designed digital filters by minimizing sum-square error of differences in magnitude and phase angles. Written in FORTRAN IV.

Lin, Chiang↗

NASA NTRS1991

Suppressing interfering scattered signals in swept-frequency radar measurements by using frequency domain Wiener filtering

A novel approach to the reduction of scattered, interfering signals that corrupt measurements of the signal backscattered from radar targets of interest is being developed. It is being explored with sphere measurements in an indoor microwave radar range. This method is based on the concept of Wiener filtering (which minimizes the difference between the signal plus noise and the desired signal in the time domain). In contrast to the traditional Wiener filter, in which the time domain error between two sequences are minimized, the approach reported uses the frequency domain phasor amplitudes of a swept frequency signal. It minimizes the difference (least-mean-square-magnitude) between the signal-plus-noise and the signal complex phasors, across the entire spectrum.

Weissman, David E.↗

NASA NTRS1995

An MME-based attitude estimator using vector observations

In this paper, an optimal batch estimator and filter based on the Minimum Model Error (MME) approach is developed for three-axis stabilized spacecraft. Three different MME algorithms are developed. The first algorithm estimates the attitude of a spacecraft using rate measurements. The second algorithm estimates the attitude without using rate measurements. The absence of rate data may be a result of intentional design or from unexpected failure of existing gyros. The third algorithm determines input-torque modeling error trajectories. All of the algorithms developed in this paper use attitude sensors (e.g., three-axis magnetometers, sun sensors, star trackers, etc.). Results using these new algorithms indicate that an MME-based approach accurately estimates the attitude, rate, and input torque trajectories of an actual spacecraft.

Crassidis, John L.↗

NASA NTRS1995

A vehicle health monitoring system for the Space Shuttle Reaction Control System during reentry

A general two tier framework for vehicle health monitoring of Guidance Navigation and Control (GN&C) system actuators, effectors, and propulsion devices is presented. In this context, a top level monitor that estimates jet thrust is designed for the Space Shuttle Reaction Control System (RCS) during the reentry phase of flight. Issues of importance for the use of estimation technologies in vehicle health monitoring are investigated and quantified for the Shuttle RCS demonstration application. These issues include rate of convergence, robustness to unmodeled dynamics, sensor quality, sensor data rates, and information recording objectives. Closed loop simulations indicate that a Kalman filter design is sensitive to modeling error and robust estimators may reduce this sensitivity. Jet plume interaction with the aerodynamic flowfield is shown to be a significant effect adversely impacting the ability to accurately estimate thrust.

Rosello, Anthony David↗

NASA NTRS1996

Nonlinear ARMA models for the D(st) index and their physical interpretation

Time series models successfully reproduce or predict geomagnetic activity indices from solar wind parameters. A method is presented that converts a type of nonlinear filter, the nonlinear Autoregressive Moving Average (ARMA) model to the nonlinear damped oscillator physical model. The oscillator parameters, the growth and decay, the oscillation frequencies and the coupling strength to the input are derived from the filter coefficients. Mathematical methods are derived to obtain unique and consistent filter coefficients while keeping the prediction error low. These methods are applied to an oscillator model for the Dst geomagnetic index driven by the solar wind input. A data set is examined in two ways: the model parameters are calculated as averages over short time intervals, and a nonlinear ARMA model is calculated and the model parameters are derived as a function of the phase space.

Vassiliadis, D.↗

NASA NTRS1999

HALOE Algorithm Improvements for Upper Tropospheric Sounding

This report details the ongoing efforts by GATS, Inc., in conjunction with Hampton University and University of Wyoming, in NASA's Mission to Planet Earth UARS Science Investigator Program entitled "HALOE Algorithm Improvements for Upper Tropospheric Soundings." The goal of this effort is to develop and implement major inversion and processing improvements that will extend HALOE measurements further into the troposphere. In particular, O3, H2O, and CH4 retrievals may be extended into the middle troposphere, and NO, HCl and possibly HF into the upper troposphere. Key areas of research being carried out to accomplish this include: pointing/tracking analysis; cloud identification and modeling; simultaneous multichannel retrieval capability; forward model improvements; high vertical-resolution gas filter channel retrievals; a refined temperature retrieval; robust error analyses; long-term trend reliability studies; and data validation. The current (first-year) effort concentrates on the pointer/tracker correction algorithms, cloud filtering and validation, and multi-channel retrieval development. However, these areas are all highly coupled, so progress in one area benefits from and sometimes depends on work in others.

McHugh, Martin J.↗

NASA NTRS2004

Mars Exploration Rovers orbit determination filter strategy

The successful delivery of the Mars Exploration Rover (MER) landers to well within the boundaries of their surface target areas in January of 2004 was the culmination of years of orbit determination analysis. The process began with a careful consideration of the filter parameters used for pre-launch covariance studies, and continued with the refinement of the filter after launch based on operational experience. At the same time, tools were developed to run a plethora of variations around the nominal filter and analyze the results in ways that had never been previously attempted for an interplanetary mission. In addition to achieving sub-kilometer Mars-relative orbit determination knowledge, the filter strategy and process detected unexpected error sources, while at the same time proving robust by indicating thecorrect solution. Consequently, MER orbit determination set a new standard for interplanetary navigation.

Mars Exploration Rover (MER)↗

NASA NTRS2005

Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations

Radio-frequency interference (RFI) is an increasingly serious problem for passive and active microwave sensing of the Earth. To satisfy their measurement objectives, many spaceborne passive sensors must operate in unprotected bands, and future sensors may also need to operate in unprotected bands. Data from these sensors are likely to be increasingly contaminated by RFI as the spectrum becomes more crowded. In a previous paper we reported on a preliminary investigation of RFI observed over the United States in the 6.9-GHz channels of the Advanced Microwave Scanning Radiometer (AMSR-E) on the Earth Observing System Aqua satellite. Here, we extend the analysis to an investigation of RFI in the 6.9- and 10.7-GHz AMSR-E channels over the global land domain and for a one-year observation period. The spatial and temporal characteristics of the RFI are examined by the use of spectral indices. The observed RFI at 6.9 GHz is most densely concentrated in the United States, Japan, and the Middle East, and is sparser in Europe, while at 10.7 GHz the RFI is concentrated mostly in England, Italy, and Japan. Classification of RFI using means and standard deviations of the spectral indices is effective in identifying strong RFI. In many cases, however, it is difficult, using these indices, to distinguish weak RFI from natural geophysical variability. Geophysical retrievals using RFI-filtered data may therefore contain residual errors due to weak RFI. More robust radiometer designs and continued efforts to protect spectrum allocations will be needed in future to ensure the viability of spaceborne passive microwave sensing.

microwave remote sensing↗

NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗

NASA NTRS2011

Lidar-Based Navigation Algorithm for Safe Lunar Landing

The purpose of Hazard Relative Navigation (HRN) is to provide measurements to the Navigation Filter so that it can limit errors on the position estimate after hazards have been detected. The hazards are detected by processing a hazard digital elevation map (HDEM). The HRN process takes lidar images as the spacecraft descends to the surface and matches these to the HDEM to compute relative position measurements. Since the HDEM has the hazards embedded in it, the position measurements are relative to the hazards, hence the name Hazard Relative Navigation.

Myers, David M.↗

NASA NTRS2014

Background Error Covariance Estimation Using Information from a Single Model Trajectory with Application to Ocean Data Assimilation

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Error Covariance↗