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NASA NTRS1972

Precision navigation for approach and landing operations.

This paper summarizes some of the practical considerations and implementation techniques used in the development of the onboard software for an experimental navigation system. This software includes (1) a Kalman filter implementation in square-root form with gyro and accelerometer noises modeled as random forcing functions in the filter; (2) operational modes for inflight alignment, ground alignment, normal aided inertial navigation operation, and postflight analysis; (3) a sophisticated time-sharing system for obtaining a very flexible input-output capability during real-time operations; and (4) a problem formulation and scaling for complete operation in single-precision arithmetic using a 24-bit word. The paper emphasizes the procedures used in formulation, scaling, and time-sharing for the real-time Kalman filter application. Some flight results are presented to illustrate the performance of the filter during real-time operation.

Schmidt, S. F.↗

NASA NTRS1999

Synoptic Mapping of Chemical Composition, Thermal Structure, and Air Motion from UARS Observations

An operational mapping algorithm was developed to process measurements of individual species observed by different satellite instruments on board UARS. Based on Fast Fourier Synoptic Mapping (FFSM), the algorithm accounts for the precessing orbit of UARS, the error of individual instruments, and gaps associated with instrument duty cycle and the satellite yaw maneuver. It provides synoptic structure and evolution on periods as short as 1 day, derived collectively from all observations of an individual species. The algorithm was applied to synoptically map temperature, thickness, and several chemical constituents observed by the instruments: MLS, CLAES, ISAMS, and HALOE. Each field variable observed by these instruments was mapped twice-daily in continuous global time series several months long. Mapped behavior produced via FFSM was compared against standard archived products generated via Kalman filtering. The standard map products reveal similar behavior, but are limited to features of larger scale. Tracer structure that develops through flow deformation and attending transport is therefore represented in those products more coarsely, eventually being sheared down to scales that are no longer represented properly. The synoptic time series also reveal a diurnal cycle for several of the constituents, one that emerges clearly in their space-time spectra. The zonal and meridional structure of diurnal variability was mapped by filtering the space-time spectrum, an intermediate product of FFSM, to those scales resolved by the UARS sampling. Geographical variations of the diurnal cycle have also been evaluated in its seasonal-mean structure by compositing distributions at individual local times. Both were compared to diurnal variations in chemical models and in dynamical models that account for transport by the diurnal tide. Diurnal variations were found to introduce spurious behavior into the archived products generated via Kalman filtering, behavior that is misrepresented in those synoptic time series. Aliasing by under-sampled diurnal variations introduces a bias into the time-mean structure of archived products. That systematic error is manifested as anomalous wave structure in the time-mean fields. By contrast, synoptic time series generated via FFSM faithfully represent such behavior as varying diurnally, so it does not corrupt time-mean structure. Tracer structure mapped via the above algorithm was being applied to determine the Brewer-Dobson circulation of the stratosphere through Lagrangian considerations. Preliminary results are encouraging: They reveal diabatic ascent in the tropics, balanced by diabatic descent over the winter hemisphere. This Lagrangian description of transport derived from UARS tracer measurements would be potentially valuable for diagnosing interannual changes of transport, specifically, in relation to interannual changes of total ozone. Regrettably, support was reduced to 50% of the approved funding level, leaving this component incomplete.

Salby, Murry L.↗

NASA NTRS2004

An Integrated Optimal Estimation Approach to Spitzer Space Telescope Focal Plane Survey

This paper discusses an accurate and efficient method for focal plane survey that was used for the Spitzer Space Telescope. The approach is based on using a high-order 37-state Instrument Pointing Frame (IPF) Kalman filter that combines both engineering parameters and science parameters into a single filter formulation. In this approach, engineering parameters such as pointing alignments, thermomechanical drift and gyro drifts are estimated along with science parameters such as plate scales and optical distortions. This integrated approach has many advantages compared to estimating the engineering and science parameters separately. The resulting focal plane survey approach is applicable to a diverse range of science instruments such as imaging cameras, spectroscopy slits, and scanning-type arrays alike. The paper will summarize results from applying the IPF Kalman Filter to calibrating the Spitzer Space Telescope focal plane, containing the MIPS, IRAC, and the IRS science Instrument arrays.

optimal estimations↗

NASA NTRS1984

Flight tests of the Digital Integrated Automatic Landing System (DIALS)

The design, development, implementation and flight tests of the Digital Integrated Automatic Landing System (DIALS) are discussed. The system was implemented and flight tested on the Transport Systems Research Vehicle (TSRV), a Boeing 737-100. The design uses modern optimal control methods. The direct digital design obtained uses a 10 Hz rate for the sampling of sensors and the control commands. The basic structure of the control law consists of a steady state Kalman filter followed by a control gain matrix. The sensor information used includes Microwave Landing System (MLS) position, attitude, calibrated airspeed, and body accelerations. The phases of the final approach considered are localized and steep glideslope capture (which may be performed simultaneously or independently), localizer and glideslope track, crab/decrab, and flare to touchdown. The system can capture, track, and flare from conventional, as well as steep, glideslopes ranging from 2.5 deg to 5.5 deg. All of the modes of the control law including the Kalman filters were implemented on the TSRV flight computers which use fixed point arithmetic with 16 bit words. The implementation considerations are described as well as an analysis of the flight test results.

Halyo, N.↗

NASA NTRS2003

Collaborative Research: Atlantic Ocean Tropical/Subtropical Processes from Seasonal to Decadal Time Scales: Model/Data, Model/Model Comparison and Model/Data Synthesis Through Assimilation

The effort of this first year of research has been focused on the assimilation of TOPEX/Poseidon altimetric data into a primitive equation model of the Atlantic tropical/subtropical circulation. A reduced-rank, stationary Kalman filter has been constructed to assimilate the altimetric sea surface height anomaly (SHA) into the model. The goal is to assess how the inter-hemispheric transports between the Atlantic subtropics and tropics are affected by the assimilation and how the subsurface thermocline structure , and its variability ,is dynamically constrained by the SHA. The model is a reduced-gravity primitive equation GCM of the upper Atlantic Ocean between 30 S and 30 N. The assimilation scheme is an approximation to the extended Kalman filter in which the error covariances of the state estimates are calculated only in a reduced- dimension subspace. The subspace is defined by the leading empirical orthogonal functions calculated from an unconstrained model calculation. Both an identical twin experiment using simulated SHA observations and assimilation of the real TOPEX data were performed. Results from the twin experiments demonstrate the ability of the method to constrain the ocean circulation and the subsurface temperature structure. The impact on the subsurface temperature structure of TOPEX assimilation was assessed using data from expandable bathythermographs. This showed a substantial improvement in the estimated temperature variability only within 13 degrees in latitude around the equator. The impact of TOPEX SHA assimilation on zonally integrated meridional transport across different latitudes was also estimated. Again within 13 degrees from the equator both the mean amplitude and interannual variability of the surface and subsurface transports were significantly enhanced, while the transports were insensitive to the assimilation in the subtropics.

Malannotte-Rizzoli, Paola↗

NASA NTRS2015

Attitude Ground System (AGS) For The Magnetospheric Multi-Scale (MMS) Mission

The Magnetospheric Multiscale (MMS) mission is a Solar-Terrestrial Probe mission consisting of four identically instrumented spin-stabilized spacecraft flying in an adjustable pyramid-like formation around the Earth. The formation of the MMS spacecraft allows for three-dimensional study of the phenomenon of magnetic reconnection, which is the primary objective of the mission. The MMS spacecraft were launched early on March 13, 2015 GMT. Due to the challenging and very constricted attitude and orbit requirements for performing the science, as well as the need to maintain the spacecraft formation, multiple ground functionalities were designed to support the mission. These functionalities were incorporated into a ground system known as the Attitude Ground System (AGS). Various AGS configurations have been used widely to support a variety of three-axis-stabilized and spin-stabilized spacecraft missions within the NASA Goddard Space Flight Center (GSFC). The original MMS operational concept required the AGS to perform highly accurate predictions of the effects of environmental disturbances on the spacecraft orientation and to plan the attitude maneuvers necessary to stay within the science attitude tolerance. The orbit adjustment requirements for formation control drove the need also to perform calibrations that have never been done before in support of NASA GSFC missions. The MMS mission required support analysts to provide fast and accurately calibrated values of the inertia tensor, center of mass, and accelerometer bias for each MMS spacecraft. During early design of the AGS functionalities, a Kalman filter for estimating the attitude, body rates, center of mass, and accelerometer bias, using only star tracker and accelerometer measurements, was heavily analyzed. A set of six distinct filters was evaluated and considered for estimating the spacecraft attitude and body rates using star tracker data only. Four of the six filters are closely related and were compared during support of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Space Technology-5 (ST-5) missions. These analyses exposed high dependency and sensitivity on the knowledge of the spacecraft inertia tensor for both body rates and accelerometer bias estimation. The conclusion of the analysis led to the design of an inertia tensor calibration technique using only star tracker data. The second most important result of the analysis was the design of two separate Kalman filters to estimate the spacecraft attitude and body rates and the accelerometer bias instead of a single combined filter. In this paper, the calibration results of the mass properties, as well as the performance of the spacecraft attitude and body rates filters using flight data are presented and compared against the mission requirements.

Estimation↗

NASA NTRS1986

Description of data on the Nimbus 7 LIMS map archive tape: Ozone and nitric acid

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) data set has been processed into a Fourier coefficient representation with a Kalman filter algorithm applied to profile data at individual latitudes and pressure levels. The algorithm produces synoptic data at noon Greenwich Mean Time (GMT) from the asynoptic orbital profiles. This form of the data set is easy to use and is appropriate for time series analysis and further data manipulation and display. Ozone and nitric acid results are grouped together in this report because the LIMS vertical field of views (FOV's) and analysis characteristics for these species are similar. A comparison of the orbital input data with mixing ratios derived from Kalman filter coefficients indicates errors in mixing ratio of generally less than 5 percent, with 15 percent being a maximum error. The high quality of the mapped data was indicated by coherence of both the phases and the amplitudes of waves with latitude and pressure. Examples of the mapped fields are presented, and details are given concerning the importance of diurnal variations, the removal of polar stratospheric cloud signatures, and the interpretation of bias effects in the data near the tops of profiles.

Remsberg, E. E.↗

NASA NTRS1991

Simulation and analyses of the aeroassist flight experiment attitude update method

A method which will be used to update the alignment of the Aeroassist Flight Experiment's Inertial Measuring Unit is simulated and analyzed. This method, the Star Line Maneuver, uses measurements from the Space Shuttle Orbiter star trackers along with an extended Kalman filter to estimate a correction to the attitude quaternion maintained by an Inertial Measuring Unit in the Orbiter's payload bay. This quaternion is corrupted by on-orbit bending of the Orbiter payload bay with respect to the Orbiter navigation base, which is incorporated into the payload quaternion when it is initialized via a direct transfer of the Orbiter attitude state. The method of updating this quaternion is examined through verification of baseline cases and Monte Carlo analysis using a simplified simulation, The simulation uses nominal state dynamics and measurement models from the Kalman filter as its real world models, and is programmed on Microvax minicomputer using Matlab, and interactive matrix analysis tool. Results are presented which confirm and augment previous performance studies, thereby enhancing confidence in the Star Line Maneuver design methodology.

Carpenter, J. R.↗

NASA NTRS1996

Combinations of Earth Orientation Measurements: SPACE94, COMB94, and POLE94

A Kalman filter has been used to combine independent measurements of the Earth's orientation taken by the space-geodetic observing techniques of lunar laser ranging, satellite laser ranging, very long baseline interferometry, and the Global Positioning System. Prior to their combination, the data series were adjusted to have the same bias and rate, the stated uncertainties of the measurements were adjusted, and data points considered to be outliers were deleted. The resulting combination, SPACE94, consists of smoothed, interpolated polar motion and UT1-UTC values spanning October 6, 1976, to January 27, 1995, at 1-day intervals. The Kalman filter was then used to combine the space-geodetic series comprising SPACE94 with two different, independent series of Earth orientation measurements taken by the technique of optical astrometry. Prior to their combination with SPACE94, the bias, rate and annual term of the optical astrometric series were corrected, the stated uncertainties of the measurements were adjusted, and data points considered to be outliers were deleted. The adjusted optical astrometric series were then combined with SPACE94 in two steps: (1) the Bureau International de l'Heure (BIH) optical astrometric series was combined with SPACE94 to form COMB94, a combined series of smoothed, interpolated polar motion and UT1-UTC values spanning January 20, 1962, to January 27, 1995, at 5-day intervals, and (2) the International Latitude Service (ILS) optical astrometric series was combined with COMB94 to form POLE94, a combined series of smoothed, interpolated polar motion values spanning January 20, 1900, to January 21, 1995, at 30.4375-day intervals.

Gross, Richard S.↗

NASA NTRS1986

Formulation and implementation of a practical algorithm for non-stationary adaptive state estimation

Background information on the Kalman filter is given first. A discussion of the filter parameters and their a priori determination follows. The discussion points out the need for adaptive determination of the process noise statistics. The filter innovations are presented as a means for developing the adaptive criteria. The criteria center around the estimation of the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of a locally stationary random process is presented. The definition of a local stationarity is presented. Local stationarity allows for the separation of the process statistics into a stationary component and a time-varying component. The separation method is discussed. A method for estimating the stationary and time-varying components is presented. As an example of its application to real problems, the algorithm is applied to the problem to the problem of reentry trajectory estimation for the Space Shuttle. Both the adaptive algorithm and the steady-state Kalman filter are applied to the problem. The results of the reconstructions are presented. The adaptive algorithm exhibits superior performance.

Whitemore, S. A.↗

NASA NTRS2009

GPS Navigation for the Magnetospheric Multi-Scale Mission

In 2014. NASA is scheduled to launch the Magnetospheric Multiscale Mission (MMS), a four-satellite formation designed to monitor fluctuations in the Earth's magnetosphere. This mission has two planned phases with different orbits (1? x 12Re and 1.2 x 25Re) to allow for varying science regions of interest. To minimize ground resources and to mitigate the probability of collisions between formation members, an on-board orbit determination system consisting of a Global Positioning System (GPS) receiver and crosslink transceiver was desired. Candidate sensors would be required to acquire GPS signals both below and above the constellation while spinning at three revolutions-per-minute (RPM) and exchanging state and science information among the constellation. The Intersatellite Ranging and Alarm System (IRAS), developed by Goddard Space Flight Center (GSFC) was selected to meet this challenge. IRAS leverages the eight years of development GSFC has invested in the Navigator GPS receiver and its spacecraft communication expertise, culminating in a sensor capable of absolute and relative navigation as well as intersatellite communication. The Navigator is a state-of-the-art receiver designed to acquire and track weak GPS signals down to -147dBm. This innovation allows the receiver to track both the main lobe and the much weaker side lobe signals. The Navigator's four antenna inputs and 24 tracking channels, together with customized hardware and software, allow it to seamlessly maintain visibility while rotating. Additionally, an extended Kalman filter provides autonomous, near real-time, absolute state and time estimates. The Navigator made its maiden voyage on the Space Shuttle during the Hubble Servicing Mission, and is scheduled to fly on MMS as well as the Global Precipitation Measurement Mission (GPM). Additionally, Navigator's acquisition engine will be featured in the receiver being developed for the Orion vehicle. The crosslink transceiver is a 1/4 Watt transmitter utilizing a TDMA schedule to distribute a science quality message to all constellation members every ten seconds. Additionally the system generates one-way range measurements between formation members which is used as input to the Kalman filter. In preparation for the MMS Preliminary Design Review (PDR), the Navigator was required to pass a series of Technology Readiness Level (TRL) tests to earn the necessary TRL-6 classification. The TRL-6 level is achieved by demonstrating a prototype unit in a relevant end-to-end environment. The IRAS unit was able to meet all requirements during the testing phase, and has thus been TRL-6 qualified

Bamford, William↗

NASA NTRS2003

Nonlinear Observers for Gyro Calibration

High precision estimation and control algorithms, to achieve unprecedented levels of pointing accuracy, will be required to support future formation flying missions such as interferometry missions. Achieving high pointing accuracy requires precise knowledge of the spacecraft rotation rate. Typically, the rotation rate is measured by a gyro. The measured rates can be corrupted by errors in alignment and scale factor, gyro biases, and noise. In this work, we present nonlinear observers for gyro calibration. Nonlinear observers are superior to extended or pseudo-linear Kalman filter type approaches for large errors and global stability. Three nonlinear gyro calibration observers are developed. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The convergence properties of all three observers are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. The observers are then combined, and the gyro calibration parameters are estimated simultaneously. The stability of the combined observers is addressed, as well as the stability of the resulting closed loop systems. Simulated test results are presented for each scenario. Finally, the nonlinear observers are compared to a pseudo-linear Kalman filter.

Thienel, Julie↗

NASA NTRS1994

The short-term prediction of universal time and length of day using atmospheric angular momentum

The ability to predict short-term variations in the Earth's rotation has gained importance in recent years owing to more precise spacecraft tracking requirements. Universal time (UT1), that component of the Earth's orientation corresponding to the rotation angle, can be measured by number of high-precision space geodetic techniques. A Kalman filter developed at the Jet Propulsion Laboratory (JPL) optimally combines these different data sets and generates a smoothed times series and a set of predictions for UT1, as well as for additional Earth orientation components. These UT1 predictions utilize an empirically derived random walk stochastic model for the length of the day (LOD) and require frequent and up-to-date measurements of either UT1 or LOD to keep errors from quickly accumulating. Recent studies have shown that LOD variations are correlated with changes in the Earth's axial atmospheric angular momentum (AAM) over timescales of several years down to as little as 8 days. AAM estimates and forecasts out to 10 days are routinely available from meteorological analysis centers; these data can supplement geodetic measurements to improve the short-term prediction of LOD and have therefore been incorporated as independent data types in the JPL Kalman filter. We find that AAM and, to a lesser extent, AAM forecast data are extremely helpful in generating accurate near-real-time estimates of UT1 and LOD and in improving short-term predictions of these quantities out to about 10 days.

Freedman, A. P.↗

NASA NTRS2009

Chemical Source Inversion using Assimilated Constituent Observations in an Idealized Two-dimensional System

We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.

Tangborn, Andrew↗

NASA NTRS1999

Improved Earth Sensor Performance Using a Sequentially Correlated Noise Model

Spacecraft attitude estimation by means of an extended Kalman filter requires a reasonably true model of the inherent noise of each sensor. For some sensors, the largest uncorrected noise comes not from the sensor itself, but from errors in the model for the predicted observations. This is certainly the case for Earth horizon sensors. The Earth horizon as seen from low Earth orbit is nearly a circle whose radius depends primarily on altitude. A straightforward latitude-dependent correction is added to this to account for the oblateness of the Earth. There also are both seasonal and stochastic variations in the horizon height. The seasonal variations can be predicted to some limited degree based on models derived from historical data. The stochastic component characteristically shows variations that are correlated both in time and space but which are unpredictable over long time spans. This work investigates whether Earth horizon sensor performance can be improved by solving for its systematic error as an augmentation of an attitude Kalman filter. It is found that using only Earth and Sun sensors, the augmented state is not fully observable. Even when magnetometer data is included, only the pitch axis component of the error can be improved; the roll component is unobservable.

Sedlak, J.↗

NASA NTRS1999

Improved Earth Sensor Performance Using a Sequentially Correlated Noise Model

Spacecraft attitude estimation by means of an extended Kalman filter requires a reasonably true model of the inherent noise of each sensor. For some sensors, the largest uncorrected noise comes not from the sensor itself, but from errors in the model for the predicted observations. This is certainly the case for Earth horizon sensors. The Earth horizon as seen from low Earth orbit is nearly a circle whose radius depends primarily on altitude. A straightforward latitude-dependent correction is added to this to account for the oblateness of the Earth. There also are both seasonal and stochastic variations in the horizon height. The seasonal variations can be predicted to some limited degree based on models de(ived from historical data. The stochastic component characteristically shows variations that are correlated both in time and space but which are unpredictable over long time spans. This work investigates whether Earth horizon sensor performance can be improved by solving for its systematic error as an augmentation of an attitude Kalman filter. It is found that using only Earth and Sun sensors, the augmented state is not fully observable. Even when magnetometer data is included, only the pitch axis component of the error can be improved; the roll component is unobservable.

Sedlak, Joseph↗

NASA NTRS2012

Towards A Model-Based Prognostics Methodology for Electrolytic Capacitors: A Case Study Based on Electrical Overstress Accelerated Aging

A remaining useful life prediction methodology for electrolytic capacitors is presented. This methodology is based on the Kalman filter framework and an empirical degradation model. Electrolytic capacitors are used in several applications ranging from power supplies on critical avionics equipment to power drivers for electro-mechanical actuators. These devices are known for their comparatively low reliability and given their criticality in electronics subsystems they are a good candidate for component level prognostics and health management. Prognostics provides a way to assess remaining useful life of a capacitor based on its current state of health and its anticipated future usage and operational conditions. We present here also, experimental results of an accelerated aging test under electrical stresses. The data obtained in this test form the basis for a remaining life prediction algorithm where a model of the degradation process is suggested. This preliminary remaining life prediction algorithm serves as a demonstration of how prognostics methodologies could be used for electrolytic capacitors. In addition, the use degradation progression data from accelerated aging, provides an avenue for validation of applications of the Kalman filter based prognostics methods typically used for remaining useful life predictions in other applications.

Celaya, Jose R.↗

NASA NTRS2011

A Model-based Prognostics Methodology for Electrolytic Capacitors Based on Electrical Overstress Accelerated Aging

Electrolytic capacitors↗