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NASA NTRS1996

ARTSN: An Automated Real-Time Spacecraft Navigation System

As part of the Deep Space Network (DSN) advanced technology program an effort is underway to design a filter to automate the deep space navigation process.The automated real-time spacecraft navigation (ARTSN) filter task is based on a prototype consisting of a FORTRAN77 package operating on an HP-9000/700 workstation running HP-UX 9.05. This will be converted to C, and maintained as the operational version. The processing tasks required are: (1) read a measurement, (2) integrate the spacecraft state to the current measurement time, (3) compute the observable based on the integrated state, and (4) incorporate the measurement information into the state using an extended Kalman filter. This filter processes radiometric data collected by the DSN. The dynamic (force) models currently include point mass gravitational terms for all planets, the Sun and Moon, solar radiation pressure, finite maneuvers, and attitude maintenance activity modeled quadratically. In addition, observable errors due to troposphere are included. Further data types, force and observable models will be ncluded to enhance the accuracy of the models and the capability of the package. The heart of the ARSTSN is a currently available continuous-discrete extended Kalman filter. Simulated data used to test the implementation at various stages of development and the results from processing actual mission data are presented.

Burkhart, P. Daniel↗

NASA NTRS1991

Alternative smoothing algorithms for on-line estimation problems

In recent years, much emphasis has been placed on the Kalman filter to solve on-line estimation problems. Smoothers, which determine state estimates at a certain time t using measurements between 0 and T, have been used primarily in off-line estimation schemes. This paper presents alternative forms of smoothers that can be used for on-line estimation problems. The alternative smoothing algorithms provide state estimates which are more refined than Kalman filtered state estimates. The alternative smoothing algorithms are illustrated in two examples. The first example considers a linear discrete-time system while the second example considers a nonlinear continuous-time system with discrete-time measurements.

Baumgartner, Eric T.↗

NASA NTRS2005

CORRELATED ERRORS IN EARTH POINTING MISSIONS

Two different Earth-pointing missions dealing with attitude control and dynamics changes illustrate concerns with correlated error sources and coupled effects that can occur. On the OrbView-2 (OV-2) spacecraft, the assumption of a nearly-inertially-fixed momentum axis was called into question when a residual dipole bias apparently changed magnitude. The possibility that alignment adjustments and/or sensor calibration errors may compensate for actual motions of the spacecraft is discussed, and uncertainties in the dynamics are considered. Particular consideration is given to basic orbit frequency and twice orbit frequency effects and their high correlation over the short science observation data span. On the Tropical Rainfall Measuring Mission (TRMM) spacecraft, the switch to a contingency Kalman filter control mode created changes in the pointing error patterns. Results from independent checks on the TRMM attitude using science instrument data are reported, and bias shifts and error correlations are discussed. Various orbit frequency effects are common with the flight geometry for Earth pointing instruments. In both dual-spin momentum stabilized spacecraft (like OV-2) and three axis stabilized spacecraft with gyros (like TRMM under Kalman filter control), changes in the initial attitude state propagate into orbit frequency variations in attitude and some sensor measurements. At the same time, orbit frequency measurement effects can arise from dynamics assumptions, environment variations, attitude sensor calibrations, or ephemeris errors. Also, constant environment torques for dual spin spacecraft have similar effects to gyro biases on three axis stabilized spacecraft, effectively shifting the one-revolution-per-orbit (1-RPO) body rotation axis. Highly correlated effects can create a risk for estimation errors particularly when a mission switches an operating mode or changes its normal flight environment. Some error effects will not be obvious from attitude sensor measurement residuals, so some independent checks using imaging sensors are essential and derived science instrument attitude measurements can prove quite valuable in assessing the attitude accuracy.

Steve Bilanow↗

NASA NTRS1993

Computationally efficient algorithms for real-time attitude estimation

For many practical spacecraft applications, algorithms for determining spacecraft attitude must combine inputs from diverse sensors and provide redundancy in the event of sensor failure. A Kalman filter is suitable for this task, however, it may impose a computational burden which may be avoided by sub optimal methods. A suboptimal estimator is presented which was implemented successfully on the Delta Star spacecraft which performed a 9 month SDI flight experiment in 1989. This design sought to minimize algorithm complexity to accommodate the limitations of an 8K guidance computer. The algorithm used is interpreted in the framework of Kalman filtering and a derivation is given for the computation.

Pringle, Steven R.↗

NASA NTRS1992

Flight evaluation of differential GPS aided inertial navigation systems

Algorithms are described for integration of Differential Global Positioning System (DGPS) data with Inertial Navigation System (INS) data to provide an integrated DGPS/INS navigation system. The objective is to establish the benefits that can be achieved through various levels of integration of DGPS with INS for precision navigation. An eight state Kalman filter integration was implemented in real-time on a twin turbo-prop transport aircraft to evaluate system performance during terminal approach and landing operations. A fully integrated DGPS/INS system is also presented which models accelerometer and rate-gyro measurement errors plus position, velocity, and attitude errors. The fully integrated system was implemented off-line using range-domain (seventeen-state) and position domain (fifteen-state) Kalman filters. Both filter integration approaches were evaluated using data collected during the flight test. Flight-test data consisted of measurements from a 5 channel Precision Code GPS receiver, a strap-down Inertial Navigation Unit (INU), and GPS satellite differential range corrections from a ground reference station. The aircraft was laser tracked to determine its true position. Results indicate that there is no significant improvement in positioning accuracy with the higher levels of DGPS/INS integration. All three systems provided high-frequency (e.g., 20 Hz) estimates of position and velocity. The fully integrated system provided estimates of inertial sensor errors which may be used to improve INS navigation accuracy should GPS become unavailable, and improved estimates of acceleration, attitude, and body rates which can be used for guidance and control. Precision Code DGPS/INS positioning accuracy (root-mean-square) was 1.0 m cross-track and 3.0 m vertical. (This AGARDograph was sponsored by the Guidance and Control Panel.)

Mcnally, B. David↗

NASA NTRS1984

The application of LQR synthesis techniques to the turboshaft engine control problem

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

Pfeil, W. H.↗

NASA NTRS1985

The application of LQR synthesis techniques to the turboshaft engine control problem

Pfeil, W. H.↗

NASA NTRS1979

Multiple scene attitude estimator performance for LANDSAT-1

Initial results are presented to demonstrate the performance of a linear sequential estimator (Kalman Filter) used to estimate a LANDSAT 1 spacecraft attitude time series defined for four scenes. With the revised estimator a GCP poor scene - a scene with no usable geodetic control points (GCPs) - can be rectified to higher accuracies than otherwise based on the use of GCPs in adjacent scenes. Attitude estimation errors was determined by the use of GCPs located in the GCP-poor test scene, but which are not used to update the Kalman filter. Initial results achieved indicate that errors of 500m (rms) can be attained for the GCP-poor scenes. Operational factors are related to various scenarios.

Rifman, S. S.↗

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.↗