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A new algorithm is proposed that smoothly integrates non-linear estimation of the attitude quaternion using Davenport s q-method and estimation of non-attitude states through an extended Kalman filter. The new method is compared to a similar existing algorithm showing its similarities and differences. The validity of the proposed approach is confirmed through numerical simulations.
Computational requirements - i.e., computing time per cycle (iteration) and required storage - which determine minimum sampling rates and computer memory size, were obtained as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then use sequential processing than to process them together via simultaneous processing.
Satellite attitude determination by simulation program using Monte Carlo sampling and Kalman-Schmidt filter
A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.
An effective multi-field wavefront control (WFC) approach is demonstrated for an actuated, segmented space telescope using wavefront measurements at the exit pupil, and the optical and computational implications of this approach are discussed. The integration of a Kalman Filter as an optical state estimator into the wavefront control process to further improve the robustness of the optical alignment of the telescope will also be discussed. Through a comparison of WFC performances between on-orbit and ground-test optical system configurations, the connection (and a possible disconnection) between WFC and optical system alignment under these circumstances are analyzed. Our MACOS-based computer simulation results will be presented and discussed.
Part of the Space Mathematics Division in CNES, the Flight Dynamics Center provides attitude and orbit determinations and maneuvers during the Launch and Early Operation Phase (LEOP) of geostationary satellites. Orbit determination is based on a Kalman filter method; when the 2 GHz CNES/NASA network is used, Doppler measurements are available and allow orbit determination during the apogee maneuvers. This method was used for TELE-X and TDF 2 LEOP (3-axis controlled satellites) and also for TELECOM 2 and HISPASAT (spun satellites): it enables us to follow the evolution of the maneuver and gives out a quite accurate estimation of the reached orbit. In this paper, we briefly describe the dynamic models of the orbit evolution in both cases, '3-axis' and 'inertial' thrust. Then, we present the results obtained for each case. Afterwards, we present some cases to show the robustness of the filter.
We have produced a 5-year mean secular variation (SV ) of the geomagnetic field for the period 2020–2025. We use the NASA Geomagnetic Ensemble Modeling System (GEMS), which consists of the NASA Goddard geodynamo model and ensemble Kalman filter (EnKF) with 400 ensemble members. Geomagnetic field models are used as observations for the assimilation, including gufm1 (1590–1960), CM4 (1961–2000) and CM6 (2001–2019). The forecast involves a bias correction scheme that assumes that the model bias changes on timescales much longer than the forecast period, so that they can be removed by successive forecast series. The algorithm was validated on the time period 2010-2015 by comparing with CM6 before being applied to the 2020–2025 time period. This forecast has been sub-mitted as a candidate predictive model of IGRF-13 for the period 2020–2025.
This paper presents for the first time a global study of the ozone catalytic destruction cycles operating in the stratosphere using a stratospheric analyses for January 1992. The chemical analyses were produced using a Kalman filter data assimilation system. Because a major component of the variability of trace gases is due to the atmospheric motions the analyses have been cast in a flow-tracking coordinate system that moves with the large scale flow pattern. Particular attention is paid to the kinetic aspects of these cycles such as the rate limiting step and chain length. Although it is an important kinetic parameter, the chain length of the various cycles is seldom considered when the various catalytic cycles are discussed. This survey highlights that in the low stratosphere the cycles involving HO2 and halogens (notably bromine) are particularly important. In approximate order of effectiveness the most important ozone loss cycles in the polar lower stratosphere are the BrO/ClO, HO2/BrO, and OH/HO2 cycles. The ClO/ClO cycle clearly delineates the regions of chlorine activation. The chain length of the HO2/ClO, OH/HO2, Br/BrO, and ClO/NO2, clearly delineate the vortex edge region. The chain length of the BrO/NO2 and Cl/NO2 cycles highlight the regions of chemical processing outside the vortex where streamers of chemically processed air are stripped-off and transported away from the vortex. This is also true in the very low stratosphere for the Cl/ClO and BrO/ClO cycles.
One function of the Deep Space Network is validation of the range data that they receive. In this paper we present an automated online sequential range predictor which shows promise of significantly reducing computational and manpower expenditures. The proposed algorithm, a U-D covariance factored Kalman filter, is demonstrated by processing a four-month record of Viking spacecraft data taken enroute to Mars.
The signatures of remote sensing data from agricultural crops exhibit significant non-stationarity, so that the performance of fixed parameter classifiers degenerates with time and distance from the initial training data. A class of adaptive decision-directed classifiers are being developed, based on Kalman filter theory. Limited results to date on two data sets indicate approximately a 25 to 40% reduction in rates of misclassification.
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
A three-axis Magnetometer/Kalman Filter attitude determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve light weight and low cost for an attitude determination system. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Accuracy near that of the International Geomagnetic Reference Field model is achieved. Covariance computation and simulation testing demonstrate the filter's accuracy. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically-anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as part of a low-cost three-axis attitude stabilization system.
In late 2017, the laser intensity monitor (LIM) current began to decline on the Lunar Reconnaissance Orbiter (LRO) miniature inertial measurement unit (MIMU). The MIMU was powered off in March 2018 and has only been used during extended eclipses, a pre-eclipse orbit phasing maneuver, and critical momentum unloads. Science slews were suspended, and the onboard extended Kalman filter (EKF) was disabled. A coarse rate was estimated through star tracker quaternion differentiation, and attitude was provided directly from a single star tracker. A complementary filter, combining the differentiated quaternions with the integrated acceleration derived from the attitude control torque, was developed, tested, and uploaded to the spacecraft in December 2018. The EKF has been enabled, using the complementary filter rate in place of the MIMU and science slews are now being performed. This paper presents an overview of the complementary filter rate estimation and EKF changes, fault detection updates without the MIMU, and inflight performance improvements.
This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.
Motion estimation is a field of great interest because of its many applications in areas such as robotics and image coding. The optic flow method is one such scheme which, although fairly accurate, is prone to error in the presence of noise. This thesis describes the use of the reduced order model Kalman filter (ROMKF) in reducing errors in displacement estimation due to degradation of the sequence. The implementation of filtering and motion estimation algorithms on the SUN workstation is also discussed. Results from preliminary testing were used to determine the degrees of freedom available for the ROMKF in the SUN software. The tests indicated that increasing the state to the left leads to slight improvement over the minimum state case. Therefore, the software uses the minimum model, with the option of adding states to the left only. The ROMKF was then used in conjunction with a hierarchical pel recursive motion estimation algorithm. Applying the ROMKF to the degraded displacements themselves generally yielded slight improvements in cases with noise degradation and noise plus blur. Filtering the images of the degraded sequence prior to motion estimation was less effective in these cases. Both methods performed badly in the case of blur alone, resulting in increased displacement errors. This is thought to be due in part to filter artifacts. Some improvements were obtained by varying the filter parameters when filtering the displacements directly. This result suggests that further study in varying filter parameters may lead to better results. The results of this thesis indicate that the ROMKF can play a part in reducing motion estimation errors from degraded sequences. However, more work needs to be done before the use of the ROMKF can be a practical solution.
The ability to detect and locate obstacles using on-board sensors and modify the nominal trajectory is necessary for safe landing of an autonomous lander on Mars. This paper examines some of the issues in the location of objects using a sequence of images from a passive sensor, and describes a Kalman filter approach to improve the range estimation to obstacles. The filter is also used to track features in the images leading to a significant reduction of search effort in the feature extraction step of the algorithm. The lack of suitable flight imagery data presents a problem in the verification of concepts for obstacle detection. An experiment is designed to acquire a sequence of images along with sensor motion parameters and the range estimation results using this imagery are presented.
A landing scheme for landing V/STOL aircraft on rolling ships was sought using computerized simulations. The equations of motion as derived from hydrodynamics, their form and the physical mechanisms involved and the general form of the approximation are discussed. The modeling of the sea is discussed. The derivation of the state-space equations for the DD-963 destroyer is described. Kalman filter studies are presented and the influence of the various parameters is assessed. The effect of various modeling parameters on the rms error is assessed and simplifying conclusions are drawn. An upper bound for prediction time of about five seconds is established, with the exception of roll, which can be predicted up to ten seconds ahead.
The Magnetospheric MultiScale Mission is a four spacecraft formation flying mission designed to study the Earth s magnetosphere. The spacecraft fly in highly elliptical orbits, forming a tetrahedron at apogee. Each spacecraft spins at 3 RPM and is equipped with a star scanner, slit sun sensor, and accelerometer. The purpose of this work is to develop an Extended Kalman Filter to simultaneously estimate the attitude, angular velocity, angular acceleration, and center of mass of each spacecraft.