# Spacecraft Attitude Determination with Sun Sensors, Horizon Sensors and Gyros: Comparison of Steady-State Kalman Filter and Extended Kalman Filter

14 Oct 2012-pp 413-437

TL;DR: This paper investigates and compares the application of two autonomous sequential attitude estimation algorithms, adopted from the literature, for attitude determination using attitude sensors (sun sensor and horizon sensors) and rate-integrating gyros, and develops detailed sensor measurement models for these algorithms.

Abstract: Attitude determination, along with attitude control, is critical to functioning of every space mission. In this paper, we investigate and compare, through simulation, the application of two autonomous sequential attitude estimation algorithms, adopted from the literature, for attitude determination using attitude sensors (sun sensor and horizon sensors) and rate-integrating gyros. The two algorithms are: the direction cosine matrix (DCM) based steady-state Kalman Filter, and the classic quaternion-based Extended Kalman Filter. To make the analysis realistic, as well as to improve the attitude determination accuracies, detailed sensor measurement models are developed. Modifications in the attitude determination algorithms for estimation of additional states to account for sensor biases and misalignments are presented. A modular six degree-of-freedom closed-loop simulation, developed in house, is used to observe and compare the performances of the attitude determination algorithms.

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01 Jan 1981TL;DR: In this paper, the authors deal with the general problem of space vehicle dynamics and control and present the various approaches of this problem in a rather unified manner; the classical simplifying assumptions are curefully pointed out.

Abstract: This paper deals with the general problem of space vehicle dynamics and control It presents the various approaches of this problem in a rather unified manner; the classical simplifying assumptions are curefully pointed out

162 citations

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TL;DR: An overview of the current state of the developments in sun position sensors used in solar technologies such as photovoltaic modules, satellites, solar collectors and other applications is presented in this article.

Abstract: This paper presents an overview of the current state of the developments in sun position sensors used in solar technologies such as photovoltaic modules, satellites, solar collectors and other applications. The working principles and geometric designs of several types of sun position sensors are discussed in detail. The studio considers the evaluation of the advantages and limitations of different design requirements such as accuracy, solar tracking errors, desired properties, field of view (FOV) and commercialization, and the evaluation of outer parameters that affect the performance of sun position sensors (climatic conditions: solar radiation, contamination, and temperature); in order to combine the technologies, increase the efficiency and expand the use of sun position sensors. On the other hand, it was determined that the main barriers that this technology faces are: cost-effectiveness, the operational range of temperature and the effective data transmission, so the future researches should be concentrated around these issues.

48 citations

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Murphy Oil

^{1}TL;DR: In this article, the authors describe a direct-to-earth (DTE) laser communications (lasercom) between spacecraft in low-Earth orbit (LEO) or medium Earth orbit (MEO) and ground terminals.

Abstract: Challenges of direct-to-Earth (DTE) laser communications (lasercom) between spacecraft in low-Earth orbit (LEO) or medium-Earth orbit (MEO) and ground terminals can include short duration transmission windows, long time gaps between the transmission windows, deleterious effects of atmospheric turbulence, and the inability to operate in cloudy weather. Direct-link optical communications systems described herein can have data rates that are high enough to empty high-capacity on-board buffer(s) (e.g., having a capacity of at least about 1 Tb to hundreds of Tb) of a spacecraft in a single pass lasting only tens of seconds to a few minutes (e.g., 1-15 minutes), and overprovisioning the buffer capacity accounts for variations in the latency between links. One or more distributed networks of compact optical ground terminals, connected via terrestrial data networks, receive and demodulate WDM optical data transmissions from a plurality of orbiting spacecraft (e.g., satellites).

25 citations

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11 Mar 2015TL;DR: In this paper, a system and methods for attitude determination using infrared Earth horizon sensors (EHSs) with Gaussian response characteristics are described. But the method can be applied when two sensors, each with known and distinct pointing directions, detect the horizon, which is defined as having their fields of view partially obscured by Earth.

Abstract: Described herein are systems and methods for attitude determination using infrared Earth horizon sensors (EHSs) with Gaussian response characteristics. Attitude information is acquired by detecting Earth's infrared electromagnetic radiation and, subsequently, determining the region obscured by Earth in the sensors' fields of view to compute a nadir vector estimation in the spacecraft's body frame. The method can be applied when two sensors, each with known and distinct pointing directions, detect the horizon, which is defined as having their fields of view partially obscured by Earth. The method can be implemented compactly to provide high-accuracy attitude within small spacecraft, such as CubeSat-based satellites.

18 citations

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08 Jan 2016TL;DR: In this paper, the authors show that free-space optical communications signals can carry far more data than radio-frequency communications signals, and that a spacecraft can transmit over 1 Tb of data in a single pass using burst wavelength-division multiplexed (WDM) optical signals.

Abstract: A satellite in low-Earth orbit (LEO) or medium-Earth orbit (MEO) with a modern image sensor and/or other remote sensing device can collect data at rates of 10 Mbps or higher. At these collection rates, the satellite can accumulate more data between its passes over a given ground station than it can transmit to the ground station in a single pass using radio-frequency (RF) communications. Put differently, the sensors fill the spacecraft's memory faster than the spacecraft can empty it. Fortunately, free-space optical communications signals can carry far more data than RF communications signals. In particular, a spacecraft can transmit over 1 Tb of data in a single pass using burst wavelength-division multiplexed (WDM) optical signals. Each burst may last seconds to minutes, and can include tens to hundreds of WDM channels, each of which is modulated at 10 Gbps or more.

14 citations

##### References

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TL;DR: In this paper, the first comprehensive presentation of data, theory, and practice in attitude analysis is presented, including orthographic globe projections to eliminate confusion in vector drawings and a presentation of new geometrical procedures for mission analysis and attitude accuracy studies which can eliminate many complex simulations.

Abstract: This classic book is the first comprehensive presentation of data, theory, and practice in attitude analysis. It was written by 33 senior technical staff members in the Spacecraft Attitude Department of the Computer Sciences Corporation and incorporates their experience in supporting more than 30 space missions. Because of the extensive cross-references, complete index, and 13 technical appendices, this book can be either a self teaching text, or a reference handbook. Among its unique features are orthographic globe projections to eliminate confusion in vector drawings; discussions of common data anomalies, data validation, attitude hardware, and associated mathematical models; and a presentation of new geometrical procedures for mission analysis and attitude accuracy studies which can eliminate many complex simulations.

2,124 citations

### "Spacecraft Attitude Determination w..." refers background or methods in this paper

...In order to generate the scan width measurements based on the semi-scan angles due to an oblate earth model, we use the equations specified in [11] and [12], along with the model of oblate earth by Liu [5], with appropriate modifications to suit our coordinate convention....

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...As these sensors have been used in various space missions, sufficient technical research exists regarding their characteristics and performance [5,6]....

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...4 have been used [5]....

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01 Jan 1986

TL;DR: In this article, the effect of internal energy dissipation on the Directional Stability of Spinning Bodies was investigated in the context of gyroscope-based spin stabilization in Orbit and dual-stabilization in Orbit.

Abstract: Introduction Rotational Kinematics Attitude Motion Equations Attitude Dynamics of a Rigid Body Effect of Internal Energy Dissipation on the Directional Stability of Spinning Bodies Directional Stability of Multispin Vehicles Effect of Internal Energy Dissipation on the Directional Stability of Gyrostats Spacecraft Torques Gravitational Stabilization Spin Stabilization in Orbit Dual-Stabilization in Orbit: Gyrostats and Bias Momentum Satellites Appendixes References Index.

1,499 citations

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TL;DR: In this article, the authors present a review of the methods of Kalman filtering in attitude estimation and their development over the last two decades, focusing on three-axis gyros and attitude sensors.

Abstract: HIS report reviews the methods of Kalman filtering in attitude estimation and their development over the last two decades. This review is not intended to be complete but is limited to algorithms suitable for spacecraft equipped with three-axis gyros as well as attitude sensors. These are the systems to which we feel that Kalman filtering is most ap- plicable. The Kalman filter uses a dynamical model for the time development of the system and a model of the sensor measurements to obtain the most accurate estimate possible of the system state using a linear estimator based on present and past measurements. It is, thus, ideally suited to both ground-based and on-board attitude determination. However, the applicability of the Kalman filtering technique rests on the availability of an accurate dynamical model. The dynamic equations for the spacecraft attitude pose many difficulties in the filter modeling. In particular, the external torques and the distribution of momentum internally due to the use of rotating or rastering instruments lead to significant uncertainties in the modeling. For autonomous spacecraft the use of inertial reference units as a model replacement permits the circumvention of these problems. In this representation the angular velocity of the spacecraft is obtained from the gyro data. The kinematic equations are used to obtain the attitude state and this is augmented by means of additional state-vector components for the gyro biases. Thus, gyro data are not treated as observations and the gyro noise appears as state noise rather than as observation noise. It is theoretically possible that a spacecraft is three-axis stabilized with such rigidity that the time development of the system can be described accurately without gyro information, or that it is one-axis stabilized so that only a single gyro is needed to provide information on the time history of the system. The modification of the algorithms presented here in order to apply to those cases is slight. However, this is of little practical importance because a control system capable of such

1,266 citations

### Additional excerpts

...For instance, horizon sensor modeling includes errors arising from Earth’s oblateness, atmospheric radiance and sensor electronics....

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23 Apr 2004TL;DR: In this paper, Kronecker Factorization and Levenberg-Marquardt method for least square estimation is used to estimate the probability of an error in a prior state estimate.

Abstract: LEAST SQUARES APPROXIMATION A Curve Fitting Example Linear Batch Estimation Linear Least Squares Weighted Least Squares Constrained Least Squares Linear Sequential Estimation Nonlinear Least Squares Estimation Basis Functions Advanced Topics Matrix Decompositions in Least Squares Kronecker Factorization and Least Squares Levenberg-Marquardt Method Projections in Least Squares Summary PROBABILITY CONCEPTS IN LEAST SQUARES Minimum Variance Estimation Estimation without a Prior State Estimates Estimation with a Prior State Estimates Unbiased Estimates Maximum Likelihood Estimation Cramer-Rao Inequality Nonuniqueness of the Weight Matrix Bayesian Estimation Advanced Topics Analysis of Covariance Errors Ridge Estimation Total Least Squares Summary REVIEW OF DYNAMICAL SYSTEMS Linear System Theory The State Space Approach Homogeneous Linear Dynamical Systems Forced Linear Dynamical Systems Linear State Variable Transformations Nonlinear Dynamical Systems Parametric Differentiation Observability Discrete-Time Systems Stability of Linear and Nonlinear Systems Attitude Kinematics and Rigid Body Dynamics Attitude Kinematics Rigid Body Dynamics Spacecraft Dynamics and Orbital Mechanics Spacecraft Dynamics Orbital Mechanics Aircraft Flight Dynamics Vibration Summary PARAMETER ESTIMATION: APPLICATIONS Global Positioning System Navigation Attitude Determination Vector Measurement Models Maximum Likelihood Estimation Optimal Quaternion Solution Information Matrix Analysis Orbit Determination Aircraft Parameter Identification Eigen-system Realization Algorithm Summary SEQUENTIAL STATE ESTIMATION A Simple First-Order Filter Example Full-Order Estimators Discrete-Time Estimators The Discrete-Time Kalman Filter Kalman Filter Derivation Stability and Joseph's Form Information Filter and Sequential Processing Steady-State Kalman Filter Correlated Measurement and Process Noise Orthogonality Principle The Continuous-Time Kalman Filter Kalman Filter Derivation in Continuous Time Kalman Filter Derivation from Discrete Time Stability Steady-State Kalman Filter Correlated Measurement and Process Noise The Continuous-Discrete Kalman Filter Extended Kalman Filter Advanced Topics Factorization Methods Colored-Noise Kalman Filtering Consistency of the Kalman Filter Adaptive Filtering Error Analysis Unscented Filtering Robust Filtering Summary BATCH STATE ESTIMATION Fixed-Interval Smoothing Discrete-Time Formulation Continuous-Time Formulation Nonlinear Smoothing Fixed-Point Smoothing Discrete-Time Formulation Continuous-Time Formulation Fixed-Lag Smoothing Discrete-Time Formulation Continuous-Time Formulation Advanced Topics Estimation/Control Duality Innovations Process Summary ESTIMATION OF DYNAMIC SYSTEMS: APPLICATIONS GPS Position Estimation GPS Coordinate Transformations Extended Kalman Filter Application to GPS Attitude Estimation Multiplicative Quaternion Formulation Discrete-Time Attitude Estimation Murrell's Version Farrenkopf's Steady-State Analysis Orbit Estimation Target Tracking of Aircraft The a-b Filter The a-b-g Filter Aircraft Parameter Estimation Smoothing with the Eigen-system Realization Algorithm Summary OPTIMAL CONTROL AND ESTIMATION THEORY Calculus of Variations Optimization with Differential Equation Constraints Pontryagin's Optimal Control Necessary Conditions Discrete-Time Control Linear Regulator Problems Continuous-Time Formulation Discrete-Time Formulation Linear Quadratic-Gaussian Controllers Continuous-Time Formulation Discrete-Time Formulation Loop Transfer Recovery Spacecraft Control Design Summary APPENDIX A MATRIX PROPERTIES Basic Definitions of Matrices Vectors Matrix Norms and Definiteness Matrix Decompositions Matrix Calculus APPENDIX B BASIC PROBABILITY CONCEPTS Functions of a Single Discrete-Valued Random Variable Functions of Discrete-Valued Random Variables Functions of Continuous Random Variables Gaussian Random Variables Chi-Square Random Variables Propagation of Functions through Various Models Linear Matrix Models Nonlinear Models APPENDIX C PARAMETER OPTIMIZATION METHODS C.1 Unconstrained Extrema C.2 Equality Constrained Extrema C.3 Nonlinear Unconstrained Optimization C.3.1 Some Geometrical Insights C.3.2 Methods of Gradients C.3.3 Second-Order (Gauss-Newton) Algorithm APPENDIX D COMPUTER SOFTWARE Index

1,205 citations