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## Wilkinson Microwave Anisotropy Probe (WMAP) Attitude Estimation Filter Comparison

Tipo: 595 flight mechanics symposium; 18-20 oct. 2005; greenbelt, md; united states
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The Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft was launched in June of 2001. The sensor complement of WMAP consists of two Autonomous Star Trackers (ASTs), two Fine Sun Sensors (FSSs), and a gyro package which contains redundancy about one of the WMAP body axes. The onboard attitude estimation filter consists of an extended Kalman filter (EKF) solving for attitude and gyro bias errors which are then resolved into a spacecraft attitude quaternion and gyro bias. A pseudo-linear Kalman filter has been developed which directly estimates the spacecraft attitude quaternion, rate, and gyro bias. In this paper, the performance of the two filters is compared for the two major control modes of WMAP: inertial mode and observation mode.

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## Attitude Sensor Pseudonoise

Tipo: 595 flight mechanics symposium; 18-20 oct. 2005; greenbelt, md; united states
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Even assuming perfect attitude sensors and gyros, sensor measurements on a vibrating spacecraft have apparent errors. These apparent sensor errors, referred to as pseudonoise, arise because gyro and sensor measurements are performed at discrete times. This paper explains the concept of pseudonoise, quantifies its behavior, and discusses the effect of vibrations that are nearly commensurate with measurement periods. Although pseudonoise does not usually affect attitude determination it does affect sensor performance evaluation. Attitude rates are usually computed from differences between pairs of accumulated angle measurements at different times and are considered constant in the periods between measurements. Propagation using these rates does not reproduce exact instantaneous spacecraft attitudes except at the gyro measurement times. Exact sensor measurements will therefore be inconsistent with estimates based on the propagated attitude. This inconsistency produces pseudonoise. The characteristics of pseudonoise were determined using a simple, one-dimensional model of spacecraft vibration. The statistical properties of the deviations of measurements from model truth were determined using this model and a range of different periods of sensor and rate measurements. This analysis indicates that the magnitude of pseudonoise depends on the ratio of the spacecraft vibration period to the time between gyro measurements and can be as much as twice the amplitude of the vibration. In cases where the vibration period and gyro or sensor measurement period are nearly commensurate...

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## Multiplicative Versus Additive Filtering for Spacecraft Attitude Determination

Tipo: 6th international conference on control of systems and structures in space; 18-22 jul. 2004; riomaggiore; italy
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The absence of a globally nonsingular three-parameter representation of rotations forces attitude Kalman filters to estimate either a singular or a redundant attitude representation. We compare two filtering strategies using simplified kinematics and measurement models. Our favored strategy estimates a three-parameter representation of attitude deviations from a reference attitude specified by a higher- dimensional nonsingular parameterization. The deviations from the reference are assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. We point out some disadvantages of the other strategy, which directly estimates the four-parameter quaternion representation.

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## The Attitude Control System for the Wilkinson Microwave Anisotropy Probe

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The Wilkinson Microwave Anisotropy Probe mission produces a map of the cosmic microwave background radiation over the entire celestial sphere by executing a fast spin and a slow precession of its spin axis about the Sun line to obtain a highly interconnected set of measurements. The spacecraft attitude is sensed and controlled using an inertial reference unit, two star trackers, a digital sun sensor, twelve coarse sun sensors, three reaction wheel assemblies, and a propulsion system. Sufficient attitude knowledge is provided to yield instrument pointing to a standard deviation (l sigma) of 1.3 arc-minutes per axis. In addition, the spacecraft acquires and holds the sunline at initial acquisition and in the event of a failure, and slews to the proper orbit adjust orientations and to the proper off-sunline attitude to start the compound spin. This paper presents an overview of the design of the attitude control system to carry out this mission and presents some early flight experience.

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## Earth Observing System (EOS) Aqua Launch and Early Mission Attitude Support Experiences

Tipo: flight dynamics symposium; 29-30 oct. 2003; greenbelt, md; united states
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The Earth Observing System (EOS) Aqua satellite was successfully launched on May 4,2002. Aqua is the second in the series of EOS satellites. EOS is part of NASA s Earth Science Enterprise Program, whose goals are to advance the scientific understanding of the Earth system. Aqua is a three-axis stabilized, Earth-pointing spacecraft in a nearly circular, sun-synchronous orbit at an altitude of 705 km. The Goddard Space Flight Center (GSFC) Flight Dynamics attitude team supported all phases of the launch and early mission. This paper presents the main results and lessons learned during this period, including: real-time attitude mode transition support, sensor calibration, onboard computer attitude validation, response to spacecraft emergencies, postlaunch attitude analyses, and anomaly resolution. In particular, Flight Dynamics support proved to be invaluable for successful Earth acquisition, fine-point mode transition, and recognition and correction of several anomalies, including support for the resolution of problems observed with the MODIS instrument.

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## Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

Tipo: nasa/tp-2003-212178; l-18277; nas 1.60:212178
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Several laws are designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as an integrated set of actuators for attitude control. General, nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as a means of compensating for damping exerted by rotor bearings. Two flywheel steering laws are developed such that torque commanded by an attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude, and illustrate the benefits of kinetic energy error feedback. Control laws for attitude hold are also developed, and used to show the amount of propellant that can be saved when flywheels assist the CMGs. Nonlinear control laws for large-angle slew maneuvers perform well, but excessive momentum is required to reorient a vehicle like the International Space Station.

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## Integrated Orbit and Attitude Control for a Nanosatellite with Power Constraints

Tipo: aas 03-100; space flight mechanics meeting; 9-12 feb. 2003; ponce, pr; united states minor outlying islands
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Small satellites tend to be power-limited, so that actuators used to control the orbit and attitude must compete with each other as well as with other subsystems for limited electrical power. The Virginia Tech nanosatellite project, HokieSat, must use its limited power resources to operate pulsed-plasma thrusters for orbit control and magnetic torque coils for attitude control, while also providing power to a GPS receiver, a crosslink transceiver, and other subsystems. The orbit and attitude control strategies were developed independently. The attitude control system is based on an application of Linear Quadratic Regulator (LQR) to an averaged system of equations, whereas the orbit control is based on orbit element feedback. In this paper we describe the strategy for integrating these two control systems and present simulation results to verify the strategy.

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## Piloted Simulator Investigation of Techniques to Achieve Attitude Command Response with Limited Authority Servos

Tipo: nas 1.26:211391; usaamcom-tr-02-a-003; nasa-cr-2002-211391; nasa-a-0207144; ad-a408332
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The purpose of the study was to develop generic design principles for obtaining attitude command response in moderate to aggressive maneuvers without increasing SCAS series servo authority from the existing +/- 10%. In particular, to develop a scheme that would work on the UH-60 helicopter so that it can be considered for incorporation in future upgrades. The basic math model was a UH-60A version of GENHEL. The simulation facility was the NASA-Ames Vertical Motion Simulator (VMS). Evaluation tasks were Hover, Acceleration-Deceleration, and Sidestep, as defined in ADS-33D-PRF for Degraded Visual Environment (DVE). The DVE was adjusted to provide a Usable Cue Environment (UCE) equal to two. The basic concept investigated was the extent to which the limited attitude command authority achievable by the series servo could be supplemented by a 10%/sec trim servo. The architecture used provided angular rate feedback to only the series servo, shared the attitude feedback between the series and trim servos, and when the series servo approached saturation the attitude feedback was slowly phased out. Results show that modest use of the trim servo does improve pilot ratings, especially in and around hover. This improvement can be achieved with little degradation in response predictability during moderately aggressive maneuvers.

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## Attitude Error Representations for Kalman Filtering

Formato: application/pdf

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The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

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## Comprehensive Evaluation of Attitude and Orbit Estimation Using Actual Earth Magnetic Field Data

Formato: application/pdf

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A single, augmented Extended Kalman Filter (EKF), which simultaneously and autonomously estimates spacecraft attitude and orbit has been developed and successfully tested with real magnetometer and gyro data only. Because the earth magnetic field is a function of time and position, and because time is known quite precisely, the differences between the computed and measured magnetic field components, as measured by the magnetometers throughout the entire spacecraft orbit, are a function of both orbit and attitude errors. Thus, conceivably these differences could be used to estimate both orbit and attitude; an observability study validated this assumption. The results of testing the EKF with actual magnetometer and gyro data, from four satellites supported by the NASA Goddard Space Flight Center (GSFC) Guidance, Navigation, and Control Center, are presented and evaluated. They confirm the assumption that a single EKF can estimate both attitude and orbit when using gyros and magnetometers only.

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## Spacecraft Attitude Representations

Tipo: aatborg (denmark) university, dept. of control eng. colloquium; 27 oct. 1999; aalborg; denmark
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The direction cosine matrix or attitude matrix is the most fundamental representation of the attitude, but it is very inefficient: It has six redundant parameters, it is difficult to enforce the six (orthogonality) constraints. the four-component quaternion representation is very convenient: it has only one redundant parameter, it is easy to enforce the normalization constraint, the attitude matrix is a homogeneous quadratic function of q, quaternion kinematics are bilinear in q and m. Euler angles are extensively used: they often have a physical interpretation, they provide a natural description of some spacecraft motions (COBE, MAP), but kinematics and attitude matrix involve trigonometric functions, "gimbal lock" for certain values of the angles. Other minimum (three-parameter) representations: Gibbs vector is infinite for 180 deg rotations, but useful for analysis, Modified Rodrigues Parameters are nonsingular, no trig functions, Rotation vector phi is nonsingular, but requires trig functions.

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## TRMM On Orbit Attitude Control System Performance

Tipo: aas-99-073; guidance and control; 3-7 feb. 1999; breckenridge, co; united states
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This paper presents an overview of the Tropical Rainfall Measuring Mission (TRMM) Attitude Control System (ACS) along with detailed in-flight performance results for each operational mode. The TRMM spacecraft is an Earth-pointed, zero momentum bias satellite launched on November 27, 1997 from Tanegashima Space Center, Japan. TRMM is a joint mission between NASA and the National Space Development Agency (NASDA) of Japan designed to monitor and study tropical rainfall and the associated release of energy. Launched to provide a validation for poorly known rainfall data sets generated by global climate models, TRMM has demonstrated its utility by reducing uncertainties in global rainfall measurements by a factor of two. The ACS is comprised of Attitude Control Electronics (ACE), an Earth Sensor Assembly (ESA), Digital Sun Sensors (DSS), Inertial Reference Units (IRU), Three Axis Magnetometers (TAM), Coarse Sun Sensors (CSS), Magnetic Torquer Bars (MTB), Reaction Wheel Assemblies (RWA), Engine Valve Drivers (EVD) and thrusters. While in Mission Mode, the ESA provides roll and pitch axis attitude error measurements and the DSS provide yaw updates twice per orbit. In addition, the TAM in combination with the IRU and DSS can be used to provide pointing in a contingency attitude determination mode which does not rely on the ESA. Although the ACS performance to date has been highly successful...

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## Efficient and Optimal Attitude Determination Using Recursive Global Positioning System Signal Operations

Tipo: journal of guidance, control and dynamics|guidance, navigation and control; 10-12 aug. 1998; boston, ma; united states
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In this paper, a new and efficient algorithm is developed for attitude determination from Global Positioning System signals. The new algorithm is derived from a generalized nonlinear predictive filter for nonlinear systems. This uses a one time-step ahead approach to propagate a simple kinematics model for attitude determination. The advantages of the new algorithm over previously developed methods include: it provides optimal attitudes even for coplanar baseline configurations; it guarantees convergence even for poor initial conditions; it is a non-iterative algorithm; and it is computationally efficient. These advantages clearly make the new algorithm well suited to on-board applications. The performance of the new algorithm is tested on a dynamic hardware simulator. Results indicate that the new algorithm accurately estimates the attitude of a moving vehicle, and provides robust attitude estimates even when other methods, such as a linearized least-squares approach, fail due to poor initial starting conditions.

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## A Novel Sensor for Attitude Determination Using Global Positioning System Signals

Tipo: navigation and control conference; 10-12 aug. 1998; boston, ma; united states
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An entirely new sensor approach for attitude determination using Global Positioning System (GPS) signals is developed. The concept involves the use of multiple GPS antenna elements arrayed on a single sensor head to provide maximum GPS space vehicle availability. A number of sensor element configurations are discussed. In addition to the navigation function, the array is used to find which GPS space vehicles are within the field-of-view of each antenna element. Attitude determination is performed by considering the sightline vectors of the found GPS space vehicles together with the fixed boresight vectors of the individual antenna elements. This approach has clear advantages over the standard differential carrier-phase approach. First, errors induced by multipath effects can be significantly reduced or eliminated altogether. Also, integer ambiguity resolution is not required, nor do line biases need to be determined through costly and cumbersome self-surveys. Furthermore, the new sensor does not require individual antennas to be physically separated to form interferometric baselines to determine attitude. Finally, development potential of the new sensor is limited only by antenna and receiver technology development unlike the physical limitations of the current interferometric attitude determination scheme. Simulation results indicate that accuracies of about 1 degree (3 omega) are possible.

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## Attitude Estimation Using Modified Rodrigues Parameters

Tipo: flight mechanics/estimation theory symposium 1996; 71-83; nasa-cp-3333
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In this paper, a Kalman filter formulation for attitude estimation is derived using the Modified Rodrigues Parameters. The extended Kalman filter uses a gyro-based model for attitude propagation. Two solutions are developed for the sensitivity matrix in the Kalman filter. One is based upon an additive error approach, and the other is based upon a multiplicative error approach. It is shown that the two solutions are in fact equivalent. The Kalman filter is then used to estimate the attitude of a simulated spacecraft. Results indicate that then new algorithm produces accurate attitude estimates by determining actual gyro biases.

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