Eric M. Klatt

Magnetometer-based Attitude and Rate Estimation for Spacecraft with Wire Booms

A magnetometer-based filter and smoother are presented for estimating attitude, rate, and boom orientations for a spinning spacecraft employing wire booms. The work is motivated by the need to estimate the attitude and boom configuration of a recent scientific sounding rocket mission. During flight, the primary payload ejected two small spinning spacecraft, or subpayloads. These each deployed four 3-m wire booms attached to small tip-mass probes. Following deployment, the booms were aligned approximately radially about the nominal spin axis. The attitude determination task is to reconstruct the attitude, rate, and boom orientations for each subpayload. The estimates are initialized by the approximate initial angular momentum for each subpayload at ejection, provided by inertial sensors onboard the primary payload, and thereafter are based on magnetic field data furnished by a three-axis magnetometer onboard each subpayload. The estimation process is complicated by the flexible wire booms whose full parameterization for even the simplest pendulous modes would require 16 state elements in addition to the 6 elements necessary to define the state of the main spacecraft body. In this work, several simplifying assumptions about the motion of the booms allow reduction of the problem to tractable complexity. A variant of an existing magnetometer-based attitude and rate estimator is developed which is suited to the time-varying model errors resulting from the simplifying assumptions. Two key features of this new estimator are its use of the inertial components of the angular momentum vector in place of the traditional angular rate vector in the state estimate and its explicit inclusion of an error model for the approximate relationship between angular rate and angular momentum. The estimator, a filter/smoother, is applied to synthetic data from a truth-model simulation and then to actual telemetry from the mission subpayloads. Although designed for a spinning spacecraft with flexible wire booms, the filter and its related smoother constitute good estimation algorithms for any spacecraft that must employ coarse Eulerian model-based estimation in the presence of significant modeling errors.

Attitude Estimation for a Flexible Spacecraft in an Unstable Spin

Anattitudereconstruction algorithm hasbeendeveloped fora e exiblesounding rocketwhosespin vectornutates unstablyaboutitsminorinertia axis.Theattitudeestimatesareneededforposte ightanalysisoftherocket’ sscience data. An additional goal of the work is to show that a e exible-body model can be used in a Kalman e lter or in a smoother. The attitude is estimated using a smoother whose dynamic model includes a main rigid body and a pair of elasticbooms. Boom e exure is the principal causeof nutation instability. Boom bending is modeled by a Markov process, but the laws of mechanics are used to determine its ine uence on the attitude dynamics. This smoother achieves a better attitude estimation accuracy than can be achieved using a rigid-body model. The peak attitude error is estimated to be 4 deg, and the principal error source seems to be the limited accuracy of the rocket’ s attitude sensors. HIS work deals with the poste ight attitude determination for a sounding rocket mission, the Cleft Accelerated Plasma Experimental Rocket (CAPER). CAPER was launched from the Andoya Rocket Range in Norway in January 1999. Its e ight lasted slightly longer than 1200 s and reached an apogee altitude of 1360 km. The goal of this mission was to study the behavior of the ionosphere during auroral events. Attitude information is needed to transform CAPER’ s measurements of electric e eld components into geodetic coordinates. An attitude accuracy of from 2 to 4 deg is considered acceptable for the mission. From an attitude determination standpoint, the important characteristics of the CAPER sounding rocket were as follows: Its attitude sensors were a vector sun sensor with a slit e eld of view, a e xed-head horizon crossing indicator (HCI), and a three-axis magnetometer that was mounted on a short boom. The rocket’ s attitude was passively spin stabilized with the nominal spin vector directed along its minor inertia axis. CAPER deployed several booms after exit from the atmosphere and after the e nal stage motor burn. The longest of these were two e exible 3-m booms that deployed perpendicular to the nominal spin axis and in opposite directions from each other. A schematic diagram of this cone guration appears in Fig. 1. Minor-axis spin stabilization is often used in sounding rocket experiments. Near the dawn of the space age, the Explorer-1 mission demonstrated that such a cone guration has an unstable nutation mode due to energy dissipation in the e exible booms. 1 In many sounding rocket experiments it is acceptable for the nutation amplitude to grow as long as the resultant coning half-angle does not become too large by the end of the e ight. There are two major challenges in doing poste ight attitude determination for CAPER. The e rst is the lack of rate-gyro data. This challenge dictates the use of an Eulerian dynamics model to propagate the attitude and rates between measurement sample times. The model becomes especially important toward the end of the e ight, when only magnetometer data are available. The attitude estimate in rotation about the magnetic e eld vector is based solely on dynamic model propagation during this phase, and model inaccuracy

Rank-ordered multifractal analysis for intermittent fluctuations with global crossover behavior

Rank-Ordered Multifractal Analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of intermittent fluctuations. The method allows one to understand the multifractal properties through rank-ordered scaling or non-scaling parametric variables. The idea of the ROMA technique is applied to analyze the multifractal characteristics of the auroral zone electric field fluctuations observed by SIERRA. The observed fluctuations span across contiguous multiple regimes of scales with different multifractal characteristics. We extend the ROMA technique such that it can take into account the crossover behavior -- with the possibility of collapsing probability distributions functions (PDFs) -- over these contiguous regimes.

Practical Design and Flight Test of a Yo-Yo Wire-Boom Deployment System

Ay o-yo-type wire-boom deployment system has been developed and flight tested on a sounding rocket mission. The goal of the work has been to validate a new mechanism that rapidly deploys wire booms from a spinning spacecraft. This work takes a theoretical system design and implements it in practical hardware. The limitations inherent in practical hardware necessitated new theoretical developments. A modified stability analysis has been developed for the case of nonzero axial separation between the wire-boom base attachment points and the spacecraft’s center of mass. This modified stability analysis dictates that a stable design is impractical for many missions because very large wire-boom tip masses are needed and because the three-dimensional deployment transients are very sensitive to small asymmetries. This problem has led to the development of design criteria and analysis techniques, which permit a short-duration mission to use a slightly unstable nutation mode. These techniques have been used to design a system that has been flown on two daughter spacecraft that were part of a formation of three sounding rocket subpayloads. Each daughter spacecraft deployed four 3-m-long wire booms in under 10 s and maintained a low level of spin instability for the remaining 700 s of the mission. The nutation oscillations showed a slow exponential growth, but the coning half-angles of both spacecraft never exceeded 16 deg.

A comparison of stochastic optimizers applied to dynamic sensor scheduling for satellite tracking

This paper presents a comparison of stochastic optimizers running inside a centralized sensor resource manager (SRM) for scheduling the tasks (observations) of an ensemble of space observing kinematic sensors. The manager is designed to operate as a receding horizon controller in a closed feedback loop with a linear filter based multiple hypothesis tracker (MHT) that fuses the disparate sensor data to produce target declarations and state estimates. The reward function is based on expected entropic information gain of satellite tracks over the planning horizon. A comparison between several stochastic optimizers, namely: particle swarm optimizers (PSO), evolutionary algorithms (EA), and the simultaneous perturbation and stochastic approximation (SPSA) algorithm is performed over the resulting high dimensional, Markovian, and discontinuous reward function. The algorithms were evaluated by simulating space surveillance scenarios using idealized optical sensors, satellite two-line element (TLE) sets from the US Space Track catalog, and relevant factors such as line of sight visibility. Simulation results show a hybrid PSO and EA algorithm outperforms the other algorithms over the tests performed.