Richard Linares

Deterministic Relative Attitude Determination of Three-Vehicle Formations

DOI: 10.2514/1.42849 This paper proves that deterministic relative attitude determination is possible for a formation of three vehicles. The results provide an assessment of the accuracy of the deterministic attitude solutions, given statistical properties oftheassumednoisymeasurements.Eachvehicleisassumedtobeequippedwithsensorstoprovideline-of-sight,and possibly range, measurements between them. Three vehicles are chosen because this is the minimum number required to determine all attitudes given minimal measurement information. Three cases are studied. The first determines the absolute (inertial) attitude of a vehicle knowing the absolute positions of the other two. The second assumes parallel beams between each vehicle to determine relative attitudes, and the third assumes nonparallel beams for relative attitude determination, which requires range information to find deterministic solutions. Covariance analyses are provided to gain insight on the stochastic properties of the attitude errors and the observability for all three cases.

Constrained Relative Attitude Determination for Two Vehicle Formations

This paper studies constrained relative attitude determination of a formation of two vehicles. A deterministic solution for the relative attitude between the two vehicles with line-of-sight measurements between them and a common object observed by both vehicles is presented. The solution represents the minimum number of measurements required to determine the relative attitudes and no ambiguities are present. To quantify the performance of the algorithm the covariance of the attitude error is derived using a linearized error model from a least-squares point of view. Simulation results are also provided to assess the performance of the proposed new approach.

Space object shape characterization and tracking using light curve and angles data

This paper presents a new method, based on a multiple-model adaptive estimation approach, to determine the most probable shape of a resident space object among a number of candidate shape models while simultaneously recovering the observed resident space object’s inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters, each operating under a different hypothesis to determine an estimate of the physical system under consideration. In this work, the shape model of the resident space object constitutes the hypothesis. Estimates of the likelihood of each hypothesis, given the available measurements, are provided from the multiple-model adaptive estimation approach. The multiple-model adaptive estimation state estimates are determined using a weighted average of the individual filter estimates, whereas the shape estimate is selected as the shape model with the highest likelihood. Each filter employs the unscented estimation approach, reducing passively collected ...

Refining Space Object Radiation Pressure Modeling with Bidirectional Reflectance Distribution Functions

High-fidelity orbit propagation requires detailed knowledge of the solar radiation pressure on a space object. The solar radiation pressure depends not only on the space object’s shape and attitude, but also on the absorption and reflectance properties of each surface on the object. These properties are typically modeled in a simplistic fashion, but are here described by a surface bidirectional reflectance distribution function. Several analytic bidirectional reflectance distribution function models exist, and are typically complicated functions of illumination angle and material properties represented by parameters within the model. In general, the resulting calculation of the solar radiation pressure would require a time-consuming numerical integration. This might be impractical if multiple solar radiation pressure calculations are required for a variety of material properties in real time; for example, in a filter where the particular surface parameters are being estimated. This paper develops a method...

Astrometric and Photometric Data Fusion for Resident Space Object Orbit, Attitude, and Shape Determination Via Multiple-Model Adaptive Estimation

This paper presents a new method, based on a multiple-model adaptive estimation approach, to determine the most probable shape of a spacecraft in orbit among a number of candidate shape models while simultaneously recovering the observed resident space object’s inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters to provide multiple resident space object state estimates, where each filter is purposefully dependent on a mutually unique resident space object model. Estimates on the conditional probability of each model given the available measurements are provided from the multiple-model adaptive estimation approach. Each filter employs the Unscented (or Sigma-Point) estimation approach, reducing passively-collected electro-optical data to infer the unknown state vector comprised of the resident space object inertial-to-body orientation, position and their respective temporal rates. Each hypothesized model results in a different observed optical cross-sectional area. The effect of solar radiation pressure may be recovered from accurate angles-data alone, if the collected measurements span a sufficiently long period of time so as to make the non-conservative mismodeling effects noticeable. However, for relatively short data arcs, this effect is weak and thus the temporal brightness of the resident space object can be used in concert with the angles data to exploit the fused sensitivity to both resident space object characteristics and associated trajectory, the very same ones which drive the non-conservative dynamic effects. Recovering these characteristics and trajectories with sufficient accuracy i s shown in this paper, where the characteristics are inherent in unique resident space object models. The performance of this strategy is demonstrated via simulated scenarios.

Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions

Polynomial chaos expansion and Gaussian mixture models are combined in a hybrid fashion to propagate state uncertainty for spacecraft with initial Gaussian errors. Polynomial chaos expansion models uncertainty by performing an expansion using orthogonal polynomials. The accuracy of polynomial chaos expansion for a given problem can be improved by increasing the order of the orthogonal polynomial expansion. The number of terms in the orthogonal polynomial expansion increases factorially with dimensionality of the problem, thereby reducing the effectiveness of the polynomial chaos expansion approach for problems of moderately high dimensionality. This paper shows a combination of Gaussian mixture model and polynomial chaos expansion, Gaussian mixture model–polynomial chaos expansion as an alternative form of the multi-element polynomial chaos expansion. Gaussian mixture model–polynomial chaos expansion reduces the overall order required to reach a desired accuracy. The initial distribution is converted to a...

Attitude observability from light curve measurements

The observability of space object attitude from light curve data is analyzed. Light curves, which are the time-varying apparent brightness of sunlight reflected off a space object and measured by an observer, depend on the object position, attitude, surface material, shape, and other parameters. Previous work employing light curve data for shape estimation requires the availability of good attitude estimates. This paper explores the possibility of obtaining attitude information from the brightness measurements themselves. Some types of attitude estimate errors are detectable from individual brightness measurements, but other attitude errors lie in the nullspace of the Fisher information matrix and are not observable in the static case. Analytical expressions for the nullspace vectors are derived. The observability of the light curve model parameters is also briefly addressed.

A methodology for reduced order modeling and calibration of the upper atmosphere

Atmospheric drag is the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO). Accurately predicting drag for objects that traverse LEO is critical to Space Situational Awareness. Atmospheric models used for orbital drag calculations can be characterized either as empirical or physics-based (first principles based). Empirical models are fast to evaluate but offer limited real-time predictive/forecasting ability, while physics-based models offer greater predictive/forecasting ability but require dedicated parallel computational resources. Also, calibration with accurate data is required for either type of models. This paper presents a new methodology based on proper orthrogonal decomposition (POD) towards development of a quasi-physical, predictive, reduced order model that combines the speed of empirical and the predictive/forecasting capabilities of physics-based models. The methodology is developed to reduce the high-dimensionality of physics-based models while maintaining its capabilities. We develop the methodology using the Naval Research Labs MSIS model and show that the diurnal and seasonal variations can be captured using a small number of modes and parameters. We also present calibration of the reduced order model using the CHAMP and GRACE accelerometer-derived densities. Results show that the method performs well for modeling and calibration of the upper atmosphere.

Entropy-Based Space Object Data Association Using an Adaptive Gaussian Sum Filter

This paper shows an approach to improve the statistical validity of orbital estimates and uncertainties as well as a method of associating measurements with the correct resident space objects and classifying events in near realtime. The approach involves using an adaptive Gaussian mixture solution to the Fokker-Planck-Kolmogorov equation for its applicability to the resident space object tracking problem. The Fokker-Planck-Kolmogorov equation describes the time-evolution of the probability density function for nonlinear stochastic systems with Gaussian inputs, which often results in non-Gaussian outputs. The adaptive Gaussian sum lter provides a computationally ecient and accurate solution for this equation, which captures the non-Gaussian behavior associated with these nonlinear stochastic systems. This adaptive lter is designed to be scalable, relatively ecient for solutions of this type, and thus is able to handle the nonlinear eects which are common in the estimation of resident space object orbital states. The main purpose of this paper is to develop a technique for data association based on entropy theory that is compatible with the adaptive Gaussian sum lter. The adaptive lter and corresponding measurement association methods are evaluated using simulated data in realistic scenarios to determine their performance and feasibility.

A Quasi‐Physical Dynamic Reduced Order Model for Thermospheric Mass Density via Hermitian Space‐Dynamic Mode Decomposition

Thermospheric mass density is a major driver of satellite drag, the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO) pertinent to space situational awareness. Most existing models for thermosphere are either physics-based or empirical. Physics-based models offer the potential for good predictive/forecast capabilities but require dedicated parallel resources for real-time evaluation and data assimilative capabilities that have yet to be developed. Empirical models are fast to evaluate, but offer very limited forecasting abilities. This paper presents a methodology of developing a reduced-order dynamic model from high-dimensional physics-based models by capturing the underlying dynamical behavior. This work develops a quasi-physical reduced order model (ROM) for thermospheric mass density using simulated output from NCARs Thermosphere-Ionosphere-Electrodynamics General Circular Model (TIE-GCM). The ROM is derived using a dynamic system formulation from a large dataset of TIE-GCM simulations spanning 12 years and covering a complete solar cycle. Towards this end, a new reduced order modeling approach, based on Dynamic Mode Decomposition with control (DMDc), that uses the Hermitian space of the problem to derive the dynamics and input matrices in a tractable manner is developed. Results show that the ROM performs well in serving as a reduced order surrogate for TIE-GCM while almost always maintaining the forecast error to within 5\% of the simulated densities after 24 hours.