The problem of estimating the state vector of a dynamical system from vector measurements, when it is known that the state vector satisfies norm equality constraints is considered. The case of a linear dynamical system with linear measurements subject to a norm equality constraint is discussed with a review of existing solutions. The norm constraint introduces a nonlinearity in the system for which a new estimator structure is derived by minimizing a constrained cost function. It is shown that the constrained estimate is equivalent to the brute force normalization of the unconstrained estimate. The obtained solution is extended to nonlinear measurement models and applied to the spacecraft attitude filtering problem.

An identification algorithm called the time-varying eigensystem realization algorithm is proposed to realize discrete-time-varying plant models from input and output experimental data. It is shown that this singular value decomposition based method is a generalization of the eigensystem realization algorithm developed to realize time invariant models from pulse response sequences. Using the results from discrete-time identification theory, the generalized Markov parameter and the generalized Hankel matrix sequences are computed via a least squares problem associated with the input-output map. The computational procedure presented in the paper outlines a methodology to extract a state space model from the generalized Hankel matrix sequence in different time-varying coordinate systems. The concept of free response experiments is suggested to identify the subspace of the unforced system response. For the special case of systems with fixed state space dimension, the free response subspace is used to construct a uniform coordinate system for the realized models at different time steps. Numerical simulation results on general systems discuss the details and effectiveness of the algorithms.

An algorithm for computation of the generalized Markov parameters of an observer or Kalman filter for discretetime-varying systems from input-output experimental data is presented. Relationships between the generalized observer Markov parameters and the system Markov parameters are derived for the time-varying case. The generalized system Markov parameters thus derived are used by the time-varying eigensystem realization algorithm to obtain a time-varying discrete-time state-space model. A qualitative relationship of the time-varying observer with the Kalman filter in the stochastic environment and an asymptotically stable realized observer are discussed briefly to develop insights for the analyst. The minimum number of repeated experiments for accurate recovery of the system Markov parameters is determined from these developments. The time-varying observer gains realized in the process are subsequently shown to be in consistent coordinate systems for observer state propagation. It is also demonstrated that the observer gain sequence realized in the case of the minimum number of experiments corresponds naturally to a time-varying deadbeat observer. Numerical examples demonstrate the utility of the concepts developed in the paper.

An analytical approach is presented for developing an estimation framework (called the Jth Moment Extended Kalman Filter (JMEKF)). This forms an important component of a class of architectures under investigation to study the interplay of major issues in nonlinear estimation such as model nonlinearity, measurement sparsity and initial condition uncertainty in the presence of low process noise. Utilizing an automated nonlinear expansion of the model about the current best estimated trajectory, a Jth order approximate solution for the departure motion dynamics about a nominal trajectory is derived in the form of state transition tensors. This solution is utilized in evaluating the evolution of statistics of the departure motion as a function of the statistics of initial conditions. The statistics thus obtained are used in the determination of a state estimate assuming a Kalman update structure. Central to the state transition tensor integration about a nominal trajectory, is the high order sensitivity calculations of the nonlinear models (dynamics and measurement), being automated by OCEA (Object Oriented Coordinate Embedding Method), a computational tool generating the required various order partials of the system differential equations without user intervention. Working in tandem with an OCEA automation of the derivation of the state transition tensor differential equations is a vector matrix representation structure of tensors of arbitrary rank, facilitating faster and more accurate computations. High order moment update equations are derived to incorporate the statistical effects of the innovations process more rigorously, improving the effectiveness of the estimation scheme. Numerical simulations on an orbit estimation example investigate the gain obtained in using the proposed methodology in situations where the classical extended Kalman filter's domain of convergence is smaller. The orbit estimation example presented examines a situation that requires us to determine the position and velocity state of the orbiter from range, azimuth and elevation measurements being made available sparsely.

This scoping review aimed to identify current evidence and gaps in the field of long-term space nutrition. Specifically, the review targeted critical nutritional needs during long-term manned missions in outer space in addition to the essential components of a sustainable space nutrition system for meeting these needs. The search phrase “space food and the survival of astronauts in long-term missions” was used to collect the initial 5432 articles from seven Chinese and seven English databases. From these articles, two independent reviewers screened titles and abstracts to identify 218 articles for full-text reviews based on three themes and 18 keyword combinations as eligibility criteria. The results suggest that it is possible to address short-term adverse environmental factors and nutritional deficiencies by adopting effective dietary measures, selecting the right types of foods and supplements, and engaging in specific sustainable food production and eating practices. However, to support self-sufficiency during long-term space exploration, the most optimal and sustainable space nutrition systems are likely to be supported primarily by fresh food production, natural unprocessed foods as diets, nutrient recycling of food scraps and cultivation systems, and the establishment of closed-loop biospheres or landscape-based space habitats as long-term life support systems.

This paper details the design and modeling of a novel morphing wing developed at Texas A & M University. Twistable sections with an elastomeric skin characterize the wing as a distinct actuator in aerospace vehicles. Aerodynamic models of the wing were developed using Prandtl's Lifting Line Theory. 1 These models were validated using wind tunnel tests conducted at the low speed wind tunnel at Texas A& M University. It was found that the operating envelope of the angle of attack of the wing was enhanced by the twistable sections.

The implicit function theorem due to Lagrange i s generalized to enable high order implicit rate calculations of general implicit functions about pre-computed solutions of in ter~ est. The sensitivities thus calculated are subsequently used in determining neighboring solutions about an exisling root (for algebraic systems) or trajectory (in case of dynamical systems). The generalization to dynamical systems, as a special case, enables the calculation of high order time varying sensiti vities of the solutions of boundary value problems with respect to the parameters of the system model and/or func tions describing the boundary condition . The generalizations thus realized are applied to various problems arising in trajectory optimization. It was found that useful information relating the neighboring extremal paths can be deduced from these implicit rates characteri zing the behavior in the neighborhood of the ex isting solutions. The accuracy of solutions obtained is subsequently enhanced using an aver

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