The optical slit sensor as a standard sensor for spacecraft attitude determination

The basic concept of an optical slit sensor as a standard altitude sensor is considered for any missions using a spinning spacecraft or where rotating sensors or mirrors could be used. Information available from a single sensor or from two sensors is analyzed. A standard slit sensor package is compared with the altitude package flown on the first synchronous meteorological satellite

An Extended Kalman Filter with a Computed Mean Square Error Bound

The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman filter. The main difference of the proposed filter from the conventional extended Kalman filter is in the use of a computed mean square error bound matrix, to calculate the filter gain, and to serve as bound on the actual mean square error. The paper shows that when the system is linear the proposed filtering algorithm reduces to the conventional Kalman filter. The theory presented in the paper is applicable to a wide class of systems, but if the system is polynomial, then the recently developed theory of positive polynomials considerably simplifies the filter's implementation.Comment: 7 pages, 1 figur

A Direct Quadrature Based Nonlinear Filtering with Extended Kalman Filter Update for Orbit Determination

Abstract-An optimal estimation of the states of a nonlinear continuous system with discrete measurements can be achieved through the solution of the Fokker-Planck equation, along with the Bayes' formula. However, solving the Fokker-Planck equation is restrictive in most cases. Recently a nonlinear filtering algorithm using a direct quadrature method of moments and the extended Kalman filter update mechanism was proposed, in which the associated Fokker-Planck equation was solved efficiently and accurately via discrete quadrature and the measurement update was done through the extended Kalman filter update mechanism. In this paper this hybrid filter based on the DQMOM and the EKF update is applied to the orbit determination problem with appropriate modification to mitigate the filter smugness. Unlike the extended Kalman filter, the hybrid filter based on the DQMOM and the EKF update does not require the burdensome evaluation of the Jacobian matrix and Gaussian assumption for system noise, and can still provide more accurate estimation of the state than those of the extended Kalman filter especially when measurements are sparse. Simulation results indicate that the advantages of the hybrid filter based on the DQMOM and the EKF update make it a promising alternative to the extended Kalman filter for orbit estimation problems

Quasi-Stochastic Integration Filter for Nonlinear Estimation

In practical applications, numerical instability problem, systematic error problem caused by nonlinear approximation, and nonlocal sampling problem for high-dimensional applications, exist in unscented Kalman filter (UKF). To solve these problems, a quasi-stochastic integration filter (QSIF) for nonlinear estimation is proposed in this paper. nonlocal sampling problem is solved based on the unbiased property of stochastic spherical integration rule, which can also reduce systematic error and improve filtering accuracy. In addition, numerical instability problem is solved by using fixed radial integration rule. Simulations of bearing-only tracking model and nonlinear filtering problem with different state dimensions show that the proposed QSIF has higher filtering accuracy and good numerical stability as compared with existing methods, and it can also solve nonlocal sampling problem effectively

Flight Mechanics/Estimation Theory Symposium

The conference emphasizes orbital position estimation and trajectory calculation methods that consider flight mechanical parameters

Nonlinear Bayesian Estimation via Solution of The Fokker-Planck Equation

A general approach to optimal nonlinear filtering can be described by a recursive Bayesian approach. The key step in this approach is to determine the probability density function of the state vector conditioned on available measurements. However, an optimal solution to the Bayesian filtering problem can only be obtained exactly for a small class of problems such as linear and Gaussian cases. Therefore, in practice, approximate solutions, such as the extended Kalman filter, have been used.An optimal nonlinear filtering in a recursive Bayesian approach is a two-step process which consists of the prediction and the update process. In the update process, the priori conditional state probability density function (PDF) from the prediction process is updated through Bayes' rule using measurements from sensors. The prediction of conditional state PDF can be made by solving the Fokker-Planck equation (FPE) that governs the time-evolution the conditional state PDF. However, it is extremely difficult to obtain an analytical solution of the Fokker-Planck equation with the exception of a few special cases. So far this estimation method has not been employed much in practice because of the high computational cost needed in solving the FPE numerically. In this dissertation, methods to improve the efficiency of the numerical method in solving the FPE are investigated to enhance the efficiency of the nonlinear filtering.Two finite difference methods, namely i) the explicit forward method and ii) the alternating direction implicit (ADI) method, are used to solve the FPE numerically. Although the explicit forward method is much simpler to implement, the ADI method is preferred for its low computational cost. To reduce the computational cost further, as the first contribution of the dissertation, a moving domain scheme is developed to reduce the domain of integration required for solving the Fokker-Planck equation numerically. Simulation results show that the accuracy of the estimation is improved as compared with the Extended Kalman Filter, and at the same time the computational cost is significantly lower with the proposed moving grid scheme than the case without it.Recently a nonlinear filtering algorithm using a direct quadrature method of moments was proposed, where the associated Fokker-Planck equation is solved efficiently via discrete quadrature based on moment constraints. For some problems, however, this approach showed the phenomenon similar to the "degeneracy'' in a particle filter, which is the concentration of weight on particular particles. The possible cause of the phenomenon is that only the weights are updated through the modified Bayes' rule. Therefore, in this dissertation, as another contribution, a new hybrid filter is proposed where the measurement update equations in the extended or the unscented Kalman filter are used along with the direct quadrature method of moments to solve the FPE. In this way the "degeneracy'' problem can be mitigated.Then, new proposed filtering methods are applied to several challenging problems such as i) the bearing-only tracking problem, ii) the relative orbit position estimation problem, and iii) the orbit determination problem to demonstrate their advantages. Simulation results indicate that the performance of the proposed filters are better than existing nonlinear filtering methods, such as the Extended Kalman Filter especially with less measurement updates

Information-rich path planning under general constraints using Rapidly-exploring Random Trees

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 99-104).This thesis introduces the Information-rich Rapidly-exploring Random Tree (IRRT), an extension of the RRT algorithm that embeds information collection as predicted using Fisher information matrices. The primary contribution of this trajectory generation algorithm is target-based information maximization in general (possibly heavily constrained) environments, with complex vehicle dynamic constraints and sensor limitations, including limited resolution and narrow field-of-view. Extensions of IRRT both for decentralized, multiagent missions and for information-rich planning with multimodal distributions are presented. IRRT is distinguished from previous solution strategies by its computational tractability and general constraint characterization. A progression of simulation results demonstrates that this implementation can generate complex target-tracking behaviors from a simple model of the trade-off between information gathering and goal arrival.by Daniel S. Levine.S.M

Nonlinear bayesian filtering with applications to estimation and navigation

In principle, general approaches to optimal nonlinear filtering can be described in a unified way from the recursive Bayesian approach. The central idea to this recur- sive Bayesian estimation is to determine the probability density function of the state vector of the nonlinear systems conditioned on the available measurements. However, the optimal exact solution to this Bayesian filtering problem is intractable since it requires an infinite dimensional process. For practical nonlinear filtering applications approximate solutions are required. Recently efficient and accurate approximate non- linear filters as alternatives to the extended Kalman filter are proposed for recursive nonlinear estimation of the states and parameters of dynamical systems. First, as sampling-based nonlinear filters, the sigma point filters, the unscented Kalman fil- ter and the divided difference filter are investigated. Secondly, a direct numerical nonlinear filter is introduced where the state conditional probability density is calcu- lated by applying fast numerical solvers to the Fokker-Planck equation in continuous- discrete system models. As simulation-based nonlinear filters, a universally effective algorithm, called the sequential Monte Carlo filter, that recursively utilizes a set of weighted samples to approximate the distributions of the state variables or param- eters, is investigated for dealing with nonlinear and non-Gaussian systems. Recentparticle filtering algorithms, which are developed independently in various engineer- ing fields, are investigated in a unified way. Furthermore, a new type of particle filter is proposed by integrating the divided difference filter with a particle filtering framework, leading to the divided difference particle filter. Sub-optimality of the ap- proximate nonlinear filters due to unknown system uncertainties can be compensated by using an adaptive filtering method that estimates both the state and system error statistics. For accurate identification of the time-varying parameters of dynamic sys- tems, new adaptive nonlinear filters that integrate the presented nonlinear filtering algorithms with noise estimation algorithms are derived. For qualitative and quantitative performance analysis among the proposed non- linear filters, systematic methods for measuring the nonlinearities, biasness, and op- timality of the proposed nonlinear filters are introduced. The proposed nonlinear optimal and sub-optimal filtering algorithms with applications to spacecraft orbit es- timation and autonomous navigation are investigated. Simulation results indicate that the advantages of the proposed nonlinear filters make these attractive alterna- tives to the extended Kalman filter

A framework for non-Gaussian signal modeling and estimation

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. [235]-240).by Shawn Matthew Verbout.Ph.D