Topic
State vector
About: State vector is a research topic. Over the lifetime, 5479 publications have been published within this topic receiving 103755 citations.
Papers published on a yearly basis
Papers
More filters
10 Apr 2007
TL;DR: The primary contribution of this work is the derivation of a measurement model that is able to express the geometric constraints that arise when a static feature is observed from multiple camera poses, and is optimal, up to linearization errors.
Abstract: In this paper, we present an extended Kalman filter (EKF)-based algorithm for real-time vision-aided inertial navigation. The primary contribution of this work is the derivation of a measurement model that is able to express the geometric constraints that arise when a static feature is observed from multiple camera poses. This measurement model does not require including the 3D feature position in the state vector of the EKF and is optimal, up to linearization errors. The vision-aided inertial navigation algorithm we propose has computational complexity only linear in the number of features, and is capable of high-precision pose estimation in large-scale real-world environments. The performance of the algorithm is demonstrated in extensive experimental results, involving a camera/IMU system localizing within an urban area.
1,435 citations
TL;DR: A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality and is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems.
Abstract: A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.
1,333 citations
TL;DR: In this paper, the authors derived a second-order approximation to the solution of a general class of discretetime rational expectations models, and showed that the coe1cients on the terms linear and quadratic in the state vector are independent of the volatility of the exogenous shocks.
998 citations
TL;DR: In this article, the optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed and an algorithm for computing FAST is presented.
Abstract: The optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed. The problem is posed with the additional constraint that the control vector u(t) is a linear time-invariant function of the output vector y(t) (u(t) = -Fy(t)) rather than of the state vector x(t) . The performance criterion is then averaged, and algebraic necessary conditions for a minimizing F\ast are found. In addition, an algorithm for computing F\ast is presented.
906 citations
TL;DR: A subclass of dynamic linear models with unknown hyperparameters called d-inverse-gamma models is defined and it is proved that the regularity conditions for convergence hold.
Abstract: We define a subclass of dynamic linear models with unknown hyperparameters called d-inverse-gamma models. We then approximate the marginal p.d.f.s of the hyperparameter and the state vector by the data augmentation algorithm of Tanner/Wong. We prove that the regularity conditions for convergence hold. A sampling based scheme for practical implementation is discussed. Finally, we illustrate how to obtain an iterative importance sampling estimate of the model likelihood. (author's abstract)
884 citations