Bayesian Parameter Estimation
S. C. Kramer,H. W. Sorenson +1 more
- Iss: 24, pp 786-790
TLDR
Taking the Bayesian approach in solving the discrete-time parameter estimation problem has two major results: the unknown parameters are legitimately included as additional system states, and the computational objective becomes calculation of the entire posterior density instead of just its first few moments.Abstract:
Taking the Bayesian approach in solving the discrete-time parameter estimation problem has two major results: the unknown parameters are legitimately included as additional system states, and the computational objective becomes calculation of the entire posterior density instead of just its first few moments. This viewpoint facilitates intuitive analysis, allowing increased qualitative understanding of the system behavior. With the actual posterior density in hand, the true optimal estimate for any given loss function may be calculated. While the computational burden may preclude on-line use, this provides a clearly justified baseline for comparison. These points are demonstrated by analyzing a scalar problem with a single unknown, and by comparing an established point estimator's performance to the true optimal estimate.read more
Citations
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Recursive Bayesian Estimation : Navigation and Tracking Applications
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Collision Avoidance Theory : with Application to Automotive Collision Mitigation
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Review Mathematical modelling of the composting process: A review
TL;DR: The most successful models in predicting temperature profiles were those which incorporated either empirical kinetic expressions for volatile solids degradation or CO2 production, or which utilised a first-order model for volatile Solids degradation, with empirical corrections for temperature and moisture variations.
Journal ArticleDOI
Terrain navigation using Bayesian statistics
TL;DR: The point-mass filter (PMF) described in this work yields an approximate Bayesian solution that is well suited for the unstructured nonlinear estimation problem in terrain navigation and solves the recursive estimation problem for all the types of terrain covered in the test.
Sequential Monte Carlo Filters and Integrated Navigation
TL;DR: This thesis considers recursive Bayesian estimation in general, and sequential Monte Carlo filters in particular, applied to integrated navigation, and shows that by applying the efficent particle filter based on Rao-Blackwellization the authors obtain nearly optimal accuracy for a tractable amount of computational load.
References
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Journal ArticleDOI
Nonlinear Bayesian estimation using Gaussian sum approximations
D. Alspach,H. Sorenson +1 more
TL;DR: In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem.
Journal ArticleDOI
Digital synthesis of non-linear filters
Richard S. Bucy,Kenneth D. Senne +1 more
TL;DR: In this article, a point mass representation on a floating rectangular grid of indices is proposed for density storage and a simple and effective convolution summation involving an ellipsoid tracking technique to determine the important points to include in the summation is developed.
Journal ArticleDOI
Bayesian system identification
TL;DR: The paper shows that on this Bayesian basis it is possible to build a consistent theory of system identification and considers problems of one-shot and real-time identification, estimation and prediction in closed control loop, redundant and unidentifiable parameters, time-varying parameters and adaptivity.
Journal ArticleDOI
Recursive Bayesian estimation using piece-wise constant approximations
S. C. Kramer,H. W. Sorenson +1 more
TL;DR: The numerical solution proposed here is obtained by modifying the recursion and using a simple piece-wise constant approximation to the density functions, yielding a bound on the maximum error growth, and a characterization of the situations with potential for large errors.