Nonlinear Bayesian estimation using Gaussian sum approximations

By D. Alspach, H. Sorenson. 1972

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Citations in the corpus

Recasting Gradient-Based Meta-Learning as Hierarchical Bayes (2018, methodology): “This could be solved by using a ﬁnite mixture of Gaussians, which can approximate many density functions arbitrarily well (Sorenson & Alspach, 1971; Alspach & Sorenson, 1972).”
Gaussian Sum Filters for Space Surveillance: Theory and Simulations (2011, methodology): “(19) inL(1), the norm of which the theory of Gaussian sums is based [4].”
High-degree cubature Kalman filter (2013, methodology): “…be used to assist particle filters to achieve higher sampling efficiency (Van der Merwe, de Freitas, Doucet, & Wan, 2000) and be combined with a Gaussian sum model to solve non-Gaussian estimation problems based on the Gaussian sum approximation (Alspach & Sorenson, 1972).”
A Tutorial on Bernoulli Filters: Theory, Implementation and Applications (2013, methodology): “The Bernoulli Gaussian sum filter (GSF) implementation [18] follows as a straightforward extension of the standard Gaussian sum filter [1], [2], [6], [62].”
Issues, progress and new results in robust adaptive control (2006, methodology): “We also remark that a similar adaptive estimation architecture, the so-called \Sum of Gaussians" method, utilizing a bank of extended Kalman fllters, was used for nonlinear flltering problems [57, 58, 59 ].”
Critical Evaluation of Extended Kalman Filtering and Moving-Horizon Estimation (2005, methodology): “Gaussian sum approximations 2 offer one method for addressing the formation of multiple modes in the a posteriori distribution for unconstrained systems.”
Kalman filters for non-linear systems: a comparison of performance (2004, unknown): “, higher order filters, [7], [8], [9] and Gaussian sum filters, [16], [17].”
Visual-inertial navigation, mapping and localization: A scalable real-time causal approach (2011, background): “These requirements admit a variety of estimation techniques, including sum-of-Gaussian filters (Alspach and Sorenson 1972), numerical integration, projection filters (Brigo et al. 1998), unscented filters (Julier and Uhlmann 1997), particle filters and extended Kalman filters (Jazwinski 1970).”
Multi-modal estimation with kernel embeddings for learning motion models (2013, background): “Parzen density and mixture model filters tile basis functions such as Gaussians or sawteeth in order to represent distributions [10], [11], but are limited to linear models and suffer from poor dimensional scaling in practice.”