A Bayesian approach to problems in stochastic estimation and control

Ho, Yu-Chi; Lee, R.

doi:10.1109/tac.1964.1105763

Cited by 522 publications

(236 citation statements)

References 1 publication

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“…The Gaussian assumption allows the posterior distribution to be completely parameterized by its mean and covariance. If the model operator f (·) and measurement operator h(·) are known linear functions and the process noise, measurement noise and prior density are drawn from known Gaussian distributions then the posterior distribution p(x k |{y 1 , .., y k }) can be proved to be Gaussian [14].…”

Section: Kalman Filtermentioning

confidence: 99%

Distributed ensemble Kalman filtering

Shahid

Üstebay

Coates

2014

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Distributed estimation in a wireless sensor network has many advantages. It eliminates the need of the centralized knowledge of the measurement model parameters and does not have a single point of failure. Also, any sensor node can be queried to retrieve the state estimate. Furthermore, for high dimensional measurements, local processing of information also results in a significant reduction in the communication overhead.The existing distributed Kalman filtering schemes have good computational and communication efficiency, but do not work well for non-linear and non-Gaussian problems. On the other hand, the distributed particle filtering schemes handle the non-linearities well, but have a much higher computational and communication cost.In this thesis, we propose novel distributed filtering schemes based on the ensemble Kalman filter (EnKF). We consider three forms of the EnKF and express their update equations in an alternative information form. This allows us to use the randomized gossip algorithm to reach consensus on the sufficient statistics and perform local updates. The simulation results show that all three forms of the EnKF have a considerably lower computational cost compared to the particle filters. The results suggest that the proposed distributed schemes outperform the existing state-of-the-art distributed filtering schemes in two scenarios, a) linear measurement model with non-linear state dynamics, and b) high dimensional measurements (model parameters known everywhere in the network) with nonlinear measurement model and state dynamics. In both of these scenarios, the proposed schemes achieve an estimation accuracy comparable to the existing state-of-the-art schemes while significantly reducing the communication cost.ii Résumé L'estimation distribuée dans un réseau de capteurs sans fil possède plusieurs avantages. Ellé elimine le besoin d'une connaissance centralisée des paramtres du modèle de mesure et n'a pas un point de défaillance unique. Aussi, n'importe quel agent-capteur peut-être consulté pour obtenir une approximation de l'état général. De plus, pour des mesures de hautes dimensions, le calcul local d'informations résulte en une réduction significative des coûts de communication.Les implémentations courantes du filtre de Kalman sont efficaces sur les plans de la charge de calcul et de la communication mais ne le sont pas pour les problmes non-linéaires et non-gaussiens. D'un autre côté, les techniques distribuées de filtrage particulaire gèrent avec succès les cas non-linéaires mais sont coûteuses sur les plans de la charge de calcul et de la communication.Dans cette thèse, nous proposons des techniques de filtrage distribué basées sur le filtre de Kalman d'ensemble (FKEn). Nous considérons trois formes du FKEn et exprimons leurséquations de changement sous une forme alternative. Cela nous permet d'utiliser un algorithme de gossip aléatoire afin d'atteindre un consensus sur les statistiques suffisantes et calculer les changements locaux. Les résultats des simulations montrent que ...

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Section: Kalman Filtermentioning

confidence: 99%

Distributed ensemble Kalman filtering

Shahid

Üstebay

Coates

2014

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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“…. , y t } has the relation by applying the Bayesian rule [4] as follows: Also from the relation in Eq. (3), we have…”

Section: Pdfs Of Predictor and Filtermentioning

confidence: 99%

GNSS Positioning Algorithms by Gaussian Sum Filtering Methods

Kubo

Munetomo

Matsunaga

et al. 2011

Stochastic Systems Theory and its Applications (SSS)

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In this paper, we derive a filtering algorithm for a discrete time system with Gaussian sum distributed measurement noise by extending and modifying the Gaussian sum filter proposed by Alspach and Sorenson[1], and its applications to satellite positioning and navigation systems are proposed. Also simulation results of the proposed Gaussian sum filter for simple first order Markov process are shown.

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“…In particular, letx n|n E{xn|z1:n} (the MMSE estimate of xn from z1:n), C n|n cov{xn|z1:n},x n|n−1 E{xn|z1:n−1}, and C n|n−1 cov{xn|z1:n−1}. Then, it is well known [11] that the time recursion (5), (6) reduces to the Kalman filter (KF) recursion, which consists of the prediction step (cf. (5))…”

Section: Time-space-sequential Distributed Kalman Filtermentioning

confidence: 99%

Time-space-sequential algorithms for distributed Bayesian state estimation in serial sensor networks

Hlinka¹,

Hlawatsch²

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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We consider distributed estimation of a time-dependent, random state vector based on a generally nonlinear/non-Gaussian state-space model. The current state is sensed by a serial sensor network without a fusion center. We present an optimal distributed Bayesian estimation algorithm that is sequential both in time and in space (i.e., across sensors) and requires only local communication between neighboring sensors. For the linear/Gaussian case, the algorithm reduces to a time-space-sequential, distributed form of the Kalman filter. We also demonstrate the application of our state estimator to a target tracking problem, using a dynamically defined "local sensor chain" around the current target position.

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A Bayesian approach to problems in stochastic estimation and control

Cited by 522 publications

References 1 publication

Distributed ensemble Kalman filtering

Distributed ensemble Kalman filtering

GNSS Positioning Algorithms by Gaussian Sum Filtering Methods

Time-space-sequential algorithms for distributed Bayesian state estimation in serial sensor networks

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