Distributed Particle Filtering via Optimal Fusion of Gaussian Mixtures

Li, Jichuan; Nehorai, Arye

doi:10.1109/tsipn.2017.2694318

Cited by 29 publications

(18 citation statements)

References 30 publications

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“…The goal is to track x t using a network of agents. This problem has been studied in the context of distributed Kalman filtering [23], [42], state estimation [43]- [45], and particle filtering [24], [46], [47]. However, as opposed to Kalman filtering, we need not assume that the system noise v t is Gaussian.…”

Section: Numerical Experiment: State Estimation and Tracking Dynamentioning

confidence: 99%

Distributed Online Optimization in Dynamic Environments Using Mirror Descent

Shahrampour

Jadbabaie

2018

IEEE Trans. Automat. Contr.

265

209

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This work addresses decentralized online optimization in non-stationary environments. A network of agents aim to track the minimizer of a global time-varying convex function. The minimizer evolves according to a known dynamics corrupted by an unknown, unstructured noise. At each time, the global function can be cast as a sum of a finite number of local functions, each of which is assigned to one agent in the network. Moreover, the local functions become available to agents sequentially, and agents do not have a prior knowledge of the future cost functions. Therefore, agents must communicate with each other to build an online approximation of the global function. We propose a decentralized variation of the celebrated Mirror Descent, developed by Nemirovksi and Yudin. Using the notion of Bregman divergence in lieu of Euclidean distance for projection, Mirror Descent has been shown to be a powerful tool in large-scale optimization. Our algorithm builds on Mirror Descent, while ensuring that agents perform a consensus step to follow the global function and take into account the dynamics of the global minimizer. To measure the performance of the proposed online algorithm, we compare it to its offline counterpart, where the global functions are available a priori. The gap between the two is called dynamic regret. We establish a regret bound that scales inversely in the spectral gap of the network, and more notably it represents the deviation of minimizer sequence with respect to the given dynamics. We then show that our results subsume a number of results in distributed optimization. We demonstrate the application of our method to decentralized tracking of dynamic parameters and verify the results via numerical experiments.

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Section: Numerical Experiment: State Estimation and Tracking Dynamentioning

confidence: 99%

Distributed Online Optimization in Dynamic Environments Using Mirror Descent

Shahrampour

Jadbabaie

2018

IEEE Trans. Automat. Contr.

265

209

View full text Add to dashboard Cite

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“…Similar to [29], it can be concluded that the main computational complexity of the proposed distributed filtering algorithm executed on each sensor node is O(K(N + I)M Gn 2 ), where I denotes the number of learning iterations in the weighted expectation-maximization algorithm, and G is the average number of Gaussian components in the Gaussian mixture models.…”

Section: Step 8 Combinationmentioning

confidence: 76%

“…Moreover, it should be noticed from the combination rule (24) that the fusion of Gaussian mixture models with non-integer exponents is involved. In this paper, the weighted mixture importance sampling method [29] is adopted to realize such a fusion. The proposed distributed filtering scheme is subsequently outlined in Algorithm 2, where only the operations conducted by sensor node i are displayed.…”

Section: B Distributed Auxiliary Particle Filtering Under the Dynamic Event-triggered Mechanismmentioning

confidence: 99%

Distributed Auxiliary Particle Filtering With Diffusion Strategy for Target Tracking: A Dynamic Event-Triggered Approach

Song

Wang

et al. 2021

IEEE Trans. Signal Process.

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This paper investigates the particle filtering problem for a class of nonlinear/non-Gaussian systems under the dynamic event-triggered protocol. In order to avert frequent data transmission and reduce the communication overhead, a dynamic event-triggered transmission mechanism is adopted to decide whether the data should be transmitted or not. We first consider a scenario where all sensor nodes selectively transmit their newly obtained measurements to a central node, and a full likelihood function at the central node is derived by fusing the transmitted measurements and the information embodied in the non-triggered measurements. Based on the derived full likelihood function, a centralized auxiliary particle filtering algorithm is proposed to select those particles that are more likely to match the current measurement information. Next, based on the diffusion strategy, a distributed auxiliary particle filtering algorithm is further developed, where the local measurements and the local posteriors (approximated by the Gaussian mixture models) are exchanged among neighboring nodes under the dynamic eventtriggered communication strategy. Finally, the effectiveness of the proposed filtering schemes is demonstrated via Monte Carlo simulations in a target tracking problem with received-signalstrength sensors.

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“…5] such as the PHD [38] factories into a cardinality distribution on the number of objects and a localization density conditioned on the cardinality. In this case, while the AA of a sum can be straightforwardly expressed as a cascaded sum of the fusing sums (after re-weighting them) that remains in the same form [42,43]te, the fractional order exponential power of a sum does not remain as a sum of the same form, and typically approximation must be resorted to; see, e.g., [64,19,31,65,66].…”

Section: Phd Averagingmentioning

confidence: 99%

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

et al. 2019

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Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing initials, respectively. In the context of target tracking, the two most common formats of data to be fused are random variables and probability density functions, namely v-fusion and f -fusion, respectively. In this work, we analyze and compare the second order statistics (including variance and mean square error) of AA and GA in terms of both v-fusion and f -fusion. The case of weighted Gaussian mixtures representing multitarget densities in the presence of false alarms and misdetection (whose weight sums are not necessarily unit) is also considered, the result of which appears significantly different from that for a single target. In addition to exact derivation, exemplifying analysis and illustrations are provided.

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Distributed Particle Filtering via Optimal Fusion of Gaussian Mixtures

Cited by 29 publications

References 30 publications

Distributed Online Optimization in Dynamic Environments Using Mirror Descent

Distributed Online Optimization in Dynamic Environments Using Mirror Descent

Distributed Auxiliary Particle Filtering With Diffusion Strategy for Target Tracking: A Dynamic Event-Triggered Approach

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

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