Sensor selection for optimal filtering of linear dynamical systems: Complexity and approximation

Zhang, Haotian; Ayoub, Raid; Sundaram, Shreyas

doi:10.1109/cdc.2015.7403001

Cited by 19 publications

(15 citation statements)

References 17 publications

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“…1) Supermodularity in Problem 1: We achieve the approximation performance of Algorithm 1, and the linear dependence of its time complexity on the planning horizon, by proving that our estimation metric is a supermodular function in the choice of the utilized sensors. This is important, since this is in contrast to the case of multi-step Kalman filtering for linear systems and measurements, where the corresponding estimation metric is neither supermodular nor submodular [20] [21]. Moreover, our submodularity result cannot be reduced to the batch estimation problems in [22], [23].…”

Section: Technical Contributionsmentioning

confidence: 99%

“…However, both of these papers focus on linear systems and measurements. The most relevant papers for Kalman filtering consider algorithms that use: myopic heuristics [12], tree pruning [13], convex optimization [14]- [17], quadratic programming [18], Monte Carlo methods [19], or submodular function maximization [20], [21]. However, these papers focus similarly on linear or nonlinear systems and measurements, and do not consider unknown dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Scheduling nonlinear sensors for stochastic process estimation

Tzoumas

Atanasov

Jadbabaie

et al. 2017

2017 American Control Conference (ACC)

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In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and mapping (SLAM). It is challenging since it involves stochastic systems whose evolution is largely unknown, sensors with nonlinear measurements, and limited operational resources that constrain the number of active sensors at each measurement step. We provide an algorithm applicable to general stochastic processes and nonlinear measurements whose time complexity is linear in the planning horizon and whose performance is a multiplicative factor 1/2 away from the optimal performance. This is notable because the algorithm offers a significant computational advantage over the polynomial-time algorithm that achieves the best approximation factor 1/e. In addition, for important classes of Gaussian processes and nonlinear measurements corrupted with Gaussian noise, our algorithm enjoys the same time complexity as even the state-of-the-art algorithms for linear systems and measurements. We achieve our results by proving two properties for the entropy of the batch state vector conditioned on the measurements: a) it is supermodular in the choice of the sensors; b) it has a sparsity pattern (involves block tri-diagonal matrices) that facilitates its evaluation at each sensor set. ⋆ The authors are with the

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Section: Technical Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scheduling nonlinear sensors for stochastic process estimation

Tzoumas

Atanasov

Jadbabaie

et al. 2017

2017 American Control Conference (ACC)

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“…And, (2) offline sensor selection (placement) where the objective is to select a best subset of sensors (locations) out of a candidate set of sensors (locations). Offline sensor selection is done at the network design time, such that a desired performance is met based on prior statistics, which do not depend on real-time measurements [6,8,10,16,17,18]. The focus of this paper is on the offline sensor selection.…”

Section: Introductionmentioning

confidence: 99%

Sensor placement and resource allocation for energy harvesting IoT networks

Bushnaq

Chaaban

Chepuri

et al. 2020

Digital Signal Processing

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The paper studies optimal sensor selection for source estimation in energy harvesting Internet of Things (IoT) networks. Specifically, the focus is on the selection of the sensor locations which minimizes the estimation error at a fusion center, and to optimally allocate power and bandwidth for each selected sensor subject to a prescribed spectral and energy budget. To do so, measurement accuracy, communication link quality, and the amount of energy harvested are all taken into account. The sensor selection is studied under both analog and digital transmission schemes from the selected sensors to the fusion center. In the digital transmission case, an information theoretic approach is used to model the transmission rate, observation quantization, and encoding. We numerically prove that with a sufficient system bandwidth, the digital system outperforms the analog system with a possibly different sensor selection.Two source models are studied in this paper: static source estimation for a vector of correlated sources and dynamic state estimation for a scalar source. The design problem of interest is a Boolean non convex optimization problem, which is solved by relaxing the Boolean constraints. We propose a randomized rounding algorithm which generalizes the existing algorithm. The proposed randomized rounding algorithm takes the joint sensor location, power and bandwidth selection into account to efficiently round the obtained relaxed solution.

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“…Amongst other related works, there have also been studies on a similar problem called optimal sensor selection, for which the objective is to select a relatively small subset of sensors to be put to use at each time step so as to minimize the estimation error. The optimal selection problem also faces the challenge of high computational complexity; indeed, it has been proved in [13] that the problem is NP-hard, which holds even if the system is stable. Various algorithms have also been proposed to deal with the computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Optimal capacity allocation for sampled networked systems

2017

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We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements.We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the average estimation error is minimized.We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.the same for all pair (i, j), for i = j, are made to simplify the notations of the paper, but are not necessary for the results to hold. The Brownian motions w i are pairwise independent and the ν i (kτ 0 ) are pairwise independent normal random variables. The w i and ν i are also assumed to be independent.We refer to the system described in (1) as subsystem S i . The samples y i (kτ 0 ), k ∈ N, are sent over a common channel to a network manager whose objective is to estimate the states x i of the subsystems S i , for all i = 1, . . . , N , from these samples. The network manager needs to decide the schedule with which it receives the samples in order to minimize the estimation error. Note that since the systems are coupled, the knowledge of y i can help with the estimation of x j , for i = j.

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Sensor selection for optimal filtering of linear dynamical systems: Complexity and approximation

Cited by 19 publications

References 17 publications

Scheduling nonlinear sensors for stochastic process estimation

Scheduling nonlinear sensors for stochastic process estimation

Sensor placement and resource allocation for energy harvesting IoT networks

Optimal capacity allocation for sampled networked systems

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