Solutions to Periodic Sensor Scheduling Problems for Formation Flying Missions in Deep Space

We consider the problem of finding optimal time-periodic sensor schedules for estimating the state of discrete-time dynamical systems. We assume that multiple sensors have been deployed and that the sensors are subject to resource constraints, which limits the number of times each can be activated over one period of the periodic schedule. We seek an algorithm that strikes a balance between estimation accuracy and total sensor activations over one period. We make a correspondence between active sensors and the nonzero columns of estimator gain. We formulate an optimization problem in which we minimize the trace of the error covariance with respect to the estimator gain while simultaneously penalizing the number of nonzero columns of the estimator gain. This optimization problem is combinatorial in nature, and we employ the alternating direction method of multipliers (ADMM) to find its locally optimal solutions. Numerical results and comparisons with other sensor scheduling algorithms in the literature are provided to illustrate the effectiveness of our proposed method. Index TermsDynamical systems, alternating direction method of multipliers, state estimation, sensor networks, sensor scheduling, sparsity.

Section: Periodicity Of Infinite Horizon Sensor Schedulingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Periodic Sensor Scheduling in Networks of Dynamical Systems

Liu

Fardad

Maşazade

et al. 2014

“…Instead of minimizing the estimation error, the trace of Fisher information (so-called T-optimality [32]) also has been used as a performance metric in problems of sensor selection [20], [33], [34]. According to [35,Lemma 1], the trace of Fisher information constitutes a lower bound to the trace of error covariance matrix given by J −1 w in (7).…”

Section: Sensor Selection By Maximizing Trace Of Fisher Informationmentioning

confidence: 99%

“…Motivated by (34) and the generalized information gain used in [20], we propose to minimize the lower bound of the objective function in (P1), which leads to the problem maximize…”

Section: Sensor Selection By Maximizing Trace Of Fisher Informationmentioning

confidence: 99%

Sensor Selection for Estimation with Correlated Measurement Noise

Liu

Chepuri

Fardad

et al. 2016

172

107

Abstract-In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime, and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

“…Compared to the finite-time horizon case, the problem of infinite-time horizon is much more difficult to handle [21]. Mcloughlin et al [22] relaxed the general infinite-time horizon sensor scheduling problem for state estimation in linear time-invariant systems. Under the relaxation, they converted the original problem to a mixed integer quadratic programming problem which can be easily solved.…”

Section: Introductionmentioning

confidence: 99%

Optimal Periodic Transmission Power Schedules for Remote Estimation of ARMA Processes

Quevedo

Lau

et al. 2013

We consider periodic sensor transmission power allocation with an average energy constraint. The sensor sends its Kalman filter-based state estimate to the remote estimator through an unreliable link. Dropout probabilities depend on the power level used. To encompass applications where the estimator needs to attend to multiple tasks, we allow for irregular sampling, following a periodic pattern. Using properties of an underlying Markov chain model, we derive an explicit expression for the estimation error covariance. The results are then used to study optimal sensor power scheduling which minimizes the average error covariance.