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96
ℓ1 Trend Filtering
, 2007
"... The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on HodrickPrescott (HP) filtering, a widely used method for trend estimation. The proposed ℓ1 trend filtering method substitutes a sum of absolute values (i.e., ..."
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Cited by 51 (7 self)
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The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on HodrickPrescott (HP) filtering, a widely used method for trend estimation. The proposed ℓ1 trend filtering method substitutes a sum of absolute values (i.e., an ℓ1norm) for the sum of squares used in HP filtering to penalize variations in the estimated trend. The ℓ1 trend filtering method produces trend estimates that are piecewise linear, and therefore is well suited to analyzing time series with an underlying piecewise linear trend. The kinks, knots, or changes in slope, of the estimated trend can be interpreted as abrupt changes or events in the underlying dynamics of the time series. Using specialized interiorpoint methods, ℓ1 trend filtering can be carried out with not much more effort than HP filtering; in particular, the number of arithmetic operations required grows linearly with the number of data points. We describe the method and some of its basic properties, and give some illustrative examples. We show how the method is related to ℓ1 regularization based methods in sparse signal recovery and feature selection, and list some extensions of the basic method.
Algorithms for leader selection in large dynamical networks: Noisefree leaders
 in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference
, 2011
"... Abstract — We examine the leader selection problem in multiagent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize th ..."
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Cited by 22 (8 self)
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Abstract — We examine the leader selection problem in multiagent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize the total variance of the stochastically forced network. Combinatorial nature of this optimal control problem makes computation of the global minimum difficult. We propose a convex relaxation to obtain a lower bound on the global optimal value, and use simple but efficient greedy algorithms to obtain an upper bound. Furthermore, we employ the alternating direction method of multipliers to search for a local minimum. Two examples are provided to illustrate the effectiveness of the developed methods. Index Terms — Alternating direction method of multipliers, consensus, convex optimization/relaxation, greedy algorithm, leader selection, performance bounds, variance amplification. I.
Energy efficient state estimation with wireless sensors through the use of predictive power control and coding
 IEEE Trans. Signal Processing
"... Abstract—We study state estimation via wireless sensors over fading channels. Packet loss probabilities depend upon timevarying channel gains, packet lengths and transmission power levels of the sensors. Measurements are coded into packets by using either independent coding or distributed zeroerro ..."
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Cited by 20 (10 self)
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Abstract—We study state estimation via wireless sensors over fading channels. Packet loss probabilities depend upon timevarying channel gains, packet lengths and transmission power levels of the sensors. Measurements are coded into packets by using either independent coding or distributed zeroerror coding. At the gateway, a timevarying Kalman filter uses the received packets to provide the state estimates. To trade sensor energy expenditure for state estimation accuracy, we develop a predictive control algorithm which, in an online fashion, determines the transmission power levels and codebooks to be used by the sensors. To further conserve sensor energy, the controller is located at the gateway and sends coarsely quantized power increment commands, only whenever deemed necessary. Simulations based on real channel measurements illustrate that the proposed method gives excellent results. Index Terms—Packet loss, power control, scheduling, source coding, state estimation, wireless sensors. I.
Sensor management: Past, present, and future
, 2011
"... Sensor systems typically operate under resource constraints that prevent the simultaneous use of all resources all of the time. Sensor management becomes relevant when the sensing system has the capability of actively managing these resources; i.e., changing its operating configuration during dep ..."
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Cited by 18 (1 self)
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Sensor systems typically operate under resource constraints that prevent the simultaneous use of all resources all of the time. Sensor management becomes relevant when the sensing system has the capability of actively managing these resources; i.e., changing its operating configuration during deployment in reaction to previous measurements. Examples of systems in which sensor management is currently used or is likely to be used in the near future include autonomous robots, surveillance and reconnaissance networks, and waveformagile radars. This paper provides an overview of the theory, algorithms, and applications of sensor management as it has developed over the past decades and as it stands today.
On efficient sensor scheduling for linear dynamical systems,”
 Automatica,
, 2012
"... Abstract Consider a set of sensors estimating the state of a process in which only one of these sensors can operate at each timestep due to constraints on the overall system. The problem addressed here is to choose which sensor should operate at each timestep to minimize a weighted function of th ..."
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Cited by 13 (2 self)
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Abstract Consider a set of sensors estimating the state of a process in which only one of these sensors can operate at each timestep due to constraints on the overall system. The problem addressed here is to choose which sensor should operate at each timestep to minimize a weighted function of the error covariances of the state estimations. This work investigates the development of tractable algorithms to solve for the optimal and suboptimal sensor schedules. A condition on the nonoptimality of an initialization of the schedule is developed. Using this condition, both an optimal and a suboptimal algorithm are devised to prune the search tree of all possible sensor schedules. The suboptimal algorithm trades off the quality of the solution and the complexity of the problem through a tuning parameter. The performance of the suboptimal algorithm is also investigated and an analytical error bound is provided. Numerical simulations are conducted to demonstrate the performance of the proposed algorithms, and the application of the algorithms in active robotic mapping is explored.
Optimal placement of phasor measurement units via convex relaxation
 IEEE Trans. Power Syst
, 2012
"... Abstract—Instrumenting power networks with phasor measurement units (PMUs) facilitates several tasks including optimum power flow, system control, contingency analysis, visualization, and integration of renewable resources, thus enabling situational awareness—one of the key steps toward realizing th ..."
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Cited by 12 (2 self)
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Abstract—Instrumenting power networks with phasor measurement units (PMUs) facilitates several tasks including optimum power flow, system control, contingency analysis, visualization, and integration of renewable resources, thus enabling situational awareness—one of the key steps toward realizing the smart grid vision. The installation cost of PMUs currently prohibits their deployment on every bus, which in turn motivates their strategic placement across the power grid. As state estimation is at the core of grid monitoring, PMU deployment is optimized here based on estimationtheoretic criteria. Considering both voltage and incident current readings per PMUinstrumented bus and incorporating conventionally derived state estimates under the Bayesian framework, PMU placementisformulatedasanoptimal experimental design task. To bypass the combinatorial search involved, a convex relaxation is developed to obtain solutions with numerical optimality guarantees. In the tests performed on standard IEEE 14, 30, and 118bus benchmarks, the proposed relaxation approaches and oftentimes attains the optimum PMU placement. Index Terms—Gradient projection method, maximum aposteriori estimation, optimal experimental design, phasor measurement units, SCADA measurements, semidefinite programming. I.
Algorithms for leader selection in stochastically forced consensus networks
 IEEE Trans. Automat. Control
"... Abstract—We are interested in assigning a prespecified number of nodes as leaders in order to minimize the meansquare deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networ ..."
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Cited by 12 (3 self)
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Abstract—We are interested in assigning a prespecified number of nodes as leaders in order to minimize the meansquare deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (which indicate whether a node is a leader) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algorithm wellsuited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms. Index Terms—Alternating direction method of multipliers (ADMMs), consensus networks, convex optimization, convex relaxations, greedy algorithm, leader selection, performance bounds, semidefinite programming (SDP), sensor selection, variance amplification. I.
Sparsitypromoting sensor selection for nonlinear measurement models
 IEEE Trans. Signal Process. (Submitted
, 2013
"... Abstract—The problem of choosing the best subset of sensors that guarantees a certain estimation performance is referred to as sensor selection. In this paper, we focus on observations that are related to a general nonlinear model. The proposed framework is valid as long as the observations are ind ..."
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Cited by 12 (9 self)
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Abstract—The problem of choosing the best subset of sensors that guarantees a certain estimation performance is referred to as sensor selection. In this paper, we focus on observations that are related to a general nonlinear model. The proposed framework is valid as long as the observations are independent, and its likelihood satisfies the regularity conditions. We use several functions of the Cramér–Rao bound (CRB) as a performance measure. We formulate the sensor selection problem as the design of a sparse vector, which in its original form is a nonconvex(quasi) norm optimization problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. The proposed solvers result in sparse sensing techniques. We also propose a projected subgradient algorithm that is attractive for largescale problems. The developed theory is applied to sensor placement for localization. Index Terms—Convex optimization, Cramér–Rao bound, nonlinear models, projected subgradient algorithm, sensor networks,
Relaxed Maximum a Posteriori Fault Identification
, 2007
"... We consider the problem of estimating a pattern of faults, represented as a binary vector, from a set of measurements. The measurements can be noise corrupted real values, or quantized versions of noise corrupted signals, including even 1bit (sign) measurements. Maximum a posteriori probability (MA ..."
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Cited by 11 (8 self)
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We consider the problem of estimating a pattern of faults, represented as a binary vector, from a set of measurements. The measurements can be noise corrupted real values, or quantized versions of noise corrupted signals, including even 1bit (sign) measurements. Maximum a posteriori probability (MAP) estimation of the fault pattern leads to a difficult combinatorial optimization problem, so we propose a variation in which an approximate maximum a posteriori probability estimate is found instead, by solving a convex relaxation of the original problem, followed by rounding and simple local optimization. Our method is extremely efficient, and scales to very large problems, involving thousands (or more) possible faults and measurements. Using synthetic examples, we show that the method performs extremely well, both in identifying the true fault pattern, and in identifying an ambiguity group, i.e., a set of alternate fault patterns that explain the observed measurements almost as well as our estimate. 1
Randomized Sensor Selection in Sequential Hypothesis Testing
, 2009
"... We consider the problem of sensor selection for timeoptimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequential hypothesis test. ..."
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Cited by 11 (7 self)
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We consider the problem of sensor selection for timeoptimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequential hypothesis test. We consider the class of sequential tests which are easy to implement, asymptotically optimal, and computationally amenable. For three distinct performance metrics, we show that, for a generic set of sensors and binary hypothesis, the fusion center needs to consider at most two sensors. We also show that for the case of multiple hypothesis, the optimal policy needs at most as many sensors to be observed as the number of underlying hypotheses.