193 research outputs found
Tracking Target Signal Strengths on a Grid using Sparsity
Multi-target tracking is mainly challenged by the nonlinearity present in the
measurement equation, and the difficulty in fast and accurate data association.
To overcome these challenges, the present paper introduces a grid-based model
in which the state captures target signal strengths on a known spatial grid
(TSSG). This model leads to \emph{linear} state and measurement equations,
which bypass data association and can afford state estimation via
sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of
the novel model, two types of sparsity-cognizant TSSG-KF trackers are
developed: one effects sparsity through -norm regularization, and the
other invokes sparsity as an extra measurement. Iterative extended KF and
Gauss-Newton algorithms are developed for reduced-complexity tracking, along
with accurate error covariance updates for assessing performance of the
resultant sparsity-aware state estimators. Based on TSSG state estimates, more
informative target position and track estimates can be obtained in a follow-up
step, ensuring that track association and position estimation errors do not
propagate back into TSSG state estimates. The novel TSSG trackers do not
require knowing the number of targets or their signal strengths, and exhibit
considerably lower complexity than the benchmark hidden Markov model filter,
especially for a large number of targets. Numerical simulations demonstrate
that sparsity-cognizant trackers enjoy improved root mean-square error
performance at reduced complexity when compared to their sparsity-agnostic
counterparts.Comment: Submitted to IEEE Trans. on Signal Processin
Optimized Data Rate Allocation for Dynamic Sensor Fusion over Resource Constrained Communication Networks
This paper presents a new method to solve a dynamic sensor fusion problem. We
consider a large number of remote sensors which measure a common Gauss-Markov
process and encoders that transmit the measurements to a data fusion center
through the resource restricted communication network. The proposed approach
heuristically minimizes a weighted sum of communication costs subject to a
constraint on the state estimation error at the fusion center. The
communication costs are quantified as the expected bitrates from the sensors to
the fusion center. We show that the problem as formulated is a
difference-of-convex program and apply the convex-concave procedure (CCP) to
obtain a heuristic solution. We consider a 1D heat transfer model and 2D target
tracking by a drone swarm model for numerical studies. Through these
simulations, we observe that our proposed approach has a tendency to assign
zero data rate to unnecessary sensors indicating that our approach is sparsity
promoting, and an effective sensor selection heuristic
Near-Optimal Sensor Scheduling for Batch State Estimation: Complexity, Algorithms, and Limits
In this paper, we focus on batch state estimation for linear systems. This
problem is important in applications such as environmental field estimation,
robotic navigation, and target tracking. Its difficulty lies on that limited
operational resources among the sensors, e.g., shared communication bandwidth
or battery power, constrain the number of sensors that can be active at each
measurement step. As a result, sensor scheduling algorithms must be employed.
Notwithstanding, current sensor scheduling algorithms for batch state
estimation scale poorly with the system size and the time horizon. In addition,
current sensor scheduling algorithms for Kalman filtering, although they scale
better, provide no performance guarantees or approximation bounds for the
minimization of the batch state estimation error. In this paper, one of our
main contributions is to provide an algorithm that enjoys both the estimation
accuracy of the batch state scheduling algorithms and the low time complexity
of the Kalman filtering scheduling algorithms. In particular: 1) our algorithm
is near-optimal: it achieves a solution up to a multiplicative factor 1/2 from
the optimal solution, and this factor is close to the best approximation factor
1/e one can achieve in polynomial time for this problem; 2) our algorithm has
(polynomial) time complexity that is not only lower than that of the current
algorithms for batch state estimation; it is also lower than, or similar to,
that of the current algorithms for Kalman filtering. We achieve these results
by proving two properties for our batch state estimation error metric, which
quantifies the square error of the minimum variance linear estimator of the
batch state vector: a) it is supermodular in the choice of the sensors; b) it
has a sparsity pattern (it involves matrices that are block tri-diagonal) that
facilitates its evaluation at each sensor set.Comment: Correction of typos in proof
Resource Management for Distributed Estimation via Sparsity-Promoting Regularization
Recent advances in wireless communications and electronics have enabled the development of low-cost, low-power, multifunctional sensor nodes that are small in size and communicate untethered in a sensor network. These sensor nodes can sense, measure, and gather information from the environment and, based on some local processing, they transmit the sensed data to a fusion center that is responsible for making the global inference. Sensor networks are often tasked to perform parameter estimation; example applications include battlefield surveillance, medical monitoring, and navigation. However, under limited resources, such as limited communication bandwidth and sensor battery power, it is important to design an energy-efficient estimation architecture. The goal of this thesis is to provide a fundamental understanding and characterization of the optimal tradeoffs between estimation accuracy and resource usage in sensor networks.
In the thesis, two basic issues of resource management are studied, sensor selection/scheduling and sensor collaboration for distributed estimation, where the former refers to finding the best subset of sensors to activate for data acquisition in order to minimize the estimation error subject to a constraint on the number of activations, and the latter refers to seeking the optimal inter-sensor communication topology and energy allocation scheme for distributed estimation systems. Most research on resource management so far has been based on several key assumptions, a) independence of observation, b) strict resource constraints, and c) absence of inter-sensor communication, which lend analytical tractability to the problem but are often found lacking in practice. This thesis introduces novel techniques to relax these assumptions and provide new insights into addressing resource management problems.
The thesis analyzes how noise correlation affects solutions of sensor selection problems, and proposes both a convex relaxation approach and a greedy algorithm to find these solutions. Compared to the existing sensor selection approaches that are limited to the case of uncorrelated noise or weakly correlated noise, the methodology proposed in this thesis is valid for any arbitrary noise correlation regime. Moreover, this thesis shows a correspondence between active sensors and the nonzero columns of an estimator gain matrix. Based on this association, a sparsity-promoting optimization framework is established, where the desire to reduce the number of selected sensors is characterized by a sparsity-promoting penalty term in the objective function. Instead of placing a hard constraint on sensor activations, the promotion of sparsity leads to trade-offs between estimation performance and the number of selected sensors. To account for the individual power constraint of each sensor, a novel sparsity-promoting penalty function is presented to avoid scenarios in which the same sensors are successively selected. For solving the proposed optimization problem, we employ the alternating direction method of multipliers (ADMM), which allows the optimization problem to be decomposed into subproblems that can be solved analytically to obtain exact solutions.
The problem of sensor collaboration arises when inter-sensor communication is incorporated in sensor networks, where sensors are allowed to update their measurements by taking a linear combination of the measurements of those they interact with prior to transmission to a fusion center. In this thesis, a sparsity-aware optimization framework is presented for the joint design of optimal sensor collaboration and selection schemes, where the cost of sensor collaboration is associated with the number of nonzero entries of a collaboration matrix, and the cost of sensor selection is characterized by the number of nonzero rows of the collaboration matrix. It is shown that a) the presence of sensor collaboration smooths out the observation noise, thereby improving the quality of the signal and eventual estimation performance, and b) there exists a trade-off between sensor selection and sensor collaboration. This thesis further addresses the problem of sensor collaboration for the estimation of time-varying parameters in dynamic networks that involve, for example, time-varying observation gains and channel gains. Impact of parameter correlation and temporal dynamics of sensor networks on estimation performance is illustrated from both theoretical and practical points of view. Last but not least, optimal energy allocation and storage control polices are designed in sensor networks with energy-harvesting nodes. We show that the resulting optimization problem can be solved as a special nonconvex problem, where the only source of nonconvexity can be isolated to a constraint that contains the difference of convex functions. This specific problem structure enables the use of a convex-concave procedure to obtain a near-optimal solution
Distributed Estimation and Performance Limits in Resource-constrained Wireless Sensor Networks
Distributed inference arising in sensor networks has been an interesting and promising discipline in recent years. The goal of this dissertation is to investigate several issues related to distributed inference in sensor networks, emphasizing parameter estimation and target tracking with resource-constrainted networks.
To reduce the transmissions between sensors and the fusion center thereby saving bandwidth and energy consumption in sensor networks, a novel methodology, where each local sensor performs a censoring procedure based on the normalized innovation square (NIS), is proposed for the sequential Bayesian estimation problem in this dissertation. In this methodology, each sensor sends only the informative measurements and the fusion center fuses both missing measurements and received ones to yield more accurate inference. The new methodology is derived for both linear and nonlinear dynamic systems, and both scalar and vector measurements. The relationship between the censoring rule based on NIS and the one based on Kullback-Leibler (KL) divergence is investigated.
A probabilistic transmission model over multiple access channels (MACs) is investigated. With this model, a relationship between the sensor management and compressive sensing problems is established, based on which, the sensor management problem becomes a constrained optimization problem, where the goal is to determine the optimal values of probabilities that each sensor should transmit with such that the determinant of the Fisher information matrix (FIM) at any given time step is maximized. The performance of the proposed compressive sensing based sensor management methodology in terms of accuracy of inference is investigated.
For the Bayesian parameter estimation problem, a framework is proposed where quantized observations from local sensors are not directly fused at the fusion center, instead, an additive noise is injected independently to each quantized observation. The injected noise performs as a low-pass filter in the characteristic function (CF) domain, and therefore, is capable of recoverving the original analog data if certain conditions are satisfied. The optimal estimator based on the new framework is derived, so is the performance bound in terms of Fisher information. Moreover, a sub-optimal estimator, namely, linear minimum mean square error estimator (LMMSE) is derived, due to the fact that the proposed framework theoretically justifies the additive noise modeling of the quantization process. The bit allocation problem based on the framework is also investigated.
A source localization problem in a large-scale sensor network is explored. The maximum-likelihood (ML) estimator based on the quantized data from local sensors and its performance bound in terms of Cram\\u27{e}r-Rao lower bound (CRLB) are derived. Since the number of sensors is large, the law of large numbers (LLN) is utilized to obtain a closed-form version of the performance bound, which clearly shows the dependence of the bound on the sensor density, the Fisher information is a linearly increasing function of the sensor density. Error incurred by the LLN approximation is also theoretically analyzed. Furthermore, the design of sub-optimal local sensor quantizers based on the closed-form solution is proposed.
The problem of on-line performance evaluation for state estimation of a moving target is studied. In particular, a compact and efficient recursive conditional Posterior Cram\\u27{e}r-Rao lower bound (PCRLB) is proposed. This bound provides theoretical justification for a heuristic one proposed by other researchers in this area. Theoretical complexity analysis is provided to show the efficiency of the proposed bound, compared to the existing bound
Kernel-based Inference of Functions over Graphs
The study of networks has witnessed an explosive growth over the past decades
with several ground-breaking methods introduced. A particularly interesting --
and prevalent in several fields of study -- problem is that of inferring a
function defined over the nodes of a network. This work presents a versatile
kernel-based framework for tackling this inference problem that naturally
subsumes and generalizes the reconstruction approaches put forth recently by
the signal processing on graphs community. Both the static and the dynamic
settings are considered along with effective modeling approaches for addressing
real-world problems. The herein analytical discussion is complemented by a set
of numerical examples, which showcase the effectiveness of the presented
techniques, as well as their merits related to state-of-the-art methods.Comment: To be published as a chapter in `Adaptive Learning Methods for
Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C.
Principe (2018). This chapter surveys recent work on kernel-based inference
of functions over graphs including arXiv:1612.03615 and arXiv:1605.07174 and
arXiv:1711.0930
Range-only SLAM schemes exploiting robot-sensor network cooperation
Simultaneous localization and mapping (SLAM) is a key problem in robotics. A robot with no previous knowledge of the environment builds a map of this environment and localizes itself in that map. Range-only SLAM is a particularization of the SLAM problem which only uses the information provided by range sensors. This PhD Thesis describes the design, integration, evaluation and validation of a set of schemes for accurate and e_cient range-only simultaneous localization and mapping exploiting the cooperation between robots and sensor networks. This PhD Thesis proposes a general architecture for range-only simultaneous localization and mapping (RO-SLAM) with cooperation between robots and sensor networks. The adopted architecture has two main characteristics. First, it exploits the sensing, computational and communication capabilities of sensor network nodes. Both, the robot and the beacons actively participate in the execution of the RO-SLAM _lter. Second, it integrates not only robot-beacon measurements but also range measurements between two di_erent beacons, the so-called inter-beacon measurements. Most reported RO-SLAM methods are executed in a centralized manner in the robot. In these methods all tasks in RO-SLAM are executed in the robot, including measurement gathering, integration of measurements in RO-SLAM and the Prediction stage. These fully centralized RO-SLAM methods require high computational burden in the robot and have very poor scalability. This PhD Thesis proposes three di_erent schemes that works under the aforementioned architecture. These schemes exploit the advantages of cooperation between robots and sensor networks and intend to minimize the drawbacks of this cooperation. The _rst scheme proposed in this PhD Thesis is a RO-SLAM scheme with dynamically con_gurable measurement gathering. Integrating inter-beacon measurements in RO-SLAM signi_cantly improves map estimation but involves high consumption of resources, such as the energy required to gather and transmit measurements, the bandwidth required by the measurement collection protocol and the computational burden necessary to integrate the larger number of measurements. The objective of this scheme is to reduce the increment in resource consumption resulting from the integration of inter-beacon measurements by adopting a centralized mechanism running in the robot that adapts measurement gathering. The second scheme of this PhD Thesis consists in a distributed RO-SLAM scheme based on the Sparse Extended Information Filter (SEIF). This scheme reduces the increment in resource consumption resulting from the integration of inter-beacon measurements by adopting a distributed SLAM _lter in which each beacon is responsible for gathering its measurements to the robot and to other beacons and computing the SLAM Update stage in order to integrate its measurements in SLAM. Moreover, it inherits the scalability of the SEIF. The third scheme of this PhD Thesis is a resource-constrained RO-SLAM scheme based on the distributed SEIF previously presented. This scheme includes the two mechanisms developed in the previous contributions {measurement gathering control and distribution of RO-SLAM Update stage between beacons{ in order to reduce the increment in resource consumption resulting from the integration of inter-beacon measurements. This scheme exploits robot-beacon cooperation to improve SLAM accuracy and e_ciency while meeting a given resource consumption bound. The resource consumption bound is expressed in terms of the maximum number of measurements that can be integrated in SLAM per iteration. The sensing channel capacity used, the beacon energy consumed or the computational capacity employed, among others, are proportional to the number of measurements that are gathered and integrated in SLAM. The performance of the proposed schemes have been analyzed and compared with each other and with existing works. The proposed schemes are validated in real experiments with aerial robots. This PhD Thesis proves that the cooperation between robots and sensor networks provides many advantages to solve the RO-SLAM problem. Resource consumption is an important constraint in sensor networks. The proposed architecture allows the exploitation of the cooperation advantages. On the other hand, the proposed schemes give solutions to the resource limitation without degrading performance
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