Distributed Adaptive Spatial Filtering in Resource-constrained Sensor Networks

Wireless sensor networks consist in a collection of battery-powered sensors able to gather, process and send data. They are typically used to monitor various phenomenons, in a plethora of fields, from environmental studies to smart logistics. Their wireless connectivity and relatively small size allow them to be deployed practically anywhere, even underwater or embedded in everyday clothing, and possibly capture data over a large area for extended periods of time. Their usefulness is therefore tied to their ability to work autonomously, with as little human intervention as possible. This functional requirement directly translates into two design constraints: (i) bandwidth and on-board compute must be used sparingly, in order to extend battery-life as much as possible, and (ii) the system must be resilient to node failures and changing environment. Due to their limited computing capabilities, data processing is usually performed by a so-called “fusion center” outside of the network. This therefore requires all the nodes within the network to send and route their data to this fusion center, putting strain on both the batteries and wireless links of the sensor nodes. Furthermore, this data centralization approach harms the network’s resilience as, if the fusion center malfunctions, the sensor network loses its ability to process its collected data. Several distributed signal processing algorithms have been developed to get around those drawbacks, by favoring local on-board data processing over data transmission. These algorithms typically work by having the nodes collaborate to solve a signal processing task “in-network”, and only forward the result, usually of significantly smaller size than the raw sensor signals, to the outside world. In particular, this approach has been successfully applied to the computation of “spatial filters”, consisting in lower-dimensional linear combinations of the aggregated raw sensor signals, that are optimal in some sense. To meet the aforementioned design requirements, a particular family of distributed signal estimation algorithms, which includes as notable examples the distributed adaptive node-specific signal estimation algorithm (DANSE) and the distributed adaptive covariance matrix eigenvectors estimation algorithm (DACMEE has introduced collaborative filter computation procedures that are energy-efficient, scalable, and adaptive. This last characteristic and the collaborative nature of the procedures allow the network to operate even in the case of node or sensor failures, and to adapt to a possibly changing environment, i.e., it can handle non-stationary signals effectively. Thanks to common algorithmic themes, this family of algorithms, which we call the “distributed signal fusion” (DSF) family of algorithms, has recently been summarized by the distributed adaptive signal fusion (DASF) framework, of which each of the DSF algorithms is a particular instance. Despite their benefits, these algorithms are limited in the scope of problems they can handle. Indeed, each DSF algorithm is problem-specific, and the DASF framework requires some technical assumptions to hold to ensure convergence and correctness, which precludes some spatial filters to be covered. In this thesis, we propose several algorithms and algorithmic extensions that improve the energy-efficiency of the procedures introduced by the DSF and DASF algorithms. Noting that nodes observing uncorrelated signals do not gain from collaborating, and hence exchanging data, we first propose a DSF algorithm for the so-called MAXVAR problem, from which we derive an efficient procedure to evaluate the inter-node correlation structure, without the need to exchange the full raw signals to compute the network-wide correlation matrix. Secondly, we prove that the key algorithmic ideas underpinning the DSF algorithms, as formalized in the DASF framework, lead DASF-based algorithms to converge to optimal spatial filters, when applied to smooth and well-posed spatial filtering problems. Then, we extend the original scope of DASF to non-smooth spatial filtering problems, which notably allows the use of sparsity-inducing regularizers in the mathematical description of the spatial filters, opening the door to a network pruning that can be performed alongside the signal processing task, rather than as an ad-hoc step. Finally, we replace the ideal exact solver assumed by DASF by a family of iterative inexact finite-time solvers, resulting in further energy savings, and relaxed computational requirements. In addition, this last extension allows DASF to produce more stable filters and to function under significantly relaxed assumptions. In particular, it is shown to converge even if the optimization problem associated with the target filter has a solution set that is discontinuous relative to the input signals. Each of our contributions is supported by numerical simulations and extensive theoretical guarantees.