Greedy Selection for Heterogeneous Sensors

Simultaneous operation of all sensors in a large-scale sensor network is power-consuming and computationally expensive. Hence, it is desirable to select fewer sensors. A greedy algorithm is widely used for sensor selection in homogeneous networks with a theoretical worst-case performance of $\boldsymbol{(\mathbf{1-1}/\mathbf{e})\mathbf{\approx 63}}$% of the optimal performance when optimizing submodular metrics. For heterogeneous sensor networks (HSNs) comprising multiple sets of sensors, most of the existing sensor selection methods optimize the performance constrained by a budget on the total value of the selected sensors. However, in many applications, the number of sensors to select from each set is known apriori and solutions are not well-explored. For this problem, we propose a joint greedy heterogeneous sensor selection algorithm. Theoretically, we show that the worst-case performance of the proposed algorithm is bounded to $50$% of the optimum for submodular cost metrics. In the special case of HSNs with two sensor networks, the performance guarantee can be improved to $63$% when the number of sensors to select from one set is much smaller than the other. To validate our results experimentally, we propose a submodular metric based on the frame potential measure that considers both the correlation among the sensor measurements and their heterogeneity. We prove theoretical bounds for the mean squared error of the solution when this performance metric is used. We validate our results through simulation experiments considering both linear and non-linear measurement models corrupted by additive noise and quantization errors. Our experiments show that the proposed algorithm results in $4 {\boldsymbol{\mathbf{-}}} 10$ dB lower error than existing methods.