Optimal Time-Resource Allocation for Activity-Detection via Multimodal Sensing

The optimal allocation of measurements for activity-level de- tection in a wireless body area network (WBAN) for health- monitoring applications is considered. The WBAN with heterogeneous sensors is deployed in a simple star topol- ogy with the fusion center receiving a fixed number of mea- surements from the sensors; the number of measurements allocated to each sensor is optimized to minimize the prob- ability of detection error at the fusion center. An analysis of the two-sensor case with binary hypotheses is presented. Since the number of measurements is an integer, an exhaus- tive search (grid search) is traditionally employed to de- termine the optimal allocation of measurements. However, such a search is computationally expensive. To this end, an alternate continuous-valued vector optimization is derived which yields approximately optimal allocations which can be found with lower complexity. Numerical case studies based on experimental data for different key activity-states are presented. It is observed that the Kullback-Leibler (KL) distances between the distributions associated with the hy- potheses dominate the optimal allocation of measurements.