  Based on the dominant paradigm, all the wearable IoT devices used in the
healthcare sector also known as the internet of medical things (IoMT) are
resource constrained in power and computational capabilities. The IoMT devices
are continuously pushing their readings to the remote cloud servers for
real-time data analytics, that causes faster drainage of the device battery.
Moreover, other demerits of continuous centralizing of data include exposed
privacy and high latency. This paper presents a novel Federated Filtering
Framework for IoMT devices which is based on the prediction of data at the
central fog server using shared models provided by the local IoMT devices. The
fog server performs model averaging to predict the aggregated data matrix and
also computes filter parameters for local IoMT devices. Two significant
theoretical contributions of this paper are the global tolerable perturbation
error (${To{l_F}}$) and the local filtering parameter ($\delta$); where the
former controls the decision-making accuracy due to eigenvalue perturbation and
the later balances the tradeoff between the communication overhead and
perturbation error of the aggregated data matrix (predicted matrix) at the fog
server. Experimental evaluation based on real healthcare data demonstrates that
the proposed scheme saves upto 95\% of the communication cost while maintaining
reasonable data privacy and low latency.
