The Internet of Things (IoT) has been recognized as the next technological revolution. It faces two challenges: 1) how to achieve energy efficient communication for the battery constrained devices and 2) how to connect a very large number of devices to the Internet with low latency, high efficiency, and reliability. To address these problems, this paper proposes two methods based on Kalman filter (KF), termed as extensions of predicable KF (EPKF). They locally reduce the unnecessary transmission (access) of end devices to the network (Internet) utilizing the spatial and temporal correlations with low algorithmic overhead. Each transmitting device (TD) independently controls its transmission using the temporal correlation; and the receiving device (RD) exploits the spatial correlation among the TDs to further improve the reconstruction quality. The reconstruction problem in the RD is nonlinear. To reduce the computation complexity, an in-depth analysis of the local estimate error is conducted and the approximated linear solutions are thereupon obtained. They are fundamental methods applicable to any IoT monitored/controlled physical system that can be modeled as a linear state space representation. The pedestrian-position application is used as a case study to demonstrate the efficiency in the simulation. Remarkably, the EPKF methods using the linear combinations of the local estimates from multiple TDs reduce the transmission rate to 10%, while achieving the same reconstruction quality as using KF in the traditional manner.