A new framework named Evidence Filtering for processing multi-modality sensor data, and a novel distributed method to implement spatio-temporal filtering applications in grid sensor networks is presented. The concept of evidence filtering is based on conditional belief notions in Dempster-Shafer (DS) evidence theory and enables one to directly process temporally and spatially distributed sensor data and infer on the 'frequency' characteristics of various events of interest. This method can accommodate partial and incomplete information from multiple sensor modalities during the process. Certain restrictions on the coefficients impose several challenges in the design of evidence filters. A design procedure and a frequency domain analysis of non-recursive and recursive evidence filters are presented. A threat assessment scenario using an evidence filter is simulated to illustrate the applications of evidence filtering. The proposed distributed method can be used to implement any general linear, spatio-temporal filter in a grid sensor network, and is based on the Fornasini-Marchesini (FM) local state space model. This approach yields significant advantages in distributed processing of information in grid sensor networks, and supports local actuation in response to local events. System stability is analyzed for the case where a fixed point data representation is used for both computation and communication. Simulation results are also presented to support the theoretical findings. A combination of these two powerful tools together provide a highly effective toolset for one to implement spatio-temporal filtering applications in a multi-modality grid sensor network.