  In this paper, we consider the distributed filtering problem over sensor
networks such that all sensors cooperatively track unknown time-varying
parameters by using local information. A distributed forgetting factor least
squares (FFLS) algorithm is proposed by minimizing a local cost function
formulated as a linear combination of accumulative estimation error. Stability
analysis of the algorithm is provided under a cooperative excitation condition
which contains spatial union information to reflect the cooperative effect of
all sensors. Furthermore, we generalize theoretical results to the case of
Markovian switching directed graphs. The main difficulties of theoretical
analysis lie in how to analyze properties of the product of non-independent and
non-stationary random matrices. Some techniques such as stability theory,
algebraic graph theory and Markov chain theory are employed to deal with the
above issue. Our theoretical results are obtained without relying on the
independency or stationarity assumptions of regression vectors which are
commonly used in existing literature.
