  Adaptive algorithms based on in-network processing over networks are useful
for online parameter estimation of historical data (e.g., noise covariance) in
predictive control and machine learning areas. This paper focuses on the
distributed noise covariance matrices estimation problem for multi-sensor
linear time-invariant (LTI) systems. Conventional noise covariance estimation
approaches, e.g., auto-covariance least squares (ALS) method, suffers from the
lack of the sensor's historical measurements and thus produces high variance of
the ALS estimate. To solve the problem, we propose the distributed
auto-covariance least squares (D-ALS) algorithm based on the batch covariance
intersection (BCI) method by enlarging the innovations from the neighbors. The
accuracy analysis of D-ALS algorithm is given to show the decrease of the
variance of the D-ALS estimate. The numerical results of cooperative target
tracking tasks in static and mobile sensor networks are demonstrated to show
the feasibility and superiority of the proposed D-ALS algorithm.
