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In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a covariance matrix distortion constraint and in the presence of side information at the decoder. For this problem, we derive lower and upper bounds on the rate-distortion function (RDF) for the Gaussian case, which in general do not coincide. We then provide somedoi:10.1109/isit.2014.6874900 dblp:conf/isit/ZahediOJNB14 fatcat:42mu2uuje5gcvhxbfgjn7h36wy