Motivated primarily by electronic surveillance applications, but also by other potential uses in passive exploitation of radio frequency (RF) signals, this paper considers the problems of detecting the presence of and characterizing a radar transmitter using data collected at a spatially distributed suite of receivers. A characterization of a particular interest is determining the rank of the transmitted signal, which enables discrimination between multiple-input multiple-output (MIMO) and conventional radar transmitters as well as distinguishing between MIMO systems that simultaneously emit different numbers of linearly independent signals from their transmit arrays. In this paper, an invariant posterior distribution for position and signal rank of a MIMO radar emitter is derived based on non-informative prior distributions for the signal parameters. This allows MAP-based detection and signal rank estimation. These estimators are shown to significantly outperform maximum likelihood (ML)/BIC position and rank estimators.