This paper considers the detection of a target in a distributed radar system, wherein the received reflections from the said target are contaminated with heterogeneous clutter returns. We model this clutter, and possibly additional interference, as a superposition of an auto-regressive process and deterministic interference coming from a known subspace. Parametric adaptive detectors for this scenario are derived based on the Generalized Likelihood Ratio (GLR), Rao, and Wald tests, and are analyzed and compared with their non-adaptive, clairvoyant counterparts, which assume a priori knowledge of the auto-regressive process parameters. Using numerical simulations, the proposed detectors are shown to have detection performances that are robust to strong subspace interference.