In this paper, we deal with the problem of detecting point-like targets in the presence of Gaussian disturbance with unknown covariance matrix. In particular, we consider the so-called partially homogeneous environment, where the disturbances in both the cell under test (CUT) and the secondary data share the same covariance matrix up to an unknown power scaling factor. Specifically, we model the disturbance as a multichannel autoregressive Gaussian process and exploit the spillover of target energy to consecutive range samples, in order to improve the performances of detection and range estimation. In this context, we come up with three adaptive architectures relying on the ad hoc modifications of the generalized likelihood ratio test and Wald test. The performance assessment, conducted resorting to both simulated data and recorded live data, highlights that the proposed decision schemes can provide accurate estimates of the target position within the CUT and ensure enhanced detection performance compared with their natural competitors.