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In radar applications, the received echo signals reach the array elements via a multiplicity of paths despite the fact that there exists only one target. We address the problem of joint direction of arrival and Doppler frequency estimation using a sensor array in partially known additive noise. We consider a specular reflection model with a radar cross section fluctuating from one pulse repetition interval to another. The proposed model allows the estimation of more paths than sensors. Two approximate maximum likelihood algorithms are proposed. The first approach uses a linear expansion of the noise covariance matrix, whereas the second employs a combination of oblique projections and a zero-forcing solution to alleviate the effect of noise. In contrast to other classical methods, the two approaches are more robust to spatially correlated noise, and they employ more compact cost functions that reduce the dimension of the optimization search. Numerical simulations are provided to assess the basic performance of the two approaches, which are compared to the Crame´r-Rao bound.