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This paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments. In many practical scenarios, the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace. We address the particularly troublesome cases of low interference-to-noise ratio (INR), relatively rapid interference motion, and correlated noise across the receiving array. A polynomial-based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time, mitigate interference subspace estimation errors, and improve canceler performance. The application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution. Here even weak residual interference after cancellation may obscure a signal of interest, so very deep beampattern nulls are required. Performance for conventional subspace projection (SP) is compared with polynomial-augmented SP using simulated and real experimental data, showing null-depth improvement of 6 to 30 dB.