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A new approach for multichannel autoregressive (AR) spectrum estimation is introduced based on an iterative gradient algorithm. In the context of dynamic programming, the approach is shown to be optimum in the reflection coefficient domain, whereas the multichannel AR Nuttall-Strand algorithm is shown to be suboptimum. The approach guarantees a stable multichannel AR filter and a nonnegative spectrum matrix estimate. It is demonstrated via simulation examples that such drawbacks of the Nuttall-Strand method as frequency bias and line splitting may be alleviated by the optimum approach. However, the improved performance is achieved at the expense of considerably more computational effort and time. The Single-channel Fougere descent method may be seen as a special case of the proposed multichannel AR approach.