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The performance of automatic speech recognition (ASR) systems severely degrades when multi-talker speech overlap occurs. In meeting environments, speech separation is typically performed to improve the robustness of ASR systems. Recently, location-based training (LBT) was proposed as a new training criterion for multi-channel talker-independent speaker separation. Assuming fixed array geometry, LBT outperforms widely-used permutation-invariant training in fully overlapped utterances and matched reverberant conditions. This paper extends LBT to conversational multi-channel speaker separation. We introduce multi-resolution LBT to estimate the complex spectrograms from low to high time and frequency resolutions. With multi-resolution LBT, convolutional kernels are assigned consistently based on speaker locations in physical space. Evaluation results show that multi-resolution LBT consistently outperforms other competitive methods on the recorded LibriCSS corpus.