Block transmission techniques have received much research interest recently for their ability to eliminate the intersymbol interference problem associated with continuous transmission. Numerous detection schemes for single carrier systems have been proposed. While these schemes may be derived from different principles, they usually rely on some prior estimate of the channel. However, channel estimation is usually affected by errors and most of existing detection schemes are known to be sensitive to such errors. In this paper, we develop robust detection schemes that explicitly account for channel and covariance matrix estimation errors by optimizing the worst-case performance over two properly selected bounded uncertainty sets, that are centered on the prior channel and covariance matrix estimates. Numerical results show an improved performance using the proposed robust approaches over the ones that ignore the prior estimation errors.