A tandem repeat is a sequence of nucleotides that occurs as multiple contiguous and near-identical copies positioned next to each other. These repeats play critical roles in genetic diversity, gene regulation, and are strongly linked to various neurological and developmental disorders. While several methods exist for detecting tandem repeats, they often exhibit low accuracy when the repeat unit length increases or the number of copies is low. Furthermore, methods capable of handling highly mutated sequences remain scarce, highlighting a significant opportunity for improvement. We introduce EquiRep, a tool for accurate detection of tandem repeats from erroneous sequences. EquiRep estimates the likelihood of positions originating from the same position in the unit by self-alignment followed by a novel approach that refines the estimation. The built equivalent classes and the consecutive position information will be then used to build a weighted graph, and the cycle in this graph with maximum bottleneck weight while covering most nucleotide positions will be identified to reconstruct the repeat unit. We test EquiRep on simulated and real HOR and RCA datasets where it consistently outperforms or is comparable to state-of-the-art methods. EquiRep is robust to sequencing errors, and is able to make better predictions for long units and low frequencies which underscores its broad usability for studying tandem repeats.