Accurate model identification and fault detection are necessary for reliable motor control. Motor-characterizing parameters experience substantial changes due to aging, motor operating conditions, and faults. Consequently, motor parameters must be estimated accurately and reliably during operation. Based on enhanced model structures of electric motors that accommodate both normal and faulty modes, this paper introduces bias-corrected least-squares(LS) estimation algorithms that incorporate functions for correcting estimation bias, forgetting factors for capturing sudden faults, and recursive structures for efficient real-time implementation. Permanent magnet motors are used as a benchmark type for concrete algorithm development and evaluation.Algorithms are presented, their properties are established, and their accuracy and robustness are evaluated by simulation case studies under both normal operations and inter-turn winding faults. Implementation issues from different motor control schemes are also discussed.