An accurate real-time gait phase estimator for normal and asymmetric gait is developed by training and testing a time-delay neural network on gait data collected from six participants during treadmill walking. The trained model can generate smooth and highly accurate predictions of the gait phase with a root mean square error of less than 3.48% and 4.31% in normal and asymmetric gait, respectively. The coefficient of determination between the estimated and target phase is greater than 99% for all subjects with both normal and asymmetric gait. The proposed gait estimator also exhibits precise heel-strike event detection with an RMSE of 2.56% and 3.70% in normal and asymmetric gait, respectively. A spatial impedance controller is then employed and tested based on the estimated gait phase of a new participant. Obtained results confirm that the controller provided assistance in coordination with the user's motion both in normal and asymmetric gait conditions. The estimated gait phase is compared in the case of walking without and with the exoskeleton in passive and active modes, indicating persistent accuracy of the gait phase estimator regardless of the walking conditions.