The odometry information used in mobile robot localization can contain a significant number of errors when robot experiences slippage. To offset the presence of these errors, the use of a lowcost gyroscope in conjunction with Kalman filtering methods has been considered by many researchers. However, results from conventional Kalman filtering methods that use a gyroscope with odometry can unfeasible because the parameters are estimated regardless of the physical constraints of the robot. In this paper, a novel constrained Kalman filtering method is proposed that estimates the parameters under the physical constraints using a general constrained optimization technique. The state observability is improved by additional state variables and the accuracy is also improved through the use of a nonapproximated Kalman filter design. Experimental results show that the proposed method effectively offsets the localization error while yielding feasible parameter estimation.