Industrial robots were initially designed to be low cost and highly repeatable for pick-and-place and assembly operations. As a result, their construction does not support the high-precision accuracy and bandwidth needed for more advanced industrial automation. Due to the growing interest in replacing high precision manufacturing equipment with industrial robots for some applications, external high-precision feedback sensors (e.g., laser trackers), are needed to improve robot position and orientation accuracy. Before external sensors can be combined with control methodologies to improve robot accuracy, it is important to properly condition the measurement signals. In this paper, a Kinematic Error Observer (KEO) is derived and used to estimate a robot's slowly changing kinematic errors in real-time. An analysis of the KEO is first conducted to demonstrate its stability properties, transient response characteristics, noise sensitivity, and performance in non-deterministic measurement systems. Next, an implementation of the KEO was used in conjunction with a laser tracker and 6DoF sensor to dynamically estimate the kinematic errors of a Yaskawa/Motoman MH180 industrial robot. The results show that the KEO is capable of estimating the robot's quasi-static kinematic errors in both static and dynamic environments. It was also found that the KEO, with small enough observer gain, attenuates high frequency measurement noise and produces a smooth estimation of the robot's kinematic error.