We demonstrate an extended Kalman filtering-enhanced linewidth measurement in short-delay self-heterodyne interferometry (SDSHI). We found that a modified SDSHI trace closely resembles a biased cosine wave, which would enable convenient linewidth estimation by its uniform envelope contrast without any correction factor. Experimentally, we adopted this approach for kHz laser linewidth measurement, taking advantages of extended Kalman filtering (EKF) to adaptively track the cosine wave. Apart from the measurement noise suppression, this approach could use as many data points as possible in the noisy trace to make a linewidth estimation at each tracked data point, from which we can deduce valuable statistical parameters such as the mean and standard deviation. This approach involves no more equipment than conventional SDSHI and sophisticated EKF so that it can be easily implemented. Therefore, we believe it will find wide applications in ultra-narrow laser linewidth measurement.