Wireless sensor networks are often deployed in large numbers, over a large geographical region, in order to monitor the phenomena of interest. Sensors used in the sensor networks often suffer from random or systematic errors such as drift and bias. Even if they are calibrated at the time of deployment, they tend to drift as time progresses. Consequently, the progressive manual calibration of such a large-scale sensor network becomes impossible in practice. In this article, we address this challenge by proposing a collaborative framework to automatically detect and correct the drift in order to keep the data collected from these networks reliable. We propose a novel scheme that uses geospatial estimation-based interpolation techniques on measurements from neighboring sensors to collaboratively predict the value of phenomenon being observed. The predicted values are then used iteratively to correct the sensor drift by means of a Kalman filter. Our scheme can be implemented in a centralized as well as distributed manner to detect and correct the drift generated in the sensors. For centralized implementation of our scheme, we compare several kriging- and nonkriging-based geospatial estimation techniques in combination with the Kalman filter, and show the superiority of the kriging-based methods in detecting and correcting the drift. To demonstrate the applicability of our distributed approach on a real world application scenario, we implement our algorithm on a network consisting of Wireless Sensor Network (WSN) hardware. We further evaluate single as well as multiple drifting sensor scenarios to show the effectiveness of our algorithm for detecting and correcting drift. Further, we address the issue of high power usage for data transmission among neighboring nodes leading to low network lifetime for the distributed approach by proposing two power saving schemes. Moreover, we compare our algorithm with a blind calibration scheme in the literature and demonstrate its superiority in detecting both linear and nonlinear drifts.