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Target tracking in wireless sensor networks is an important area of research with applications in both the military and civilian domains. One of the most fundamental and widely used approaches to target tracking is the Kalman filter. In presence of unknown noise statistics there are difficulties in the Kalman filter yielding good results. In Kalman filter operation for state variable models with near constant noise and system parameters, it is well known that after the initial transient the gain tends to a steady state value. Hence working directly with Kalman gains it is possible to obtain good tracking results dispensing with the use of the usual covariances. The present work applies an innovations based cost function minimization approach to the target tracking problem in wireless sensor networks, in order to obtain the constant Kalman gain for both the stand-alone and data-fusion modes. Our numerical studies show that the constant gain Kalman filter gives good comparative performance in both the stand-alone and data-fusion modes for the target tracking problem. This is a significant finding in that the constant gain Kalman filter circumvents or in other words trades the gains with the filter statistics which are more difficult to obtain. To the best of our knowledge, these are the only studies of a constant gain Kalman filter in wireless sensor network scenarios, that also incorporate data fusion.