In this study, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in Saber and Murray (2005), Carli et al. (2009) and Xiao et al. (2004) has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimised, thereby improving the filter design considerably and characterising the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimisation is alleviated with the application of a particular finite impulse response filter. Simulation results are showing the effectiveness of the developed estimation algorithm.