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In tracking applications of wireless sensor networks (WSNs), the classification of an object or event of interest is envisaged to be one of the most computationally intensive tasks that recur frequently over the lifetime of the network. It is imperative that the implementations of such tasks be power efficient and computationally feasible for resource-constrained WSNs. Existing implementations of the best known classifiers such as maximum Aposterior (MAP) classifier are computationally infeasible for WSN environments. The focus of this paper is to investigate computational techniques to realize power efficient distributed implementation of the MAP classifier. In the MAP classifier, one of the most computationally challenging steps is the computation of the inverse of the covariance matrices. In this paper, we study computationally efficient methods for realizing the inverse of a matrix. We present a detailed discussion of one-sided Jacobi Iterations and LU Decomposition for approximating and computing the inverse of the covariance matrices. For LU Decomposition-based solutions, we also apply folding techniques to ensure equal power dissipation among the sensor network nodes. Our contribution lies in the power consumption analysis of executing the MAP classifier using LU decomposition and one-sided Jacobi Iterations to substitute the inverse of the covariance matrices. We show that MAP with one-sided Jacobi Iterations greatly simplifies classification process and makes it more feasible and efficient choice for sensor network applications.