This paper proposes a robust decoding algorithm in delivery of network coded data which is in particular correlated and delay-sensitive. We consider ad-hoc sensor network topologies, where a correlated data is delivered based on network coding techniques in conjunction with approximate decoding algorithm in order for efficient and robust data delivery. The approximate decoding algorithm has been developed as a decoding solution to ill-posed problems for network coded correlated data sources. In this paper, we improve the performance of approximate decoding algorithm by explicitly considering more information, which is used to additionally refine the recovered data. The information includes potential results that are from finite field operations and the set of such information is referred to as position information matrix in this paper. We deploy the position information matrix into approximate decoding algorithm and investigate its corresponding properties. We then analytically show that this improves the performance of approximate decoding algorithm. Our simulation results confirm the properties of the proposed approximate decoding algorithm with position information matrix and improved performance.