For a connected network of sensors we consider deriving the linear update weights required by a 1-hop distributed linear averaging algorithm (denoted 1-DLA) such that average-consensus is reached when the sensor nodes simultaneously track, by linear stochastic approximation, a set of distinct Markov chains with time-varying regime. It is found the desired consensus is infeasible for any 1-hop 1-DLA type algorithm in this setting, which includes the consensus filter proposed in . However, assuming a symmetric communication graph we show the average-consensus can be approached with zero asymptotic error by an alternative 1-hop algorithm (denoted 4-DLA) that requires each sensor compute 4 estimates {picirc s, s⁰, scirc} rather than only {s} as required under 1-DLA. We demonstrate a simulation of 4-DLA and explain its advantages compared to alternative multihop algorithms.