This paper proposes a novel in-network estimation approach for state estimation within delay constraints in wireless sensor networks. The approach jointly designs in-network estimation operations and an aggregation scheduling algorithm. The in-network estimation performed at relays optimally fuses estimates from different sensors and predicts estimates from upstream sensors that cannot be aggregated to the sink before deadlines. The proposed estimate aggregation scheduling algorithm is able to aggregate estimate information to the sink within delay constraints in an interference-free manner. Simulation results show the approach obtains significant estimation accuracy gains under different network settings.