With growing connection of distributed energy resources, availability of demand side response technologies, deployment of smart meters, the distribution system needs advanced network automation for running the system efficiently. State estimation is the core driver of network automation. While the output from SMs will make the state estimation more accurate, advanced metering infrastructures come with several challenges such as noisy, erroneous measurement including lost or missed measurements, exposure to cyber attack and so on. This study proposes a three-phase unbalanced distribution system state estimation which is robust against noisy distribution system measurements, bad data attacks and missing or delayed measurements. This method considers measurement from hybrid sources such as SCADA, micro-phasor measurement units (μμPMUs) and SMs. Kalman smoother is used to fill the missing measurements and expectation-maximisation based forecasting is used to interpolate the hybrid measurements to a common timestamp and compensate for the delay in SM measurements. Extensive numerical comparisons are made on IEEE 13, 37 and 123 bus systems to test the robustness of the proposed DSSE against delayed SM measurements and bad or noisy data. An IEEE 24 bus system is modelled and real-time measurement devices are interfaced to it in Hypersim. The data from the hybrid measurement devices of IIT Kanpur smart grid is also used to test the robustness of the proposed method.