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Practical and efficient state estimation is essential for the safe and stable operation of future smart grid. In rectangular coordinates, distribution system state estimation (DSSE) problem can be described as a sparse quadratic constraint quadratic estimation (QCQE) model, which enhances efficiency of the program implementation for DSSE. However, the scarcity of measurements in distribution network brings a formidable challenge to provide reasonably meaningful estimation of the distribution system state. This paper is concerned about application of QCQE in under-determined distribution network. Observability analysis technique is proposed by considering the characteristics of actual distribution network. The observable islands are recognized accordingly, and then unobservable areas can be accurately defined. Pseudo-measurements are adopted to meet the observability requirement. Simulation on IEEE 33-bus shows effectiveness of the proposed method.