A critical issue in origin-destination (O-D) demand estimation is under-determination: the number of O-D pairs to be estimated is often much greater than the number of monitored links. In real world, some centroids tend to be more popular than others, and only few trips are made for intro-zonal travel. Consequently, a large portion of trips will be made for a small portion of O-D pairs, meaning many O-D pairs have only a few or even zero trips. Mathematically, this implies that the O-D matrix is sparse. Also, the correlation between link flows is often neglected in the O-D estimation problem, which can be obtained from day-to-day loop detector count data. Thus, sparsity regularisation is combined with link flow correlation to provide additional inputs for the O-D estimation process to mitigate the issue of under-determination and thereby improve estimation quality. In addition, a novel strategic user equilibrium model is implemented to provide route choice of users for the O-D estimation problem, which explicitly accounts for demand and link flow volatility. The model is formulated as a convex generalised least squares problem with regularisation, the usefulness of sparsity assumption, and link flow correlation is presented in the numerical analysis.