It often happens that we cannot acquire all information available to locate targets as obstacles exist between observation stations and targets or there is something wrong with some observation stations. Both cases are called the circumstance of missing information where partial information can be observed, resulting in poor positioning performance of multi-target location. Considering the sparse characteristic and random subsampling of Compressed Sensing (CS) theory, we think of a possibility of applying Compressed Sensing Direct Position Determination (CSDPD) to lessen the impact of missing information on multi-target location. Orthogonal matching pursuit (OMP) algorithm is a kind of greedy algorithm of CS, which can be utilized to lessen the impact of missing information. For better positioning accuracy, an improved OMP algorithm based on DPD (IOMP-DPD) is proposed through a new method of updating index set to lessen the possibility of incomplete location. It confirms by simulations that the improved method yields more accurate positioning results than OMP algorithm and outperforms than the existed MUSIC algorithm based on DPD (MUSIC-DPD), revealed in estimating more target locations in the same positioning conditions and smaller positioning errors when locating the same targets.