The Lagrangian data assimilation (LaDA) is a method for the direct assimilation of Lagrangian observations. By augmenting the model state vector with the Lagrangian coordinates, the LaDA removes the need for any commonly used approximations to transform Lagrangian observations into Eulerian (i.e., velocity) observations. We demonstrate the LaDA's effectiveness for the ocean applications and present its positive effect in the light of observability. Lagrangian instruments in the oceans, such as drifters and floats, are often designed to remain on a two-dimensional surface in the three-dimensional ocean except when descending to or ascending from the desired depth. By considering a volume of influence, we examine how and to what extent the LaDA propagates the information vertically to estimate the three-dimensional ocean structure. Using the judicious design of the deployment strategy, the LaDA is strikingly efficient in tracking the local coherent structures, such as ocean eddies, as well as estimating the large-scale ocean circulation. We demonstrate the tracking ability of the LaDA for the loop-current eddy in the Gulf of Mexico, which can impact the hurricane forecasts for the numerical weather prediction.