Data assimilation (DA), by merging observation and background information, is an important tool in the field of geosciences. However, in the presence of geophysical structures such as cyclones or ocean eddies, classic DA schemes in gridded space fail to properly estimate the structure properties, for example, their position and intensity. In this work, we propose a new DA scheme, in a reduced parametric space, which assimilates only the relevant parameters to describe the structures, with an application to a one-dimensional ocean eddy. Comparison of DA performed in the classic gridded field and in the parametric space is made through a series of experiments with perturbed eddy parameters. Results show that DA in the parametric space can account for the nonlinearity of the eddy parameters and preserve eddy properties. This is not the case for classic DA in the gridded space. Moreover, DA in the parametric space considerably reduces the computational cost.