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A parametric estimation algorithm for a single-axis gradiometer is described. The most influential parameters are isolated and estimated; their bias and variance are discussed. Even though the system is closed-loop controlled, only plant parameters are estimated using an open-loop identification equation, which simplifies the identification procedure. The estimates are obtained using the method of instrumental variables (IV). The advantage of this method is that it remains bias-free even when the system states are correlated with the measurement noise. The problem is described in a one-dimensional frame, but it can be extended to the multivariate case if necessary. The estimated parameters are then used to reconstitute the closed-loop transfer function, which allows the input disturbance that caused the observed signal to be deduced. The estimation algorithm is applied to the laser interferometer space antenna (LISA) technology package, which is the scientific payload of the LISA Pathfinder spacecraft (SC), an ESA/NASA technology demonstrator to be launched in 2014. The analysis is operated on a simulated dataset produced with the mission end-to-end simulator (E2E) as well as with a simple linear simulator. The on-board software and hardware constraints are taken into account since they are important performance drivers. The results are detailed along with the experiment model.