This work addresses state estimation in presence of outliers in observed data. Outlying data and measurements have a most relevant impact in many control and signal processing applications including marine systems related ones: underwater navigation systems exploiting acoustic data, for example, are frequently affected by outlying measurements. Other on-board sensors and devices are likely to produce measurements contaminated by outlier because of the harsh operating conditions of marine systems. Given the general interest for dealing with measurement outliers in a number of applications, this paper describes a state estimation solution exhibiting robustness to output outliers. The system model is assumed to be linear (either time varying or time invariant) discrete time. The proposed observer is designed by extending an outlier robust static parameter identification algorithm to the case of a linear dynamic plant. The designed estimator has a predictor/corrector structure like the Kalman filter and the Luenberger observer. Simulation and experimental results are provided illustrating the robustness of the derived solution to measurement outliers as compared with the Kalman filter. The proposed solution is also compared with alternative outlier robust state estimation filters showing its effectiveness, in particular, in the presence of measurements outliers occurring in a consecutive sequence. Because of its deterministic execution time and limited numerical complexity, the proposed state estimator can be readily applied in real-time applications. Figure 4. Noisy output with outliers (depicted as blue stars, D 0:2) and non-outliers in grey generated through the model in (41). [Colour figure can be viewed at wileyonlinelibrary.com] The LEL Filter column refers to the interval of singular values over 3000 Monte Carlo runs assuming outliers generated through the model in (41). LEL, least entropy like.with synthetic and real data have been discussed showing the potentiality of the proposed filter as compared with the standard KF. Comparison with alternative robust filtering approaches have shown its robustness to sequences of successive measurement outliers as well. The proposed robust LEL filter may be exploited in real-time applications because of its limited and predictable (i.e. deterministic) computational effort.