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Robust filtering for state-space estimation has been studied. The application domain emphasises air-to-ground target tracking with remote sensing devices such as radar. An analysis indicates that in this application, target model uncertainties predominantly exist in the observation model and target input process noise model. For this reason, the development of a filter with robustness towards these two types of uncertainties has been the focus of the authors. A challenge to the design is that the uncertainties are highly non-stationary with the result that predefined bounds on uncertainties generally cannot provide the required filtering accuracy. Therefore, a successful robust filter for such applications must include a mechanism to predict instant bounds on certainties and, to this end, an iterative robust filter is developed on the basis of least squares optimisation criteria. Compared with existing robust filters, the novelty of this new filtering is to predict the worst-case uncertainty so that tight bounds on the involved uncertainties can be applied and the state estimates can be obtained more accurately.