A novel adaptive version of the divided difference filter (DDF) applicable to non-linear systems with a linear output equation is presented in this work. In order to make the filter robust to modeling errors, upper bounds on the state covariance matrix are derived. The parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality (LMI) constraint, which ensures that the predicted output error covariance is larger than the observed output error covariance. The resulting sub-optimal, high-gain filter is applied to the problem of joint state and parameter estimation. Simulation results demonstrate the superior performance of the proposed filter as compared to the standard DDF. (C) 2009 Elsevier Ltd. All rights reserved.