Abstract The paper proposes algorithms for set-bounded joint parameter and variable estimation in networks. Both the batch and the stable recursive algorithms are derived under the measurement and modelling errors. The stability and tight bounds are obtained by employing a concept of moving information window. The non-probabilistic set-bounded approach to modelling uncertainty allows to achieve desired robustness of the estimates. The estimation scheme is very flexible in integrating the information available. In particular, it can be used as a network simulator under uncertain mathematical model and the network inputs. A mixed integer solver of the optimisation tasks needed to be solved during the estimation steps is also proposed. Excellent results have been obtained in estimating a model parameter and a conductivity in a physical water network.
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