  Real-time information processing applications such as those enabling a more
intelligent infrastructure are increasingly focused on analyzing
privacy-sensitive data obtained from individuals. To produce accurate
statistics about the habits of a population of users of a system, this data
might need to be processed through model-based estimators. Moreover, models of
population dynamics, originating for example from epidemiology or the social
sciences, are often necessarily nonlinear. Motivated by these trends, this
paper presents an approach to design nonlinear privacy-preserving model-based
observers, relying on additive input or output noise to give differential
privacy guarantees to the individuals providing the input data. For the case of
output perturbation, contraction analysis allows us to design convergent
observers as well as set the level of privacy-preserving noise appropriately.
Two examples illustrate the approach: estimating the edge formation
probabilities in a dynamic social network, and syndromic surveillance relying
on an epidemiological model.
