Dynamic state and parameter estimation for nonlinear systems usually leads to large nonlinear problems when the governing differential constraints are discretized under a simultaneous solution strategy, as the optimality conditions for each data set are coupled to the conditions of other data sets. This NLP problem grows not only in the number of variables, but also in the number of degrees of freedom if an error in all variables method (EVM) approach is used. In this paper we discretize the set of ODEs using a one-step integration method, and use the SQP method to solve the resulting NLP. The optimality conditions for each data set at the QP subproblem level are decoupled using an affine transform, so that the first-order conditions in the state and input variables can be solved recursively and expressed as functions of the optimality conditions in the parameters, thus reducing the size of the problem and turning the effort of solving it linear with the number of data sets. As seen in our examples, this approach is therefore over two orders of magnitude faster than general purpose NLP solvers. This technique can also be viewed as an extension of a decomposition strategy that has been successfully applied to optimal control problems.