Suppose imprecise observations are made on imprecisely defined nonlinear processes, and one wishes to estimate the state of the process at certain fixed instants of time lying within the interval of observation. Furthermore, assume that it is required to update these estimates as additional observations become available. This is precisely the problem of sequential interpolation. The equations of the sequential interpolating filter, when a least-squares estimation criterion is used, are obtained in this paper. The interpolation problem is first shown to be equivalent to a two-point boundary-value problem. The two-point boundary-value problem is converted to an initial-value problem using invariant imbedding. The initial-value problem leads directly to a sequential filter.