This paper discusses a summary derivation of maximum aposterioriestimation for continuous and discrete non-linear systems. It is known that with Gaussian aprioristatistics, the maximum aposterioriestimate is equivalent to an appropriate least squares fit. Filtering, fixed interval and fixed point smoothing algorithms for approximate non-linear estimation are obtained for the least squares eurve fit using ‘ running time ’ and ‘ fixed time ’ invariant embedding. Examples illustrating the use of the algorithms are presented.