  A linear Gaussian state-space smoothing algorithm is presented for estimation
of derivatives from a sequence of noisy measurements. The algorithm uses
numerically stable square-root formulas, can handle simultaneous independent
measurements and non-equally spaced abscissas, and can compute state estimates
at points between the data abscissas. The state space model's parameters,
including driving noise intensity, measurement variance, and initial state, are
determined from the given data sequence using maximum likelihood estimation
computed using a expectation maximisation iteration. In tests with synthetic
biomechanics data, the algorithm has equivalent or better accuracy compared to
other automatic numerical differentiation algorithms.
