A method for estimating downhole speed and force variables at an arbitrary location of a moving drill string based on surface measurements of the same variables. The method includes a) using properties of said drill string to calculate transfer functions describing frequency-dependent amplitude and phase relations between cross combinations of said speed and force variables at the surface and downhole; b) selecting a base time period; c) measuring surface speed and force variables, conditioning the measured data by applying anti-aliasing and/or decimation filters, and storing the conditioned data, and d) calculating the downhole variables in the frequency domain by applying an integral transform, such as Fourier transform, of the surface variables, multiplying the results with said transfer functions, applying the inverse integral transform to sums of coherent terms and picking points in said base time periods to get time-delayed estimates of the dynamic speed and force variables.