1. A method of state-estimator for the estimation or initialization of the state of a discrete-time state-space dynamical model based on sensor measurements of the model output, comprising fitting a continuous-time function to acquired sensor measurement data-points of each model output, and subsequently sampling the continuous time function at exactly the sample-period of the state-space dynamic model for which the state is being estimated or initialized, in order to construct a model state via a synthesized output trajectory; wherein (a) sensor re-calibrations are included, by permitting the fitted function to be discontinuous in its value, but not its derivatives, at the point of re-calibration, and wherein the magnitude of the discontinuity is identified by the optimization, and wherein the sampling of the fitted function is performed ignoring the re-calibration discontinuity; (b) the function fit employs sensor measurement time-stamps and the state-estimator call-time, wherein: (i) delays between the sensor and state-estimator are at least partially mitigated by sampling the fitted function backwards in time starting at exactly the estimator call time; and (ii) sensor data collected at irregular time-intervals, or time-intervals that are not the sample-period of the model for which the state is being estimated or initialized, can be accommodated; (c) the model for which the state is being estimated or initialized may have inputs, and if inputs are present historical input data is employed in construction of the state; (d) the state of the model is observable or reconstructible; (e) when the model for which the state is being estimated or initialized has one single output then the current model state is constructed to reflect the synthesized output trajectory without offset, and when the model for which the state is being estimated or initialized has multiple outputs then a trade-off strategy is employed to reconcile mismatching outputs.