Estimation of continuously differentiable signal with allowance for constraints

Consideration was given to the estimation of a piecewise‐polynomially representable signal subject to continuity and smoothness and with allowance for the constraints on the value of signal and its derivative. Such representation may be used also for perturbation generating the estimated signal. The measurement noise was assumed to have stochastic description. Given was an analytical definition of the domain of values of the coefficients of the piecewise‐polynomial representation of the signal under which it satisfies the stipulated requirements. A two‐step computation‐efficient solution of the problem was proposed, and an example of its efficient use was given.