The article proposes an adaptive algorithm that generates all object signals, including those for which measurements are not performed due to the difficulties associated with on-line measurements. The algorithm is modeled on the idea of the Kalman filter using its equation, however, the selection of gains is optimized in a different way, i.e. the constant values depend on the adopted ranges of adaptation errors. Moreover, the knowledge of the statistics of all noise signals is not imposed and there is no linearity constraint. This approach allowed to reduce the complexity of calculations. This algorithm can be used in real-time systems to generate signals of objects described by non-linear differential equations and it is universal, which allows it to be used for various objects. In the conducted research, on the example of a biochemically contaminated river, only easily measurable signals were used to generated the object signals, and in addition, in the case of absence some measurements, the functioning of the algorithm did not destabilize.

The article presents the algorithm that enables adaptive determination of the amplification coefficient in the filter equation provided by Kalman. The method makes use of an estimation error, which was defined for this purpose, and its derivative to determine the direction of correction changes of the gain vector. This eliminates the necessity to solve Riccati equation, which causes reduction of the method computational complexity. The experimental studies carried out using the proposed approach relate to the estimation of state coordinates describing river pollution using the BOD (biochemical oxygen demand) and DO (dissolved oxygen) indicators).The acquired results indicate that the suggested method does better estimations than the Kalman filter. Two indicators were used to measure the quality of estimates: the Root Mean Squared Error (RMSE) and the Mean Percentage Error (MPE).

The paper presents an off-line application that determines the maximum accuracy of the reference points for the given dynamics parameters of a CNC machine. These parameters are maximum speed, acceleration, and JERK. The JERK parameter determines the rate of change of acceleration. These parameters are defined for each working axis of the machine. The main achievement of the algorithm proposed in the article is the determination of the smallest error specified for each reference point resulting from the implemented G-code for the considered dynamic parameters of the CNC machine. The solutions to this problem in industry consider the improvement in the accuracy of hitting the reference points, but they do not provide information on whether the obtained solution is optimal for such parameters of the machine dynamics. The algorithm makes the accuracy dependent on the adopted dynamic parameters of the machine and the parameters of the PLC controller used in the CNC machine.