For five single machine total tardiness problems a fully polynomial-time approximation scheme (FPTAS) based on a graphical algorithm is presented. The FPTAS has the best running time among the known approximation schemes for these problems.

This paper considers the principles for designing digital controllers for measurement channels of proper acceleration and angular velocity in modern strapdown inertial navigation systems by examples of a quartz pendulous accelerometer and electromechanical sensor of angular velocity. Various approaches to synthesis of digital controllers are applied. The ob-tained results are compared. Also, the main principles of the mathematical software development to carry out actual tests of the measurement channels of proper acceleration and angular velocity, as well as inertial measurement units (IMU) based on them, in conditions of production are considers in this work. The principles of the software development, its connection with a type of the tested device and its mathematical model are discussed.

Analysis and structure of generalized algorithm for relative positioning of moving object is given. This algorithm is based on measuring of low-frequency alternating magnetic field of three transmitters with non-overlapping spectra. A theo-retical description of the positioning algorithm is given. Basic features of generalized algorithm which provide required ac-curacy of coordinates and attitude angles estimation is described.