The problem of course alignment of inertial navigation systems is considered. Error equations of nonlinear character have been obtained at a considerable level of a priori course uncertainty. The algorithm for solving the problem of optimal estimation of the state vector described by nonlinear equations from linear measurements has been developed for the analysis of a potential alignment accuracy with the piecewise-Gaussian approximation of a posteriori density used. The results of the study of efficiency of various suboptimal alignment algorithms obtained by the use of the software developed are presented and discussed.

Binocular disparity and motion parallax are the most important cues for depth estimation in human and computer vision. Here, we present an experimental study to evaluate the accuracy of these two cues in depth estimation to stationary objects in a static environment. Depth estimation via binocular disparity is most commonly implemented using stereo vision, which uses images from two or more cameras to triangulate and estimate distances. We use a commercial stereo camera mounted on a wheeled robot to create a depth map of the environment. The sequence of images obtained by one of these two cameras as well as the camera motion parameters serve as the input to our motion parallax-based depth estimation algorithm. The measured camera motion parameters include translational and angular velocities. Reference distance to the tracked features is provided by a LiDAR. Overall, our results show that at short distances stereo vision is more accurate, but at large distances the combination of parallax and camera motion provide better depth estimation. Therefore, by combining the two cues, one obtains depth estimation with greater range than is possible using either cue individually.

This article is in honor of the 80th birthday of Rudolf Emil Kalman. A brief biography of R.E. Kalman is presented. The most important facts concerned with the creation of the celebrated Kalman filter are briefly outlined. Some trends in the development of applied methods for solution of filtering problems are analyzed. Kalman’s relations and contacts with Russian scientists as well as their contribution to filtering theory and its applications are discussed.

The problem of gravity anomaly estimation aboard an aircraft solved by using the data from a gravimeter and the differential satellite navigation system is formulated in the framework of the optimal filtering and smoothing theory. Relying upon this statement both the problem of the potential accuracy analysis and problem of designing efficient filtering and smoothing algorithms are solved. In particular, the efficiency of filtering and smoothing in estimating gravity anomalies using various satellite measurements is investigated. A unified algorithm for solving the filtering and smoothing problems is suggested. An example illustrating the results obtained is considered.