The PSO (Particle Swarm Optimization) algorithm uses a population of single particles, randomly distributed over the function search space, in order to construct an optimal flight path. During the algorithm iteration execution, each particle evaluates its fitness function according to the actual position. Then, every particle moves towards a direction dependent on its actual best position and the position of the best particle so far. The procedure ends when the iteration limit is reached or fitness criterium is met. In the presented autonomous UAV 3D path planning method, a PSO algorithm is used to build a feasible path, optimized in terms of fuel and threat cost. The process begins when the UAV detects or receives information about threats appearing on its primary trajectory. The population of particles moves in the search space of three variables, which are the angles of pitch, roll and yaw. These angles determine the spatial orientation of the UAV, indicating its direction of movement in each step. Further waypoints are chosen with consideration of the distance to the target and violation of threat areas. As a final result, the PSO algorithm constructs a suboptimal, feasible path which could be used as a reference trajectory for the UAV’s automatic control system. Simulation results turned out to be completely repeatable and indistinguishable, despite the stochastic nature of the algorithm, which proves its great optimization abilities. Moreover, its short execution time (within seconds) allows this procedure to be used in real time applications.
The paper presents the results of the development of a method and an algorithm for the synthesis of optimal basic signalcode structures in the form of code binary sequences, with a minimum criterion for the side lobes of the periodic autocorrelation function of the indicated sequences. To develop this method, approaches based on set theory and number theory were used. The method is based on a discrete representation of the periodic autocorrelation function of sequences in the form of a system of equations defined on a set of integers, set-theoretic interpretation of the constituent parts of sequences, their integer transformations, mutual properties and relations. A number of transformations of the constituent parts of the sequences are developed, analytical expressions for the dependence of the sum modulus of the sequence elements on the sum of the side lobe levels of their periodic autocorrelation function are derived, and the necessary conditions for the existence of sequences are defined and formulated. The relationship between the parameters of the code binary sequence and the canonical representation of the Euler function on the dimension of the sequence is determined. Analytical relationships between the levels of the side lobes of the periodic autocorrelation function and the parameters of the transformed sequence structures are obtained. The criterion of the effectiveness of the developed method and the corresponding algorithm is the ratio of the number of all possible variants of code binary sequences of a given dimension to a quantity that is determined by the developed algorithm; an expression was obtained to estimate the indicated amount. This efficiency is confirmed by the results of simulation and experimental research. The developed method can be used for the creation of secretive noise-proof data transmission radio systems, remote control systems, radar, and communications.
In navigation systems with nonlinear filtration algorithms extended Kalman filter is being used to estimate position. In
this filter, the state model distribution and all relevant noise destinies are approximated by Gaussian random variable.
What is more, this approach can lead to poor precision of estimation. Unscented Kalman filter UKF approximates
probability distribution instead of approximating nonlinear process. The state distribution is represented by a Gaussian
random variable specified using weighted sigma points, which completely capture true mean and covariance of the
distribution. Another solution for the general filtering problem is to use sequential Monte Carlo methods. It is particle
filtering PF based on sequential importance sampling where the samples (particles) and their weights are drawn from
the posterior distribution.