An Investigation of Purely Azimuthal Passive Localization and Position Adjustment in Attempted UAV Formation Flights

When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.

Novel passive localization algorithm based on double side matrix-restricted total least squares

In order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares （DSMRTLS） is proposed. First, the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector. Second, the corresponding optimization problem of the DSMRTLS problem without constraint is derived, which can be approximated as the generalized Rayleigh quotient minimization problem. Then, the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition. Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms.