To reduce costs, an unmanned swarm usually consists of nodes with high-accuracy navigation sensors (HAN) and nodes with low-accuracy navigation sensors (LAN). Transmitting and fusing the navigation information obtained by HANs enables LANs to improve their positioning accuracy, which in general is called cooperative navigation (CN). In this method, the accuracy of relative observation between platforms in the swarm have dramatic effects on the positioning results. In the popular research, constructing constraints in three-dimensional (3D) frame could only optimize the position and velocity of LANs but neglected the attitude estimation so LANs cannot maintain a high attitude accuracy when utilizing navigation information obtained by sensors installed during maneuvers over long periods. Considering the performance of the inertial measurement unit (IMU) and other common sensors, this paper advances a new method to estimate the attitude of LANs in a swarm. Because the small unmanned nodes are strictly limited by relevant practical engineering problems such as size, weight and power, the method proposed could compensate for the attitude error caused by strapdown gyroscopic drift, which only use visual vectors built by the targets detected by cameras with the function of range finding. In our method, the coordinates of targets are mainly given by the You Only Look Once (YOLO) algorithm, then the visual vectors are built by connecting the targets in the covisibility graph of the nodes in the swarm. The attitude transformation matrices between each camera frame are calculated using the multivector attitude determination algorithm. Finally, we design an information filter (IF) to determine the attitude of LANs based on the observation of HANs. Considering the problem of positioning reference, the field test was conducted in the open air and we chose to use two-wheeled robots and one UAV to carry out the experiment. The results show that the relative attitude error between nodes is less than 4 degrees using the visual vector. After filtering, the attitude divergence of LANs’ installed low precision IMU can be effectively constrained, and the high-precision attitude estimation in an unmanned CN swarm can be realized.

When unmanned platforms perform precise target detection, the configuration of detection nodes will significantly impact accuracy. Aiming to obtain the minimum dilution of precision (DOP), this paper innovatively proposes an optimal detection configuration design method focused on the heterogeneous unmanned cooperative swarm based on the nested cone model. The proposed method first divides the swarm into different groups according to the performances of platforms and then uses a conical nested configuration to arrange the placement of each node independently. The paper considers the problem of the inaccurate prior position of the target and replaces the single-point DOP with the average DOP on the prior region of the target as the optimization objective. Considering the unavoidable positioning errors in engineering practice, this paper provides the optimal configuration of the detection group (DG) and anchor group (AG) in the swarm to reduce the impact caused by positioning errors of detection nodes. We set a certain swarm consisting of 3 types of platforms to design the configuration by simulation experiments and find the optimal parameters for nested cones to realize accurate detection.

Various attitude estimation methods are based on an optimization problem posed in 1965 by Grace Wahba, which is called Wahba’s problem in the field of attitude estimation. As a key for attitude determination, many different algorithms for minimizing Wahba’s loss function have been proposed in the past 60 years. Among the most representative are Quaternion Estimator (QUEST), Singular Value Decomposition (SVD), and Fast Optimal Attitude Matrix (FOAM), which are briefly introduced in this research paper, and new algorithms proposed in recent years such as Fast Linear Quaternion Attitude Estimator (FLAE), are also included. The calculation principle and derivation process are given in the article, and simulation under high noise conditions for algorithms mentioned has been completed. Finally, several practical engineering applications related to Wahba’s problem are introduced and the future development trend of attitude estimation is discussed.