# Co-Operatively Increasing Smoothing and Mapping Based on Switching Function
## 2 Related Work  
### Relative Positioning in GPS/BeiDou Denial  
This paper specifically addresses the relative-positioning technology in an environment where GPS/BeiDou signals are unavailable. According to the different measurement objects, it can be categorized into in-cluster measurement and out-of-cluster measurement. Intra-cluster measurement refers to the mutual measurement between UAVs, which can improve the positioning accuracy of the cluster vehicle itself; extra-cluster measurement refers to the measurement of non-co-operative targets by UAVs, which can realize the precise positioning of targets.  
Among the techniques for intra-cluster measurements, some scholars have proposed methods for co-operative localization using incomplete measurements. The article in [12] proposes an a posteriori linearized belief propagation (PLBP) algorithm for co-operative localization in wireless sensor networks with nonlinear measurements. The paper in [13] outlines the cooperative localization method and applies it to ultra-wideband (UWB) wireless networks. The authors propose a fully distributed localization algorithm (SPAWN) by mapping a statistically inferred graphical model onto the network topology, resulting in a network factor graph, and developing a suitable network messaging scheme. The article in [10] proposes a cluster localization architecture and relative localization algorithm based on pigeon flock bionics for collaborative work, flexible configuration, and the efficient operation of unmanned clusters. The paper creatively proposes a relative localization method to construct the relative position relationship with the North Line without resorting to extra-cluster information. The article in [14] proposes batch inverse covariance intersection (BICI) and BICI multi-sensor fusion localization methods with interacting multi-models (IMMs), which are based on the batch form of the sequential inverse covariance intersection (SICI) fusion method. It is also demonstrated that BICI is robust. Compared to SICI, BICI-IMM reduces the estimation error variance of the motion model and has less conservatism. The article in [15] describes a complex micro-vehicle swarm control system stabilized by on-board visual relative localization, the core component of which is a novel and efficient black and white pattern detection algorithm. The system aims to validate the possibility of the self-stabilization of a multi-micro-vehicle swarm in the absence of GNSS. However, limitations on constraints of the testing algorithm lead to non-advantageous practicality.  
Among the techniques for out-of-cluster measurements, some scholars have proposed methods for co-operative localization using incomplete measurements. For example, the paper in [16] proposes a collaborative smoothing and mapping (C-SAM) method in 2008. The iSAM algorithm is an incremental smoothing and mapping algorithm based on factor graph optimization [17], which can efficiently deal with large-scale nonlinear least-squares problems and is suitable for state estimation in dynamic scenarios [18], but there were two serious problems in the paper [19]. The first one was that the robots shared observations of the environment among themselves and that the robots made measurements among themselves by observing each other, and the article used black and white tessellated lattices with specific shapes to observe each other. The observation was difficult and required a large amount of shared memory. The other was that the initialization of the algorithm was achieved through multiple iterations, in which virtual anchor nodes were introduced and least squares were used to compute offsets and rotations in different local co-ordinate systems, which was computationally intensive and tedious.