# Multi-Sensor Fusion Positioning Method Based on Batch Inverse Covariance Intersection and IMM
## 1 Introduction  
With the advent of the era of Internet of everything, indoor and outdoor positioning information with high accuracy, high reliability, large capacity and low delay has became indispensable, which is vital for intelligent robots, unmanned driving and other unmanned platforms. The sensor positioning algorithm usually adopts time of arrival (ToA), difference of arrival (TDoA), angle of arrival (AoA), direction of arrival (DoA), frequency difference of arrival (FDoA), time of flight (ToF) and received signal strength indication (RSSI) [1, 2, 3, 4]. The sensor measurement for positioning comes from global navigation satellite systems (GNSS), Wi-Fi [5], RFID [6], Bluetooth [7], vision [8], UWB [9], etc. GNSS has been widely applied in various scenes; unfortunately, it is difficult to position in indoor and canyon environments due to its inherent fragility [10]. Although many other sensors are available, they have are defects such as a small coverage and high cost. Therefore, a single sensor is hard to position with high precision, high reliability and availability in challenging scenarios. Compared with a single sensor, multiple-sensor fusion can improve coverage, estimation accuracy and reliability because it combines the advantages of each information source. Multi-sensor fusion algorithms usually adopt Kalman filtering, support vector machine (SVM), Bayesian inference, Dempster-Shafer theory of evidence and artificial neural networks (ANN) [11]. The Kalman filter is frequently chosen for real-time fusion positioning in robotic applications because of its high computational efficiency. Multi-sensor fusion methods are mainly divided into centralized and distributed methods, where the difference is whether the original measurements are capable of direct fusion. The former can obtain a global optimal state estimation by expanded measurement equations and covariance matrix, but there are some drawbacks such as its computational complexity,fault tolerance and flexibility. The latter accesses a global optimal estimation from local filters. Distributed fusion methods include diagonal matrix, scalar weighted fusion and minimum covariance determinant (MCD) [12; 13], etc., which need covariance among local filters. However, it is difficult to obtain covariance in the actual scene. For the multi-sensor fusion estimation problem with an unknown covariance, [PERSON] and [PERSON] proposed a covariance intersection (CI) method, which uses the conservative error variance upper bound to avoid covariance calculation [14]. The accuracy of fusion positioning algorithms of batch covariance intersection (BCI) [15], sequential covariance intersection (SCI) [16] and parallel covariance intersection (PCI) [17] is limited because of the more conservative CI method. [PERSON] et al. showed an ellipsoid intersection (EI) algorithm, which used a common error to model the unknown correlation. The estimation accuracy of EI is better than CI [18]. However, EI has a worse robustness of fusion estimation because of its inconsistent estimation [19; 20]. [PERSON] et al. changed the parameters of EI to ensure consistency, and proposed an inverse covariance intersection (ICI) method [21]. Based on the ICI method, [PERSON] et al. designed a sequential inverse covariance intersection (SICI) fusion method for packet dropouts, which solved the fusion problem with unknown covariances and had good estimation performance [22]. [PERSON] et al. showed an information geometric fusion method [23], which adopted the information center of local posterior densities and had a high computational burden. The current research on fusion positioning with an unknown motion model mainly focuses on model uncertainty and has precise noise variance. However, sensor noise variance is time-varying and unknown due to the signal blocking, electromagnetic interference, working temperature, etc., in actual scenes. Moreover, the limited number of models and uncertain noise variance reduce positioning reliability and accuracy in actual scenes.