# An Improved Multi-Sensor Fusion Navigation Algorithm Based on the Factor Graph
## 1 Introduction  
In recent years, the use of low-cost miniature unmanned aerial vehicles (MUAVs) for civilian applications has evolved from imagination to actual implementation. Systems have been designed for environmental monitoring, search and rescue, mapping, and mining and post seismic emergency management [1; 2; 3; 4; 5]. In order to obtain an acceptable cost/benefit ratio of these systems, there have been many techniques to reduce the cost including the aspects of the sensor, the platform, and the algorithm [6]. However, cost reduction of the sensor can lead to lower stability and accuracy, which is directly related to the reliability of the system. Thus, dependence on a single sensor cannot satisfy the demand and makes it difficult to obtain the accurate response to external environment. Through integrated usage of multiple-source information, people can get more objective and intrinsic knowledge of a certain target [7]. As a matter of fact, multi-sensor integrated navigation is becoming a hot area of research. Many studies focus on the integration of the GPS/INS system with additional sensors such as magnetometers, cameras, ultrasonic sensors, laser scanners, barometers, or earth/sun/star sensors [8]. The combination scheme can make use of all information from these sensors and overcome their limitations, which allows for the provision of reliable navigation solutions [9]. In order to achieve the optimal solution in the integrated navigation, the fundamental problem is information fusion [10]. In general, multi-sensor information fusion is a form of sensor integration, which involves combining the outputs of different sensor systems to obtain a better estimate of what they are sensing according to some fusion rules [11; 12]. Nowadays, multi-sensor data fusion has attracted widespread attention, its theory and methods have been applied to a lot of research fields [13; 14]. The conventional approach employed in reference [15] uses the centralized Kalman filtering method which processes all of the measurements at a central processor and provide a global optimal estimate. The advantage of this method is that it involves minimal information loss. However, the centralized filter can result in a large computational burden and poor fault tolerance due to overloading of the filter with too many data [16]. To deal with these problems, decentralized information fusion methods [17; 18; 19] have been developed in fields such as distributed control systems and integrated navigation. In decentralized fusion, a processor at the center of the network is used to manage all nodes. The decentralized fusion algorithms are based on the global optimality criterion, which has reasonable fusion accuracy, good fault-tolerance, and lower computing effort requirements. Among them, the federated Kalman filtering algorithm [20] and the parallel Kalman filtering algorithm [21] are representative. However, if the dimensions of the measurement vector are too high, the order of the measurement noise covariance matrix complicates the calculation of an inverse. Dempster-Shafer theory (DST) is an efficient method to deal with incomplete data coming from different information sources in data fusion [22]. It does not rely on any prior knowledge of the probability distribution. Thus, how to combine the information from different sources, which may be conflicting, becomes a challenging problem in complex decision making. The method referred in reference [23] focuses on the research on sequential decentralized filters. This method saves a great deal of computing time, especially for the systems with some measurement delays within one sampling period, where the updates are operated without waiting for all the data [24]. However, in the practical applications, an MUAV may be equipped with a set of multi-rate sensors, and these sensors generally operate at different frequencies. So it may complicate the processing of these measurements [25]. In addition, the output signals of some sensors appear non-linear in character.