# Improved Adaptive Federated Kalman Filtering for INS/GNSS/VNS Integrated Navigation Algorithm
## 1 Introduction  
In recent years, with the rapid development of unmanned autonomous systems, the application fields of unmanned vehicles have become increasingly extensive. After major natural disasters, buildings such as houses and bridges may collapse, forming a sheltered space. Due to the complex environment and narrow and dim space, satellite signals are easily interfered with or blocked, which often leads to the failure of the navigation and positioning of unmanned vehicles in the sheltered space. Therefore, providing accurate, reliable, and real-time navigation information such as position, velocity, and attitude for unmanned vehicles in obstructed spaces is an important guarantee for obtaining disaster information and improving search and rescue efficiency and has significant importance. Inertial navigation systems (INSs) [1] have the advantages of small size, easy integration, and pure autonomy, and they are widely used in various navigation fields. However, the errors [2, 3] of INSs accumulate rapidly over time. INS/GNSS [4, 5, 6] can obtain higher-precision carrier velocity and position information using the global navigation satellite system [7] (GNSS). Visual navigation systems [8, 9] (VNSs) can obtain the high-precision attitude information of a carrier, but they suffer from the drawbacks of increased measurement error in environments with insufficient feature points or significant changes in illumination. Therefore, combining INS, GNSS, and VNS can compensate for their respective shortcomings and further improve the positioning accuracy [10] of unmanned vehicle navigation systems in complex scenarios. A centralized Kalman filter [11; 12; 13] can achieve multi-source fusion navigation using the effective information from various sensors for optimal estimation, thus achieving a higher positioning accuracy. However, as the dimension of the state vector increases, the consumption of computational resources increases, and real-time performance deteriorates. [PERSON] et al. [14; 15] proposed a federated Kalman filter [16; 17] (FKF), which utilizes the principle of information distribution, not only reducing the computational load but also improving the fault-tolerant performance of integrated navigation. In an FKF, all sub-filters evenly distribute the information sharing factor (ISF) [11; 18; 19] for information sharing. However, in practical applications, the performance and estimation accuracy of subsystems constantly change with the complexity of the navigation environment, and the fixed ISF in an FKF cannot meet the different navigation requirements of the navigation system in complex scenarios. [PERSON] et al. [20] combined an odometer with an INS/GPS integrated navigation system and proposed a strategy of using an adaptive information allocation factor, which improved the disturbance rejection capability of the integrated navigation system. [PERSON] et al. [21] used a dual-state chi-square detection algorithm to calculate the parameters corresponding to each state, ensuring that states with a higher accuracy obtain a larger information distribution coefficient. [PERSON] et al. [22] proposed an adjustment strategy using a degree of abnormality to correct the error covariance matrix and Kalman gain, which improved the fault tolerance and accuracy of the positioning system. [PERSON] et al. [23] proposed a time-varying information sharing factor adaptive federated Kalman filter. In a complex GNSS environment, the proposed adaptive information fusion strategy could autonomously adjust the information sharing factors and their error states of each navigation sensor. [PERSON] et al. [24] developed a novel adaptive federated interacting multiple model (IMM) filter for autonomous underwater vehicle integrated navigation systems. The information sharing coefficients of the adaptive federated IMM filter are dynamically adjusted based on the performance of each local system, ensuring the optimal fusion of information from different sources. [PERSON] et al.