# Research on the SSUKF Integrated Navigation Algorithm Based on Adaptive Factors
## 1 Introduction
Since standard Kalman Filtering is only applicable to linear systems and not to nonlinear ones, the Extended Kalman Filter (EKF) was proposed, which linearizes the state transition and observation equations of a nonlinear system using a first- or second-order Taylor expansion [11] for state estimation. Building on this, scholars proposed the Error-State Extended Kalman Filter [12] (ESEKF), which estimates the error in the state vector to reduce the impact of nonlinearity on the system, though this approach can be computationally intensive for high-dimensional systems or complex models. Unscented Kalman Filtering (UKF) was firstly proposed by [PERSON] and [PERSON] in 1997 [13] and has gained widespread attention as a new filtering method in recent years [14]. Unlike EKF, UKF handles nonlinear systems more accurately through the \"unscented transformation\" rather than linearization. By using unscented transformation, UKF captures higher-order statistical information about the system state, providing higher estimation accuracy. However, UKF requires the computation of transformations and covariance matrices for multiple \"sampling points,\" which increases computational complexity and resource consumption [15]. Other researchers have proposed a model predictive-based unscented Kalman Filter (MP-UKF) to improve the adaptiveness of UKF [16]. To further improve the computational efficiency and accuracy of UKF, researchers proposed the Sim plified Spherical Unscented Kalman Filter [17] (SSUKF). SSUKF is an improved version of UKF, designed to address the state estimation problem for high-dimensional nonlinear systems and optimize computational efficiency in certain application scenarios. This method simplifies some of the computational steps of UKF [18], incorporating spherical geometry features to improve both the algorithm's accuracy and computational efficiency. In situations where measurements are unreliable, various adaptive Kalman filters have been developed for practical applications in different fields. Adaptive filters based on functional models and stochastic models are two adaptive filtering strategies, including multi-model-based adaptive estimation [19] and innovation-based adaptive estimation strategies [20]. Unlike the two strategies mentioned above, some researchers have developed an adaptive robust filter by introducing an adaptive factor estimation method [21]. This adaptive robust filter provides both adaptability and robustness and has been successfully applied in many applications [22; 23]. However, these methods assume constant measurement noise characteristics and have high computational complexity. SSUKF typically relies on fixed-noise models and prior knowledge, making it unable to promptly perceive the characteristics of observational data in complex environments [24] (such as sensor noise, environmental changes, etc. ), which limits its ability to provide sufficiently accurate estimates and can even lead to failure due to inaccurate prior assumptions. To address this issue, this paper proposes an Adaptive Simplified Spherical Unscented Kalman Filter (ASSUKF), which adjusts the noise covariance matrix using an adaptive factor based on the error in the state vector, resulting in more accurate state estimation. The proposed method can dynamically adjust the noise covariance matrix to adapt in real time to changes in the system state and environment, providing high-precision estimates even in environments with high uncertainty. Unlike traditional filtering methods that rely on fixed-noise models, ASSUKF can adaptively adjust based on actual observation data, suppressing filter divergence and demonstrating higher precision and robustness.