# Summary of Lunar Constellation Navigation and Orbit Determination Technology
## 3 Overview of Single-Satellite Navigation and Orbit Determination Methods
### Navigation Data Processing Technology  
A navigation algorithm, which can use the navigation information containing noise to achieve the state estimation of the target, is one of the most important directions in research into navigation technology methods. The first estimation algorithm used for satellite navigation is the least squares algorithm (LS). Least squares estimation uses the minimum sum of squares of the residuals as the risk function and does not make any assumptions about the observation sample. Because of its wide applicability and ease of operation, it is widely used in navigation calculations. The parameters of interest, as well as the dominant error sources, are often time-varying. If these time variations can be modeled, the parameters can be resolved based on minimum mean squared error prediction, filtering and smoothing techniques [44]. Of the  
Figure 6: Basic principles of spaceborne GNSS orbit determination. various such techniques, the most commonly used filter methods in navigation research include the Kalman filter (KF) [45], extended Kalman filter [46], unscented Kalman filter [47] and improved algorithms based on these filter methods. The EKF algorithm is simple to calculate and easy to implement. However, due to errors introduced by the linearization process, the estimation accuracy of highly nonlinear problems is poor. Although the UKF algorithm avoids the linearization errors introduced in Taylor approximation, it is still based on the Gaussian assumption. [PERSON] et al. provide a good example of filtering and processing in direct lunar transfers using UKF [48]. Whether it is KF, EKF or UKF, they all require relatively accurate a priori statistical information on the system model and measurement model noise, but any statistical information has a certain degree of distortion. When the prior noise statistics error is large, the accuracy of the navigation filter methods will decrease or even diverge. In order to reduce the influence of prior noise statistical information distortion on EKF and UKF, scholars have proposed the Sage-Husa filter [49; 50], evanescent filter [51; 52], robust adaptive filter [53; 54; 55], multi-model adaptive filter and other adaptive filter methods. The Sage-Husa [56] adaptive filter method calculates the observation residual or prediction residual by selecting the observations within an observation epoch interval, and then re-estimates the system noise covariance matrix \(\mathbf{Q}\) and the measurement noise covariance matrix \(\mathbf{R}\). This method adaptively estimates system and measurement noise based on real-time measurement conditions, thereby improving the accuracy and reliability of sensor measurement data. [PERSON] proposed an evanescent filter algorithm [57] for system state model errors. Specifically, the method of determining the forgetting factor enables the filtering algorithm to still maintain a certain optimality when there is an error in the state model or the state is disturbed. [PERSON] and others proposed a robust adaptive filter algorithm [58] to address the status and measurement anomalies existing in dynamic carrier navigation to improve the accuracy of dynamic carrier navigation. [PERSON] et al. proposed multi-model based adaptive estimation (MMAE) from the perspective of model adaptation [59]. Compared with a single model, the multi-model adaptive estimation method estimates through a set of parallel filtering estimators, and calculates the model probability at all times, which meets the needs of changing noise sequences in this process and can achieve an adaptive effect. Depending on the model characteristics and noise characteristics of the navigation systems, the navigation filter algorithms used are also different. Applicable algorithms need to be designed for different navigation systems to improve the accuracy of state estimation. The navigation system will suffer external interference during operation, and this interference may have a greater impact on the state estimation results.