For precise point positioning (PPP), Kalman filter is usually used to estimate the position and velocity parameters. But, the positioning accuracy and convergence time are highly susceptible to gross errors in observations and dynamic model errors in motion states. In addition, the weights of different types of observation are generally determined by the prior variance are usually inaccurate, which affects the performance of PPP. In order to achieve a more desirable positioning solutions, an improved robust adaptive filtering method is proposed. First in this method, classification robust equivalent weight model based on t-test statistic is developed to construct the equivalent weight matrix for each types of observation separately. Second, variance component estimation weighting method based on innovations is proposed to determine the scale factor of each types of observation. Finally, adaptive factor function model based on innovations is adopted to acquire the optimal adaptive factor. The availability of the proposed classification robust equivalent weight model and variance component estimation weighting method are verified with the static test data, and the performance of the improved robust adaptive filtering method is further validated with the dynamic test data. The results indicate that compared with the conventional robust adaptive filter, the improved one has a better performance in positioning accuracy, convergence time, and the stability of PPP.

The accurate weighting of pseudorange observations is important to improve the convergence time and positioning quality of Precise Point Positioning (PPP). Currently, the weight of a pseudorange observation is mainly determined with empirical stochastic models. However, in a complex environment, due to the inability to adapt for the dynamic changes of the user environment, the empirical stochastic models usually cannot reflect the real error level of pseudorange observations. To address this problem, a resilient adjustment method to weigh pseudorange observations is proposed, which constructs the real-time estimation and inflation model for the variance of pseudorange multipath error and measurement noise to replace the empirical stochastic model to determine the weights of pseudorange observations. A set of static and dynamic Global Positioning System (GPS) test data are used to verify the effectiveness of the proposed method. The test results indicate that the proposed real-time estimation model can provide a better representation of the pseudorange accuracy, and the positioning performance of PPP using the real-time estimation model is better than that with the empirical stochastic model. Compared with the optimal empirical stochastic model, the positioning accuracy of PPP with the real-time estimation model is improved by at least 20%, and the convergence time is reduced by at least 50%.

In recent years, Wireless Sensor Networks (WSNs) have seen increasing application in GPS-Denied environments, such as indoor localization and mobile robot navigation. Among various positioning algorithms, the Least Squares Method is widely used for its simplicity and robustness. While numerous optimization algorithms have been developed to reduce localization error, comprehensive studies on the sources and propagation of positioning errors remain limited.This paper focuses on the error propagation mechanisms in range-based WSN localization. It conducts an in-depth analysis of the primary sources of positioning error, including ranging errors, anchor node position errors, and the influence of network topology on error propagation. A novel, simplified error propagation model based on covariance theory is proposed to quantitatively estimate the cumulative impact of these errors on localization accuracy.To evaluate the accuracy and practicality of the proposed algorithm, comprehensive assessments were carried out through both MATLAB simulations and physical experiments in representative indoor environments. The results show that the average discrepancy between the estimated and actual positioning errors remains within a few centimeters, demonstrating strong predictive capability. Furthermore, the Geometric Dilution of Precision is introduced to assess the influence of base station configurations. The experimental results further confirm that the proposed algorithm maintains strong robustness even in suboptimal geometric configurations of the network. In conclusion, the error propagation model proposed in this study not only significantly simplifies the theoretical computation of localization errors but also offers high accuracy in error estimation, making it particularly suitable for multi-sensor fusion scenarios that require precise error modeling. It also provides new insights and quantitative tools for optimizing WSN structures and improving overall localization performance.

The integrity of airborne inertial navigation systems (INSs) is the key to ensuring the safe flight of civil aircraft. The airborne attitude and heading reference system (AHRS) is introduced into the construction of a redundant inertial navigation system. As a backup system for an airborne INS, the AHRS exhibits a different device performance. A sequential weighted generalized likelihood ratio test (SWGLT) method, based on a principal component parity vector (PPV), is proposed. The PPV method improves the adaptability of the detection threshold to the inertial sensors’ noise and improves the probability of correct detection. At the same time, the multiscale problem of a heterogeneous redundant system error is solved by sequential weighting, and the false alarm rate is reduced. Simulation experiments show that the proposed method can improve fault detection sensitivity, reduce false alarm rates, and ensure the integrity of civil aircraft navigation systems.

During civil aviation flights, the aircraft needs to accurately monitor the real-time navigation capability and determine whether the onboard navigation system performance meets the required navigation performance (RNP). The airborne flight management system (FMS) uses actual navigation performance (ANP) to quantitatively calculate the uncertainty of aircraft position estimation, and its evaluation accuracy is highly dependent on the position estimation covariance matrix (PECM) provided by the airborne integrated navigation system. This paper proposed an adaptive PECM estimation method based on variational Bayes (VB) to solve the problem of ANP misevaluation, which is caused by the traditional simple ANP model failing to accurately estimate PECM under unknown time-varying noise. Combined with the 3D ANP model proposed in this paper, the accuracy of ANP evaluation can be significantly improved. This enhancement contributes to ensured navigation integrity and operational safety during civil flight.