A novel artificial bee colony algorithm was introduced for the eruption event of the Sakurajima volcano on August 9, 2020, to invert the magma source characteristics below the volcano based on the point source Mogi model. Considering that the Sakurajima volcano is surrounded by sea, all the deformation data are used to obtain the location and magma eruption volume of the volcano. In response to the weak local search capability of the artificial swarm algorithm, the difference between the global optimal individual and the un-roulette screened individual is introduced as the variance component in the onlooker stage. Detailed simulation experiments verify the improvement of the algorithm in terms of convergence speed. In real experiments, the Sakurajima volcano inversion shows closer fitting results and smaller residuals compared to the existing literature. Meanwhile, the convergence speed of the algorithm echoes with the simulation experiments.

Geodetic functional models, stochastic models, and model parameter estimation theory are fundamental for geodetic data processing. In the past five years, through the unremitting efforts of Chinese scholars in the field of geodetic data processing, according to the application and practice of geodesy, they have made significant contributions in the fields of hypothesis testing theory, un-modeled error, outlier detection, and robust estimation, variance component estimation, complex least squares, and ill-posed problems treatment. Many functional models such as the nonlinear adjustment model, EIV model, and mixed additive and multiplicative random error model are also constructed and improved. Geodetic data inversion is an important part of geodetic data processing, and Chinese scholars have done a lot of work in geodetic data inversion in the past five years, such as seismic slide distribution inversion, intelligent inversion algorithm, multi-source data joint inversion, water reserve change and satellite gravity inversion. This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years, analyzes the methods used by scholars and the problems solved, and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.

This paper considers setting different dips for different sub-faults to fit the actual rupture situation based on the fault rupture of the 2013 Lushan M_S7.0 earthquake. Meanwhile, combined with the coseismic GNSS data of the Lushan earthquake, the source parameters and sliding distribution of the Lushan earthquake fault are inversed. Firstly, we use the gradient based optimizer (GBO) in nonlinear inversion to obtain the source parameters of this seismic fault. The inversion results indicate that the strike of the fault is 206.52°, the dip is 44.10°, the length is 21.92 km, and the depth is 12.79 km. To refine the sliding distribution of the seismic fault, the seismic fault is divided into 3 × 3 sub-faults. Then, we fix the central sub-fault dip of 44.10°; the dip of other sub-faults is obtained by iteration. After that, the model is further divided into a fault layer model composed of 23 × 19 sub fault slices, and using the Matlab fitting function is used to fit the dip of the 23 × 19 sub faults. Finally, the Lushan seismic fault plane is established as a shovel structure with steep upper and gentle lower, steep south and gentle north. The slip distribution inversion results indicate that the depth of the slip peak is 13 km, the corresponding maximum slip momentum is 0.67 m, the seismic moment is 1.10 × 10¹⁹ N·m and the corresponding moment magnitude is M_W6.66. The results above are consistent with the research results of seismology.

To estimate the parameters of the mixed additive and multiplicative (MAM) random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array, we introduce a derivative-free cat swarm optimization for parameter estimation. We embed the Powell method, which uses conjugate direction acceleration and does not need to derive the objective function, into the original cat swarm optimization to accelerate its convergence speed and search accuracy. We use the ordinary least squares, weighted least squares, original cat swarm optimization, particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity, respectively. The experimental results show that the improved cat swarm optimization has faster convergence speed, higher search accuracy, and better stability than the original cat swarm optimization and the particle swarm algorithm. At the same time, the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations. The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault parameters inversion has nonlinear characteristics, and the gradient-based optimizer (GBO) has the characteristics of fast convergence speed and falling into local optimum hardly. This paper applies GBO algorithm to simulated earthquakes and real LuShan earthquakes in the nonlinear inversion of the Okada model to obtain the source parameters. The simulated earthquake experiment results show that the algorithm is stable, and the seismic source parameters obtained by GBO are slightly closer to the true value than the multi peak particle swarm optimization (MPSO). In the 2013 LuShan earthquake experiment, the root mean square error between the deformation after forwarding of fault parameters obtained by the introduced GBO algorithm and the surface observation deformation was 3.703 mm, slightly better than 3.708 mm calculated by the MPSO. Moreover, the inversion result of GBO algorithm is better than MPSO algorithm in stability. The above results show that the introduced GBO algorithm has a certain practical application value in seismic fault source parameters inversion.

After the first Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC), the traditional method using least-squares extrapolation and autoregressive (LS + AR) models was considered as one of the polar motion prediction methods with higher accuracy. The traditional method predicts individual polar motion series separately, which has a single input data and limited improvement in prediction accuracy. To address this problem, this paper proposes a new method for predicting polar motion by combining the difference between polar motion series. The X, Y, and Y-X series were predicted separately using LS + AR models. Then, the new forecast value of X series is obtained by combining the forecast value of Y series with that of Y-X series; the new forecast value of Y series is obtained by combining the forecast value of X series with that of Y-X series. The hindcast experimental comparison results from January 1, 2011 to April 4, 2021 show that the new method achieves a maximum improvement of 12.95% and 14.96% over the traditional method in the X and Y directions, respectively. The new method has obvious advantages compared with the differential method. This study tests the stability and superiority of the new method and provides a new idea for the research of polar motion prediction.

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model (MAM error model), we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model. The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation. The experimental results show that based on the weighted least squares criterion, the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation. The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods, which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

The traditional genetic algorithm (GA) has unstable inversion results and is easy to fall into the local optimum when inverting fault parameters. Therefore, this article considers the combination of GA with other non-linear algorithms in order to improve the inversion precision of GA. This paper proposes a genetic Nelder-Mead neural network algorithm (GNMNNA). This algorithm uses a neural network algorithm (NNA) to optimize the global search ability of GA. At the same time, the simplex algorithm is used to optimize the local search capability of the GA. Through numerical examples, the stability of the inversion algorithm under different strategies is explored. The experimental results show that the proposed GNMNNA has stronger inversion stability and higher precision compared with the existing algorithms. The effectiveness of GNMNNA is verified by the Bodrum–Kos earthquake and Monte Cristo Range earthquake. The experimental results show that GNMNNA is superior to GA and NNA in both inversion precision and computational stability. Therefore, GNMNNA has greater application potential in complex earthquake environment.

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

When the total least squares (TLS) solution is used to solve the parameters in the errors-in-variables (EIV) model, the obtained parameter estimations will be unreliable in the observations containing systematic errors. To solve this problem, we propose to add the nonparametric part (systematic errors) to the partial EIV model, and build the partial EIV model to weaken the influence of systematic errors. Then, having rewritten the model as a nonlinear model, we derive the formula of parameter estimations based on the penalized total least squares criterion. Furthermore, based on the second-order approximation method of precision estimation, we derive the second-order bias and covariance of parameter estimations and calculate the mean square error (MSE). Aiming at the selection of the smoothing factor, we propose to use the U curve method. The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information, which validates the feasibility and effectiveness of the proposed method.