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This paper aims to present a novel transfer alignment method based on combined double-time observations with velocity and attitude for ships’ poor maneuverability to address the system errors introduced by flexural deformation and installing which are difficult to calibrate.

Based on velocity and attitude matching, redesigning and deducing Kalman filter model by combining double-time observation. By introducing the sampling of the previous update cycle of the strapdown inertial navigation system (SINS), current observation subtracts previous observation are used as measurements for transfer alignment filter, system error in measurement introduced by deformation and installing can be effectively removed.

The results of simulations and turntable tests show that when there is a system error, the proposed method can improve alignment accuracy, shorten the alignment process and not require any active maneuvers or additional sensor equipment.

Calibrating those deformations and installing errors during transfer alignment need special maneuvers along different axes, which is difficult to fulfill for ships’ poor maneuverability. Without additional sensor equipment and active maneuvers, the system errors in attitude measurement can be eliminated by the proposed algorithms, meanwhile improving the accuracy of the shipboard SINS transfer alignment.

Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.