Conventionally, the filtering technique for attitude estimation is performed using gyros or attitude dynamics models. In order to extend the application range of an attitude filter, this paper proposes a quaternionbased filtering framework for gyroless attitude estimation without an attitude dynamics model. The attitude estimation system is established based on a quaternion kinematic equation and vector observation models. The angular velocity in the system is determined through observation vectors from attitude sensors and the statistical properties of the angular velocity error are analysed. A Kalman filter is applied to estimate the attitude error such that the effect from the angular velocity error is compensated with its statistical properties at each sampling moment. A numerical simulation example is presented to illustrate the performance of the proposed algorithm.
When the distribution of water quality samples is roughly balanced, the Bayesian criterion model of water-inrush source generally can obtain relatively accurate results of water-inrush source identification. However, it is often difficult to achieve desired classification results when training samples are imbalanced. Sample imbalance is common in the source identification of mine water-inrush. Therefore, we propose a three-dimensional (3D) spatial resampling method based on rare water quality samples, which achieves the balance of water quality samples. Based on the virtual water sample points distributed by the 3D grid, the method uses the 3D Inverse Distance Weighting (IDW) method to interpolate the groundwater ion concentration of the virtual water samples to achieve oversampling of rare water samples. Case study in Gubei Coal Mine shows that the method improves overall discriminant accuracy of the Bayesian criterion model by 5.26%, from 85.26% to 90.69%. In particular, the discriminative precision of the rare class is improved from 0% to 83.33%, which indicates that the method can improve the discriminant accuracy of the rare class to large extent. In addition, this method increases the Kappa coefficient of the model by 19.92%, from 52.26% to 72.19%, increasing the degree of consistency from “general” to “significant”. Our research is of significance to enriching and improving the theory of prevention and treatment of mine water damage.
The single-phase voltage loss is a common fault. Once the voltage-loss failure occurs, the amount of electrical energy will not be measured, but it is to be calculated so as to protect the interest of the power supplier. Two automatic calculation methods, the power substitution and the voltage substitution, are introduced in this paper. Considering the lack of quantitative analysis of the calculation error of the voltage substitution method, the grid traversal method and MATLAB tool are applied to solve the problem. The theoretical analysis indicates that the calculation error is closely related to the voltage unbalance factor and the power factor, and the maximum calculation error is about 6% when the power system operates normally. To verify the theoretical analysis, two three-phase electrical energy metering devices have been developed, and verification tests have been carried out in both the lab and field conditions. The lab testing results are consistent with the theoretical ones, and the field testing results show that the calculation errors are generally below 0.2%, that is correct in most cases.