High-precision coordinate transformation is vital for high-quality data fusion involving different coordinate systems. The transformation precision is mainly evaluated by the transformation parameters’ estimation precision, the root mean square error (RMSE) of the conversion of common points, or the RMSE of the conversion of check points. However, there are a number of issues associated with the rotation parameters’ precision estimated by the existing transformation methods. First, the estimated precision is related to the rotation matrix, so it is not suitable for scenarios where different rotation matrices are used. Second, the RMSE of the conversion of check points may not be consistent with the RMSE of the conversion of common points, so that the RMSE of the conversion of common points should not be used as a transformation precision index. In addition, some engineering applications do not have check points, and many applications need to know which range of points can meet our requirements. To deal with these limitations, this paper proposes a new way to calculate the translation parameters and evaluate the transformation precision. A lot of experimental data was used to verify the effectiveness and applicability of the proposed transformation model.

The precision of target-based registration is related to the geometry distribution of targets, while the current method of setting the targets mainly depends on experience, and the impact is only evaluated qualitatively by the findings from empirical experiments and through simulations. In this paper, we propose a new quantitative evaluation model, which is comprised of the rotation dilution of precision ( $rDOP$ , assessing the impact of targets’ geometry distribution on the rotation parameters) and the translation dilution of precision ( $tDOP$ , assessing the impact of targets’ geometry distribution on the translation parameters). Here, the definitions and derivation of relevant formulas of the $rDOP$ and $tDOP$ are given, the experience conclusions are theoretically proven by the model of $rDOP$ and $tDOP$ , and an accurate method for determining the optimal placement location of targets and the scanner is proposed by calculating the minimum value of $rDOP$ and $tDOP$ . Furthermore, we can refer to the model ( $rDOP$ and $tDOP$ ) as a unified model of the geometric distribution evaluation model, which includes the $DOP$ model in GPS.

Focusing on the global integrity monitoring performance of the BDS-3, the integrity failure model and effect analysis (IFMEA) of the system space segment and the ground control segment were carried out, and the system integrity risk tree model was established according to the IFMEA results. To evaluate the system’s integrity risk probability more reasonably, this paper establishes an abnormal event prediction model with a Bayesian method, based on actual operation data, under a situation in which the BDS-3 just opened service. With statistical analysis results of system anomalies since 27 December 2018—which is the date the BDS-3 began providing basic service—according to the anomaly prediction model, the system’s integrity risk probability under the 95% confidence limit was calculated to be approximately 0.9e-7/h, meeting the design index requirements of 1e-7/h. The analysis results also show that the main risk factors affecting the integrity of BDS-3 are ‘pseudorange measurement anomaly’ and ‘miss-detection of satellite autonomous integrity monitoring’. The results are important references with practical engineering significance for improving the integrity performance of BDS-3.

Precise and rapid extraction of spherical target features from laser point clouds is critical for achieving high-precision registration of multiple point clouds. Existing methods often use linear models to represent spherical target characteristics, which have several drawbacks. This paper proposes a rigorous estimation algorithm for spherical target features based on least squares configurations, in which the point-cloud data error is used as a random parameter, while the spherical center coordinates and radius are used as nonrandom parameters, emphasizing correlation between spherical parameters. The implementation details of this algorithm are illustrated by deriving calculation formulas for three variance–covariance matrices: variance–covariance matrices of the new observations, variance–covariance matrices of the new observation noise, and variance–covariance matrices of random parameters and the new observation noise. Experiments show that the estimation accuracy of sphere centers using our method is improved by at least 5.7% compared to classical algorithms, such as least squares, total least squares, and robust weighted total least squares.