Systematic error is one of the major factors that affect positioning accuracy owing to the changeable and complex nature of seawater environments. Based on a Global Navigation Satellite System-acoustic intelligent buoys system, whose acoustic array consists of a series of surface buoys, a single-difference method for underwater dynamic positioning is proposed to eliminate systematic error. Positioning configuration optimisation was addressed using dilution of precision (DOP). A simulation of DOP proved that for the single-difference method, a radiation network with a centre-difference reference point was superior to a regular polygon network. The positioning experiment showed that the novel method could effectively eliminate systematic error, improving vertical positioning accuracy from a metre- to a decimetre scale.

Exact knowledge of the position and proper calibration of robots that move by wheels form an important foundation in mobile robot applications. In this context, a variety of sensory systems and techniques have been developed for accurate positioning of differential drive mobile robots. This paper, first, provides a brief overview of mobile robots positioning techniques and then, presents a new benchmark method capable of calibrating mobile robots with differential drive mechanisms to correct systematic errors. The proposed method is compared with the commonly used University of Michigan Benchmark (UMBmark) odometry method. Two sets of comparisons are conducted on six prototyped robots with differential drives. The first set of tests establishes the workability and accuracy that can be achieved with the new method and compares them with the ones obtained from the UMBmark technique. The second experiment compares the performance of a mobile robot, calibrated with either the UMBmark or the new method, for an unseen path. It is demonstrated that the proposed method of calibration is simple to implement, and leads to accuracy comparable to the UMBmark method. Specifically, while the error corrections in both methods are within ±5% of each other, the proposed method requires single straight line motion for calibration, which is believed to be simpler and less timely to implement than the square path motion required by the UMBmark technique. The method should therefore be considered seriously as a new tool when calibrating differential drive mobile robots.

Context: Setup error significantly affects the accuracy of treatment and outcome in high precision radiotherapy.

Aims: To determine total, systematic, random error and clinical target volume (CTV) to planning target volume (PTV) margin with alpha cradle (VL) and ray cast (RC) immobilisation in abdominopelvic region.

Methods and material: Setup error was compared by using digitally reconstructed radiograph (DRR) as reference image with electronic portal image (EPI) taken during the treatment. Statistical analysis used: The total errors in mediolateral (ML), craniocaudal (CC) and anteroposterior (AP) directions were compared by t-test. For systematic and random errors variance ratio test (F-statistics) was used. Margins were calculated using International Commission of Radiation Units (ICRU), Stroom’s and van Herk’s formula.

Results: A total number of 306 portal images were analysed with 144 images in RC group and 162 images in VL group. For VL, in ML, CC, AP directions systematic errors were, in cm, (0.45, 0.29, 0.41), random errors (0.48, 0.32, 0.58), CTV to PTV margins (1.24, 0.80, 1.25), respectively. For RC, systematic errors were (0.25, 0.37, 0.80), random error (0.46, 0.80, 0.33), CTV to PTV margins (0.82, 1.30, 1.08), respectively. The difference of random error in CC and AP directions were statistically significant.

Conclusions: Geometric errors and CTV to PTV margins are different in different directions. For abdomen and pelvis in VL immobilisation, the margin ranged from 8 mm to 12.4 mm and for RC it was 8.2 mm to 13 mm. Therefore, a margin of 10 mm with online correction would be adequate.

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

Three-dimensional (3D) grain sizes and size distribution functions (SDFs) are generally obtained by converting the 2D or ID grain sizes to 3D with the methods based on a spherical grain shape model (S-model), which can produce large systematic errors. In this report, a new polyhedral grain model (P-model) is developed and experimentally checked with the directly measured 3D grain sizes. The results show that the systematic error originating from the S-model can be corrected by using the new polyhedral grain model.