Volume 13, Issue 2

Real-time Precise Point Positioning (RT PPP) is a primary positioning method used in natural hazard warning systems (NHWS) such as monitoring tsunami and earthquakes. The method relays on precise orbit and clock corrections to eliminate satellite-related errors and its performance can be significantly improved by using measurements from multi-GNSS constellations compared with using only one system, such as GPS. The Japanese Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) provides these corrections for GPS, GLONASS and QZSS satellites enabling a multi-GNSS RT-PPP. However, the accuracy of RT PPP will suffer a major decline in case of presence of an outage in receiving these corrections, for instance due to a temporary failure of the user modem. For that reason, a method is proposed to maintain RT PPP when such a break takes place. For short outages less than 30 minutes we predict MADOCA orbits using a Holt-Winters’ auto-regressive model, and for longer outages up to 1 hr, the most recent International GNSS Service (IGS) ultra-rapid orbits can be used, but only for GPS. In addition, the clock corrections are predicted as a time series using a linear model with sinusoidal terms. The best regression period to estimate the required model parameters is discussed based on analysis of the autocorrelation of the corrections. The prediction model parameters are estimated using a sliding time window. Evaluation of the proposed method showed that positioning accuracy of 15 cm was maintained during the prediction period, which is twice better than using IGS ultra-rapid predicted products. For NHSW, the displacement errors due to prediction errors were generally within ±6 cm with one min interval and ±10 cm with five min interval.

An apparent delay is occurred in GPS signal due to both refraction and diffraction caused by the atmosphere. The second region of the atmosphere is the ionosphere. The ionosphere is significantly related to GPS and the refraction it causes in GPS signal is considered one of the main source of errors which must be eliminated to determine accurate positions. GPS receiver networks have been used for monitoring the ionosphere for a long time. The ionospheric delay is the most predominant of all the error sources. This delay is a function of the total electron content (TEC). Because of the dispersive nature of the ionosphere, one can estimate the ionospheric delay using the dual frequency GPS. In the current research our primary goal is applying Precise Point Positioning (PPP) observation for accurate ionosphere error modeling, by estimating Ionosphere delay using carrier phase observations from dual frequency GPS receiver. The proposed algorithm was written using MATLAB and was named VIDE program. The proposed Algorithm depends on the geometry-free carrier-phase observations after detecting cycle slip to estimates the ionospheric delay using a spherical ionospheric shell model, in which the vertical delays are described by means of a zenith delay at the station position and latitudinal and longitudinal gradients. Geometry-free carrier-phase observations were applied to avoid unwanted effects of pseudorange measurements, such as code multipath. The ionospheric estimation in this algorithm is performed by means of sequential least-squares adjustment. Finally, an adaptable user interface MATLAB software are capable of estimating ionosphere delay, ambiguity term and ionosphere gradient accurately.

The best unbiased estimates of unknown parameters in linear models have the smallest expected mean-squared errors as long as the residuals are weighted with their true variance–covariance matrix. As this condition is rarely met in real applications, the least-squares (LS) estimator is less trustworthy and the parameter precision is often overoptimistic, particularly when correlations are neglected. A careful description of the physical and mathematical relationships between the observations is, thus, necessary to reach a realistic solution and unbiased test statistics. Global Navigation Satellite Systems and terrestrial laser scanners (TLS) measurements show similarities and can be both processed in LS adjustments, either for positioning or deformation analysis. Thus, a parallel between stochastic models for Global Navigation Satellite Systems observations proposed previously in the case of correlations and functions for TLS range measurements based on intensity values can be drawn. This comparison paves the way for a simplified way to account for correlations for a use in LS adjustment.

In the last two decades, the integration of a terrestrial laser scanner (TLS) and digital photogrammetry, besides other sensors integration, has received considerable attention for deformation monitoring of natural or man-made structures. Typically, a TLS is used for an area-based deformation analysis. A high-resolution digital camera may be attached on top of the TLS to increase the accuracy and completeness of deformation analysis by optimally combining points or line features extracted both from three-dimensional (3D) point clouds and captured images at different epochs of time. For this purpose, the external calibration parameters between the TLS and digital camera needs to be determined precisely. The camera calibration and internal TLS calibration are commonly carried out in advance in the laboratory environments. The focus of this research is to highly accurately and robustly estimate the external calibration parameters between the fused sensors using signalised target points. The observables are the image measurements, the 3D point clouds, and the horizontal angle reading of a TLS. In addition, laser tracker observations are used for the purpose of validation. The functional models are determined based on the space resection in photogrammetry using the collinearity condition equations, the 3D Helmert transformation and the constraint equation, which are solved in a rigorous bundle adjustment procedure. Three different adjustment procedures are developed and implemented: (1) an expectation maximization (EM) algorithm to solve a Gauss-Helmert model (GHM) with grouped t-distributed random deviations, (2) a novel EM algorithm to solve a corresponding quasi-Gauss-Markov model (qGMM) with t-distributed pseudo-misclosures, and (3) a classical least-squares procedure to solve the GHM with variance components and outlier removal. The comparison of the results demonstrates the precise, reliable, accurate and robust estimation of the parameters in particular by the second and third procedures in comparison to the first one. In addition, the results show that the second procedure is computationally more efficient than the other two.

The development of an algorithm to describe a dynamic system and to predict its future behaviour in further consequence is the aim of the present study. Non parametric models provide a general description of object dynamics and artificial neural networks (ANN), which are a very flexible and universal learning method, belong to it. However, the standard estimation procedures for ANN like Levenberg-Marquardt (LM) do not consider that data is observed and consequently is uncertain. The combination with the extended Kalman filter (EKF) enables the consideration of the uncertainty in the estimation process. The analogies between EKF and LM are discussed and thereon the advantages of the EKF are outlined. The integration of ANN into EKF will be evaluated on an industrial robot arm. At first, a simplified model is determined; the ANN describes the robot position deviations as a function of the joint encoder values. The robot reference positions are measured by a laser tracker. In order to compare it with the robot outputs, the observations need to be transformed to the robot frame and the offset between the end-effector and the robot flange has to be determined. A method to estimate both parameters simultaneously is developed and the results are verified on basis of simulated data. This paper comprises two novel approaches. First, uncertainty is considered in the ANN estimation on basis of the combination with the EKF. Considering the full covariance matrix of the robot deviations leads to a better prediction of the robot’s behaviour. Second, an integrated transformation and lever arm determination is introduced and the robot’s repeatability presents the limiting factor of the achievable parameter uncertainty.

The spherical cap harmonics (SCH) method can be used in regional geoid modeling. The core of this approach is the computation of its associated Legendre functions (ALF) with non-integer degree. However, it is unlikely to obtain a large number of zero-root values for the non-integer ALF. To overcome this problem, a new approach called virtual spherical harmonics (VSH) is proposed in this paper to transform the cap range into the whole sphere so that unlimited numbers of zero-root values can be obtained. The new approach was tested using four cap ranges with the radii of 30∘{30^{\circ }}, 15∘{15^{\circ }}, 10∘{10^{\circ }} and 5∘{5^{\circ }}, and geoid undulations for each of the regions are calculated from EGM2008. For each of the regions, the geoid undulations were used to construct three models with three different degrees of 20, 30 and 40. Numerical results showed that with the increase in the degree of the VSH model, the value of the maximum error decreases; and the maximum error of the model was less than 1 mm while the maximum degree is 40.