Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods

Mustafin, M.G.; Bykasov, D. A.

doi:10.3390/computation9120131

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…After vector state updating performed by (16) as well as the error covariance matrix of the state estimation (17), the error should be set to zero:…”

Section: Es Ekf Error Resetmentioning

confidence: 99%

“…This method increases the reliability of the system along with the accuracy of estimated parameters by merging information from a collection of sensors. On the other hand, by providing redundant measurements this method results in significant computational costs and requires the use of powerful CPUs or special optimization techniques [16,17].…”

Section: Introductionmentioning

confidence: 99%

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Error State Extended Kalman Filter Localization for Underground Mining Environments

2023

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The article addresses the issue of mobile robotic platform positioning in GNSS-denied environments in real-time. The proposed system relies on fusing data from an Inertial Measurement Unit (IMU), magnetometer, and encoders. To get symmetrical error gauss distribution for the measurement model and achieve better performance, the Error-state Extended Kalman Filter (ES EKF) is chosen. There are two stages of vector state determination: vector state propagation based on accelerometer and gyroscope data and correction by measurements from additional sensors. The error state vector is composed of the velocities along the x and y axes generated by combining encoder data and the orientation of the magnetometer around the axis z. The orientation angle is obtained from the magnetometer directly. The key feature of the algorithm is the IMU measurements’ isolation from additional sensor data, with its further summation in the correction step. Validation is performed by a simulation in the ROS (Robot Operating System) and the Gazebo environment on the grounds of the developed mathematical model. Trajectories for the ES EKF, Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) algorithms are obtained. Absolute position errors for all trajectories are calculated with an EVO package. It is shown that using the simplified version of IMU’s error equations allows for the achievement of comparable position errors for the proposed algorithm, EKF and UKF.

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“…After vector state updating performed by (16) as well as the error covariance matrix of the state estimation (17), the error should be set to zero:…”

Section: Es Ekf Error Resetmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error State Extended Kalman Filter Localization for Underground Mining Environments

2023

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“…The advantages of the application of search methods of nonlinear programming for processing results of geodetic measurements, including works on geodetic monitoring are marked in many publications by Russian and foreign authors [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

2023

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While carrying out work to ensure the technical safety of buildings and structures in the Arctic regions, one of the important stages is geodetic monitoring. Provided that the complexity of ensuring the stability of reference points in the Arctic zone when conducting geodetic monitoring of engineering facilities, geodetic networks should preferably be equated as free, i.e., to equate the reference points on a par with the defined ones. The present article provides variants how to to equalize geodetic networks to carry out a search method of non-linear programming, which is given a theoretical substantiation for the method and the order of estimating accuracy of the outcomes of the equalization of the generalized Makarov method. The procedure of pseudo transformation of a matrix of normal equations of unknowns with the application of an algorithm of a search method of nonlinear programming is given. The correctness of the application of the search method to the pseudo transformation of a matrix of normal equations of unknowns by the coincidence of outcomes of the pseudo transformation of the given matrix based on skeleton expansion done in M. Mashimov's work is proved. Equalization and estimation of accuracy of free leveling network with the application of search method and generalized Makarov's method are carried out. The conclusion about the correctness of the application of a search method of nonlinear programming for the processing of free geodetic networks at the performance of geodetic monitoring of buildings and constructions in the Arctic area is made.

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“…In the works [17,18], the tunnel face stability of flat-lying formation is analyzed. An approach to assessing the tunnel face stability is described from the point of view of two limiting state, exceeding the criteria of which leads to the impossibility of construction the tunnel, loss of serviceability, determined by subsidence on the surface [19]. An analytical review of approaches to the assessment of subsidence on the surface is presented in [20].…”

mentioning

confidence: 99%

Prediction of the stress-strain state and stability of the front of tunnel face at the intersection of disturbed zones of the soil mass

Protosenya

Alekseev

Verbilo

2022

PMI

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The article presents a numerical solution of the spatial elastic-plastic problem of determining the stability of the tunnel face soils at the intersection of disturbed zones of the soil mass. The relevance of the study is related to the need to take into account the zones of disturbed soils when assessing the face stability to calculate the parameters of the support. Based on the finite element method implemented in the PLAXIS 3D software package, the construction of a finite element system "soil mass-disturbance-face support" and modeling of the intersection of the disturbed zones of the soil mass were performed. To assess the condition of soils, deformation and strength criteria are taken. The deformation criterion is expressed by the value of the calculated displacement of the tunnel contour in the face, and the strength criterion - by the safety coefficient until the maximum values of the stress state are reached according to the Coulomb–Mohr criterion. The results of the study are presented in the form of histograms of the safety coefficient dependences on the distance to the disturbance at different bending stiffness of the face support structure, as well as the isofields of deformation development. The parameters of rockfall formation in the face zone at the intersection of zones of disturbed soils were determined. The local decrease in strength and deformation properties in the rock mass along the tunnel track should be taken into account when assessing the stability of the tunnel face and calculating the parameters of the support. Within the framework of the constructed closed system, a qualitative agreement of the simulation results with the case of a collapse in the face during the construction of the Vladimirskaya-2 station of the St. Petersburg Metro was obtained.

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Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods

Cited by 8 publications

References 25 publications

Error State Extended Kalman Filter Localization for Underground Mining Environments

Error State Extended Kalman Filter Localization for Underground Mining Environments

Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

Prediction of the stress-strain state and stability of the front of tunnel face at the intersection of disturbed zones of the soil mass

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