Spherical Error Probable Research Articles

Research on the Shearer Positioning Method Based on SINS and LiDAR with Velocity and Absolute Position Constraints

Accurate positioning of the shearer with a strapdown inertial navigation system (SINS) is the key technology to realize the automation of the longwall face. Unfortunately, the existing positioning methods have a strong dependence on the attitude accuracy of the SINS. The position errors gradually increase with the drift of the SINS attitude. To reduce the dependence on the SINS attitude and further increase the shearer positioning accuracy, this paper proposes a positioning method based on SINS and light detection and ranging (LiDAR) with velocity and absolute position constraints. A Kalman filter (KF) model based on these constraints was established. Simulation analysis shows that the attitude calibration between the shearer body, SINS and LiDAR, and the initial attitude alignment of the SINS are the keys to determining the shearer positioning accuracy. Even if there are small horizontal bends in the running track of the shearer and the features have small horizontal errors, an excellent positioning effect can still be obtained. In addition, four cutting processes were simulated with a reciprocating travel of 44.6 m and an advance distance of 1.2 m. Compared with the relative positioning method, the positioning accuracy of the proposed method was improved by 37%, 63%, 76%, and 69% from the first to the fourth cutting cycle, respectively, calculated by spherical error probable (SEP) values, and positioning accuracy had a lower dependence on the installation deflection angles between the SINS, the LiDAR, and the SINS attitude accuracy.

Estimation of ionospheric delay of NavIC/IRNSS signals using the Taylor Series Expansion

The delay in Navigation with Indian Constellation (NavIC)/Indian Regional Navigation Satellite System (IRNSS) signals due to the ionosphere are decisive because it leads to significant changes in the positional accuracy of the system. In this paper, we try to estimate the ionospheric time delay (ionodelay) precisely using the local Taylor Series Expansion (TSE) algorithm for a single frequency NavIC/IRNSS system. The performance of the local TSE algorithm is examined by considering two cases. In case I, the TSE was validated under the influence of an intense geomagnetic storm (8 September 2017) by considering NavIC/IRNSS data from the Indian equatorial and Equatorial Ionization Anomaly (EIA) regions. In case II, based on the quiet and disturbed days data, the local TSE model was examined at different locations in the local area (<10 km) using two NavIC/IRNSS receivers (i.e. reference and rover). The results of ionodelay and positional accuracy (Three Dimensional Distance Root Mean Square [3DRMS], Circular Error Probability [CEP], and Spherical Error Probability [SEP]) of NavIC/IRNSS for both the cases indicates that the single frequency local TSE algorithm performs the same as the reference dual frequency model, where as the global eight coefficient Klobuchar and the regional Grid Ionospheric Vertical Error (GIVE) model behaves differently. Therefore, the single-frequency TSE model improves the performance of the NavIC/IRNSS receiver in the local area, and the mathematical coefficient computation and additional frequency hardware cost have been reduced, with the acceptance of a maximum 0.8 m of errors.

A Geometry Surveying Model and Instrument of a Scraper Conveyor in Unmanned Longwall Mining Faces

To maintain the straightness of an unmanned longwall mining face, a track geometry surveying model of the scraper conveyor was constructed based on the position of the shearer. A surveying instrument was developed employing an inertial measurement unit and axial encoder. Surveying tests were conducted using a longwall mining face mock-up, and the 3-D accuracy of the surveying instrument based on the mean radial spherical error and the spherical error probable (SEP) radius was determined to be 20.78 mm and 16.57 mm, respectively. The accuracy of the surveying system satisfied the requirements of a longwall mining face.

Modified Kalman Filter for GPS Position Estimation over the Indian Sub Continent

Position accuracy is the measure of a system's capability to provide quality estimates, which in turn depends mainly on measurement noise and the type of algorithm employed. Though many positioning algorithms have emerged, due to its exceptional performance in a wide range of real time applications, the Kalman Filter Estimator (KFE) is used often for their implementation. So this paper concentrates in improving its accuracy further while introducing a new observation matrix in its estimation process and succeeds in performing the same. This paper also extends the modified algorithm for GPS receiver position estimation over the Indian subcontinent. Real time data collected from GPS receiver located at IISC, Bangalore (Lat/Lon: 13.010N /77.560E), India is used to evaluate the performance of this developed algorithm called Modified Kalman Filter Estimator (MKFE). GPS Statistical Accuracy Measures (SAM) such as Circular Error Probability (CEP), Spherical Error Probability (SEP) etc. are used for performance evaluation. From the results it is observed that the proposed MKFE has faster convergence rate with high accuracy and is suitable for real time defence applications over the Indian subcontinent.

Analysis of Direct P(Y)-Code Acquisition

Global Positioning System (GPS) signal acquisition consists of a two-dimensional search in a time/frequency space to synchronize a receiver-generated reference signal with the received GPS signal in code phase and fre- quency. User uncertainties in code phase and frequency offsets determine the size of the region to be searched, and hence, the code acquisition time. Encrypted P(Y) code, transmitted on L 1 and L2 fiequen- ties, provides more precise (16 m - spherical error proba- ble (SEP)) user positioning inherently more jamming immunity than does C/A code. The purpose of this study is to explore and use existing signal detection concepts to quantify the time to achieve direct acquisition of the P(Y) code in a jamming environ- ment. Of particular interest is the mitigating effect paral- lel processing has in shrinking acquisition time in the presence of initial (receiver) position, time, velocity, and frequency errors and/or uncertainties.

Tightly Coupled IFOG-Based GPS Guidance Package

An interferometric fiber-optic gyroscope (IFOG)-based GPS Guidance Package (GGP) achieved 4 m spherical error probable (SEP) in an integrated GPS/inertial mode and 10 m error growth after 5 min without GPS reception under harsh field conditions. The 295 in 3 , 14 lb Phase 1 GGP systems were evaluated under controlled laboratory conditions and during van testing, as well as in a U.S. Army Fire Support Team Vehicle (FISTV). During the FISTV demonstration, the GGP significantly outperformed the Army's currently used equipment. The results of these tests validated the tightly coupled GPS/inertial design approach with fiber-optic sensors and the system's suitability for applications with demanding environmental requirements. Current development is focused on 0.8 nmi/h inertial performance and miniaturization of the system to a 100 in 3 , 7 lb package. The Phase 2 design provides capabilities of high dynamics and low jamming susceptibility, as well as adaptability to multiple military and commercial applications with a low-cost production system.

A series representation of the spherical error probability integral

The author derives an infinite series representation of the spherical error probability integral (SEPI). The SEPI characterizes missile miss distance distributions resulting from Monte Carlo simulations. The SEPI is used when these distributions occupy a three-dimensional region of space. Truncation of this series provides a computationally efficient tool for approximating the SEPI. A series convergence analysis is presented that provides an upper bound on the approximation accuracy. The accuracy bound may be used to determine a sufficient number of terms needed for approximation to any desired accuracy. Presentation of numerical results provides empirical confirmation of the validity of the series expression. Calculation of the truncated series and numerical integration of the SEPI generate the numerical results. It is shows that the SEPI converges to the circular error probability integral as the standard deviation of a given component approaches zero. Approximation error bounds, as a function of sigma, are derived. >

Two New Measures of Position Error

Circular average error (CAE) and spherical average error (SAE) are defined as alternatives to the circular error probable (CEP) and spherical error probable (SEP) as univariate measures of error ellipses and ellipsoids for two-and three-dimensional radars. Results are expressed graphically. Approximate formulas are given for all four measures.

A Computation of Radar SEP and CEP

Recently the concept of spherical error probable (SEP) has been gaining acceptance as a means of defining the error ellipsoid for radar accuracy in three dimensions. The corresponding quantity for a two-dimensional case is circular error probable (CEP). Both SEP and CEP are defined and a set of curves is given to determine their values for most radar situations.