For other types of easing curves and ultrahigh-curvature function expression, the reader can refer to the literature [61]. This coordinate system is a rectangular coordinate system (X, Y, Z) which follows the orthogonal "right hand" rule. {\displaystyle \textstyle {M_{r}}\,\!} When SNR is low to −25 dB, the range–slow time image of the target is given in Fig. The displacements in both coordinate systems are shown in Figure 1.13. [5] France adopted Greenwich Mean Time in place of local determinations by the Paris Observatory in 1911. In terms of the Euler angles φ, ψ and ω shown in Fig. Most of the current research is on the first line of discrete points, and then fitted to a cubic spline curve [59−60][59][60]; this method is well adapted to existing railway-related research. Therefore, the micro-Doppler features corresponding to the three rotational scatterers are extracted reasonably successfully. Examples of JACK (left) and AMS (right) coordinate systems. Several body scatterers randomly distribute around the rotation center. Micro-Doppler Features Extracted by Complex Image OMP Decomposition (in the Third Situation). 4.6). The Equator divides the globe into Northern and Southern Hemispheres. The OMP decomposition results of micro-Doppler signal are shown in Table 5.8. This is a reasonable assumption, taking into account that for beam structures, the cross-section dimensions are relatively small compared to the beam-wise dimension. 5.25A shows the range–slow time image of the target when the SNR is −10 dB. Likewise, the nodal force qi is related to the global components QX,i and QY,i by, It follows that nodal forces and displacements in global coordinates are related by, where [ke], the member stiffness matrix in global coordinates, is, and [T], a coordinate transformation matrix, is, The cosine and sine in the above equations are given by, where (Xi, Yi) and (Xj, Yj) are the coordinates of nodes i and j, respectively, and L is the length of the member. By continuing you agree to the use of cookies. 5.26A. Then the residual signal is decomposed with the dictionary constructed according to Eq. 17, June 10, 1975. Cartesian coordinates simplify many mathematical calculations. The prime meridian determines the proper Eastern and Western Hemispheres, although maps often divide these hemispheres further west in order to keep the Old World on a single side. To achieve uniform motion in DHMs, coordinate systems must be either communicated in protocols or standardized. Because the power of the micro-Doppler signal is much lower than that of the body echoes, the micro-Doppler curves in the figure are much obscured. High-speed railways in our country have adopted slow–round–slow standard railway lines, for which curvature, angle, and coordinates of the center line of the ideal line can be expressed as in Eqs. Fig. Three scatterers rotate around C and all of their angular velocities and radii are ω = (0,0,4π)T rad/s and ‖C′P′→‖=5.6569m, respectively. After obtaining the direction cosines, the element matrices in the global coordinate system can be obtained. Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. This problem does not exist in the isoparametric formulation using the natural coordinates, because the transfer mapping effectively equips every element with the same idealized geometry where ξ and η both range from −1 to 1 along the horizontal and vertical axes, respectively. Three scatterers rotate around C and all of their angular velocities and radii are ω = (0,0,4π)T rad/s and ‖C′P′→‖=2.8284m, respectively. Micro-Doppler feature extraction when scattering coefficients are time varying. It can be found that the extracted micro-Doppler feature parameters of the first six iterations are close to the set values, while the micro-Doppler feature parameters of the latter iterations are not very precise. Fig. The North Pole is 90° N; the South Pole is 90° S. The 0° parallel of latitude is designated the Equator, the fundamental plane of all geographic coordinate systems. [11] Table 5.5. A geographic coordinate system (GCS) is a coordinate system associated with positions on Earth (geographic position). Mathematical cartography resumed in Europe following Maximus Planudes' recovery of Ptolemy's text a little before 1300; the text was translated into Latin at Florence by Jacobus Angelus around 1407. (7.12) and (7.13), the internal force of the member is, Qun Zhang, ... Yong-an Chen, in Micro-Doppler Characteristics of Radar Targets, 2017. Micro-Doppler Features Extracted by Complex Image OMP Decomposition After Eliminating the Body Echoes (SNR = −20 dB, in the Second Situation). In an airplane, most objects of interest are below the aircraft, so it is sensible to define down as a positive number. We use cookies to help provide and enhance our service and tailor content and ads. ϕ The "longitude" (abbreviation: Long., λ, or lambda) of a point on Earth's surface is the angle east or west of a reference meridian to another meridian that passes through that point. The translational velocity of the target is v = (0,300,0)T m/s. 80, No. The initial location of the target center o is (30km,0km,5km) in the global coordinate system. {\displaystyle y'} λ {\displaystyle \textstyle {\varphi }\,\!} J.-C. Debus, in Applications of ATILA FEM Software to Smart Materials, 2013. 15, 675-15, 681, 1991. International Terrestrial Reference System, Spatial Reference System Identifier (SRID), International Terrestrial Reference Frame, Learn how and when to remove this template message, Geographic coordinate conversion § From ECEF to ENU, "WGS 84: EPSG Projection -- Spatial Reference", "Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas",, Wikipedia indefinitely move-protected pages, Wikipedia pending changes protected pages, Short description is different from Wikidata, Articles needing additional references from May 2015, All articles needing additional references, Articles with unsourced statements from December 2007, Articles to be expanded from December 2018, Creative Commons Attribution-ShareAlike License, as a set of numbers, letters or symbols forming a, The origin at the center of mass of the Earth, a point close to the Earth's, The Z axis on the line between the North and South Poles, with positive values increasing northward (but does not exactly coincide with the Earth's rotational axis), The X and Y axes in the plane of the Equator, The X axis passing through extending from 180 degrees longitude at the Equator (negative) to 0 degrees longitude (, The Y axis passing through extending from 90 degrees west longitude at the Equator (negative) to 90 degrees east longitude at the Equator (positive), North, East, down (NED), used specially in aerospace, The cartographic coordinate systems for almost all of the solid bodies in the, This page was last edited on 25 November 2020, at 21:07. 51.4). Axes directions are selected as follows: along the axis - along the pipe axis projection on the horizontal plane (Xmm) transverse-transverse to the pipe axis in the horizontal plane (Ymm) vertical (Zmm) In the 1st or 2nd century, Marinus of Tyre compiled an extensive gazetteer and mathematically-plotted world map using coordinates measured east from a prime meridian at the westernmost known land, designated the Fortunate Isles, off the coast of western Africa around the Canary or Cape Verde Islands, and measured north or south of the island of Rhodes off Asia Minor. In such situations, special techniques, such as a “stabilizing matrix,” have to be used to solve the global system equations. Figure 5.28. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". Local systems exist for convenience. The translational velocity of the target is v = (0,7800,0)T m/s. The coordinates of the rotation center C in the local coordinate system are (5m,5m,5m). In this section, we analyze the robustness of the proposed algorithm by three simulations corresponding to three degradation situations. Using house numbers to locate a house on a street; the street is a local coordinate system within a larger system composed of city townships, states, countries, postal codes, etc. The global coordinate system defines the position and translation of a body in space. (5.46) is used to eliminate the negative influence of body echo, which results in Fig. {\displaystyle \textstyle {\tan \beta ={\frac {b}{a}}\tan \varphi }\,\!}