METHODS FOR MODELING MULTIPATH REFLECTIONS OF GNSS SIGNALS USING A TEST INSTALLATION AND APPARATUSES FOR IMPLEMENTING TEST METHODS

Abstract

A test installation for simulating multiple reflections of GNSS signals, the installation including a bottom screen that is reflective in the radio frequency spectrum; a top screen above the bottom screen, wherein the top screen is partly transparent in a radio frequency spectrum, and wherein the top screen is substantially dome-shaped and has a height of 1 to 3 meters; and a GNSS antenna between the top screen and the bottom screen; wherein the test installation is configured to measure the GNSS signals received by the antenna and to simulate the multipath reflections.

Claims

1. A method of manufacturing a test installation for simulating multipath reflections of GNSS signals, the method comprising: providing a top screen that is partly transparent in a radio frequency spectrum; providing a bottom screen that is reflective in the radio frequency spectrum; placing the top screen over the bottom screen; placing a GNSS antenna between the top screen and the bottom screen; and measuring the GNSS signals received by the antenna, wherein the top screen is substantially dome-shaped and has a height of 1 to 3 meters, and wherein the test installation is configured to simulate the multipath reflections.

2. The method of claim 1, wherein an angular period of oscillations (To) of a directional diagram (DD) is in a range of 1.5-11 degrees.

3. The method of claim 1, wherein an angular period of oscillations (To) of a directional diagram (DD) is related to a radius (R) of the top screen, as follows: $\frac{R}{\lambda }=\left(50\pm 5\right).Math.\frac{1}{T_{\theta }},$ where λ is a wavelength.

4. The method of claim 1, wherein an angular period of oscillations (T.sub.θ) of a directional diagram (DD) is $T_{\theta }=\left(50\pm 5\right).Math.\frac{\lambda }{R},\mathrm{deg}.$

5. The method of claim 1, wherein a phase diagram oscillations depth (ΔΦ) for a phase diagram (PD) varies from 40 to 120 degrees.

6. The method of claim 1, wherein a phase diagram oscillations depth (ΔΦ) for a phase diagram (PD) relates to an impedance module Z.sub.S/W.sub.0 for the top screen as $.Math.\frac{Z_S}{W_0}.Math.=\left(55\pm 5\right).Math.\frac{1}{\Delta .Math..Math.\Phi },$ where W.sub.0 is a characteristic impedance of free space.

7. The method of claim 1, wherein a phase diagram oscillations depth (ΔΦ) for a phase diagram (PD) is ΔΦ=180*(2n+1) degrees, where n=1, 2, 3 . . . and an impedance Z.sub.S for the top screen is in a range of 0.1-0.45;

8. The method of claim 1, wherein amplitude diagram (AD) oscillation depth (ΔF) is |ΔF|=20 . . . 4 dB and impedance module Z.sub.S/W.sub.0 of the top screen is $.Math.\frac{Z_S}{W_0}.Math.=\left(2\pm 0.2\right).Math.{10}^{-0.05.Math..Math.\Delta .Math..Math.F.Math.}$ and is in a range of 0.2-1.2, where W.sub.0 is a free space characteristic impedance.

9. The method of claim 1, wherein amplitude diagram (AD) oscillation depth (ΔF) is |ΔF|=20 . . . 4 dB and impedance module Z.sub.S/W.sub.0 of the top screen is $.Math.\frac{Z_S}{W_0}.Math.=\left(2\pm 0.2\right).Math.{10}^{-0.05.Math..Math.\Delta .Math..Math.F.Math.}.$

10. The method of claim 1, wherein the bottom screen is comprised of metal or a metalized foil or a metal mesh with a mesh period d.sub.g<0.2λ and a wire diameter 2r.sub.g>0.01λ, and wherein the bottom screen projects beyond a lower edge of the top screen by a distance L, where 0<L<5λ.

11. The method of claim 1, wherein the top screen is shaped as a semi-cylindrical tunnel; and wherein the antenna is mounted on a movable platform and is oriented such that angle α between a ray from the antenna towards a top edge point of the top screen and a horizon is no more than 30 degrees.

12. The method of claim 1, wherein the top screen is shaped as a semi-ellipse.

13. The method of claim 1, wherein the top screen is shaped as a hemisphere.

14. The method of claim 1, wherein the top screen is a slot mesh with capacitive and/or resistive-capacitive impedance, or a tape mesh with inductive and/or resistive-inductive impedance.

15. A test installation for simulating multiple reflections of GNSS signals, the test installation comprising: a bottom screen that is reflective in the radio frequency spectrum; a top screen above the bottom screen, wherein the top screen is partly transparent in a radio frequency spectrum, and wherein the top screen is substantially dome-shaped and has a height of 1 to 3 meters; and a GNSS antenna between the top screen and the bottom screen; wherein the test installation is configured to measure the GNSS signals received by the antenna and to simulate the multipath reflections.

16. The installation of claim 15, wherein an angular period of oscillations (To) of a directional diagram (DD) is in a range of 1.5-11 degrees.

17. The installation of claim 15, wherein an angular period of oscillations (To) of a directional diagram (DD) is $T_{\theta }=\left(50\pm 5\right).Math.\frac{\lambda }{R},\mathrm{deg}.$

18. The installation of claim 15, wherein a phase diagram oscillations depth (ΔΦ) for a phase diagram (PD) varies from 40 to 120 degrees.

19. The installation of claim 15, wherein the bottom screen projects beyond a lower edge of the top screen by a distance L, where 0<L<5λ.

20. The installation of claim 15, wherein the top screen is shaped as a semi-cylindrical tunnel.

Description

BRIEF DESCRIPTION OF THE ATTACHED FIGURES

[0049] The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

[0050] In the drawings:

[0051] FIG. 1 shows a diagram of multi-reflections for satellite signals between lower obstruction part (foliage) and the ground.

[0052] FIG. 2 shows a test installation with a semi-spherical top screen, where: 2001 is the antenna; 2002 is the top semi-spherical screen; 2003 is the bottom reflecting screen; R is the radius of the top screen; H is the antenna height (2001) above the bottom screen; L is the projections of the bottom screen (2003) over the limit of the top screen (2002).

[0053] FIG. 3 shows an embodiment of the top semi-spherical screen, where: 3001 are printed circuit boards (PCB) with etched slot or tape meshes (with/without soldered resistors); 3002 is the dielectric frame to fix PCB 3001; 3003 is the fixtures to attach the dielectric frame 3002 to the ground.

[0054] FIG. 4 shows a dependence of a minimal possible oscillation period relative to elevation angle T.sub.θ in degrees on the ratio of the screen radius R to the wavelength computed according to (F1).

[0055] FIG. 5 shows a dependence of oscillations depth in the amplitude DD ΔF in dB on impedance module/magnitude of the screen normalized to the free-space characteristic impedance

[00001]$.Math.\frac{Z_S}{W_0}.Math.$

calculated based on expression (F3).

[0056] FIG. 6 shows a dependence of oscillations depth ΔΦ in degrees in phase DD on the impedance module normalized to the free-space characteristic impedance

[00002]$.Math.\frac{Z_S}{W_0}.Math..$

[0057] FIG. 7a presents amplitude and phase directional diagrams for example 1.

[0058] FIG. 7b presents amplitude and phase directional diagrams for example 2.

[0059] FIG. 7c presents amplitude and phase directional diagrams for example 3.

[0060] FIG. 7d presents amplitude and phase directional diagrams for example 4.

[0061] FIG. 7e presents amplitude and phase directional diagrams for example 5.

[0062] FIG. 8a shows a possible design of slot mesh with capacitive impedance, where: 8001 is the metallized squares separated by slots forming a slot structure; 8002 is the dielectric substrate; d is the period of the slot structure; 2a is the width of the slot; h is the thickness of the substrate.

[0063] FIG. 8b shows a possible design of slot mesh with resistive-capacitive impedance, where: 8001 is the metallization squares separated by slots forming a slot structure; 8002 is the dielectric substrate; 8003 is the resistor; d is the period of the slot structure; 2a is the width of the slot; h is the thickness of the substrate.

[0064] FIG. 9a shows a possible design of tape mesh with inductive impedance, where: 9001 is the metallized tapes; 9002 is the dielectric substrate; d is the period of the tape structure; 2a is the width of the tape; h is the thickness of the substrate.

[0065] FIG. 9b shows a possible design of tape mesh with resistive-inductive impedance, where: 9001 is the metallized tapes; 9002 is the dielectric substrate; 9003 is the resistor; d is the period of the tape structure; 2a is the width of the tape; h is the thickness of the substrate.

[0066] FIG. 10 shows a variant of using the test installations with a anechoic chamber, where: 1001 are walls and ceiling of the anechoic chamber; 1002 is the floor of anechoic chamber; 1003 is the top screen; 1004 is the external receiving antenna; 1005 is the radiating antenna; 1006 is the receiving antenna; 1007, 1008, 1009 are the directions to satellites; 1010 is the direction to the radiating antenna; 1011 is the trajectory of traveling the radiating antenna; 1012 is the cable.

[0067] FIG. 11 shows a test installation with a top “tunnel”-shaped screen (the bottom reflecting screen is not shown); where: 2001 is the antenna; 11001 is the top “tunnel”-shaped screen; R is the radius of the top screen; H is the antenna (2001) height over the bottom screen; a is the angle between the ray from the antenna to the uppermost point of the top screen and direction to the horizon; 11002 is the movable platform with the fixed antenna.

[0068] FIG. 12 shows a photograph of test installation with a top “tunnel”-shaped screen of a length of about 30 meters.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0069] Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0070] It is common practice for antenna engineering to describe antenna characteristics in the transmitting mode.

[0071] The reciprocity theorem states the equivalence of directional diagrams for receiving and transmitting modes.

[0072] For the sake of computation and simulation, distortions of received signals are equivalent to those of directional diagrams (amplitude DD and phase DD) for the receiving antenna of the test receiver.

[0073] Actual obstructions (similar to trees) are equivalent to sharp oscillations in amplitude and phase in DD.

[0074] The distortions are characterized by DD minimal angular oscillation period T.sub.θ [deg], oscillations depth of the amplitude DD ΔF [dB], and oscillations depth in the phase DD ΔΦ [deg].

[0075] The satellite signal is the electromagnet wave that interacts with the screen.

[0076] Parameters of such interaction (degree of reflection and passage through the screen) are described by a value called “layer impedance” (in radio engineering, called Z.sub.S).

[0077] By varying Z.sub.S one can provide a desirable degree of signal reflection, absorption and passage through the mesh.

[0078] Elevation angle θ varies from 0 to 90 degrees, the angle 0 degree corresponding to the zenith direction and 90 degrees−the horizon direction.

[0079] A minimal antenna height over the bottom reflecting screen is 0.4 radius of the top screen.

[0080] The bottom reflecting screen can be made from metal or metallized foil (sheet), and metal mesh with mesh period d.sub.3<0.2λ and conductor diameter 2r.sub.3>0.012λ.

[0081] To reduce effects of the top screen, the mesh projects over the obstruction edge by distance L within range 0<L<5λ.

Calculation of Geometric Parameters and Impedance for the Screen

[0082] Approximate expressions (F1-F6) are applied to calculation of geometric parameters and impedance for the top semi-transparent screen.

[0083] A dependence of DD minimal angular oscillation period on the ratio of the screen radius to wavelength T.sub.θ is approximately described by (F1).

[00003]$\begin{array}{cc}{T}_{\theta }=\left(50\pm 5\right).Math.\frac{\lambda }{R},.Math.\mathrm{deg}& \left(\mathrm{F1}\right)\end{array}$

[0084] where: R is the radius of hemi-spherical top screen (typically about 1 to 3 meters); λ is the wavelength. Note that the top screen need not need be a perfect hemisphere, and other shapes (e.g., paraboloids, hyperboloids, ellipsoids, tunnels, and so on) will work as well (although the mathematics become more complex).

[0085] A working range of the screen radius is a range of R/λ=5 . . . 30.

[0086] In this case DD angular oscillations are realized with period T.sub.θ=1.5 . . . 11 deg.

[0087] FIG. 4 presents a dependence of minimal period of oscillations relative to elevation angle T.sub.θ in degrees on the ratio of the screen radius R to the wavelength. The dependence has been determined in accordance with expression (F1).

[0088] Expression (F2) follows from (F1) and allows the determination of the required screen radius R on the basis of the assigned minimal period of angular oscillations

[00004]$\begin{array}{cc}{T}_{\theta }.Math.\text{:}.Math..Math.\frac{\lambda }{R}=\left(50\pm 5\right).Math.\frac{1}{T_{\theta }}& \left(\mathrm{F2}\right)\end{array}$

[0089] A dependence of amplitude DD oscillations depth ΔF on screen impedance module normalized to free space characteristic impedance

[00005]$.Math.\frac{Z_S}{W_0}.Math.$

is approximately described by expression (F3):

[00006]$\begin{array}{cc}\Delta .Math..Math.F=20.Math.\lg \left(\left(0.5\pm 0.05\right).Math..Math.\frac{Z_S}{W_0}.Math.\right),\mathrm{dB}& \left(F.Math..Math.3\right)\end{array}$

[0090] where:

[00007]$.Math.\frac{Z_S}{W_0}.Math.$

is the screen module normalized to free space characteristic impedance; lg(10) is the base 10 logarithm.

[0091] A dependence of amplitude DD oscillations depth ΔF measured in dB on screen impedance module normalized to free space characteristic impedance

[00008]$.Math.\frac{Z_S}{W_0}.Math.$

calculated according to expression (F3) is shown in FIG. 5.

[0092] An operating range of screen impedance module is approximately equal to

[00009]$.Math.\frac{Z_S}{W_0}.Math.=0.1.Math..Math.\mathrm{.Math.}.Math..Math.1.2$

[0093] In the range of screen impedance module

[00010]$.Math.\frac{Z_S}{W_0}.Math.=0.1.Math..Math.\mathrm{.Math.}.Math..Math.0.2$

amplitude oscillations of DD with depth |ΔF|>20 dB are implemented.

[0094] In the range of screen impedance module

[00011]$.Math.\frac{Z_S}{W_0}.Math.=0.2.Math..Math.\mathrm{.Math.}.Math..Math.1.2$

amplitude oscillations of DD with depth |ΔF|=20 . . . 4 dB are implemented.

[0095] Expression (F4) follows from (F3), it allows to determine a required screen impedance module

[00012]$.Math.\frac{Z_S}{W_0}.Math.$

on the basis of the assigned amplitude DD oscillations depth ΔF:

[00013]$\begin{array}{cc}.Math.\frac{Z_S}{W_0}.Math.=\left(2\pm 0.2\right).Math.{10}^{-0.05.Math..Math.\Delta .Math..Math.F.Math.}& \left(\mathrm{F4}\right)\end{array}$

[0096] Expression (F5) approximately describes a dependence of phase DD oscillations depth ΔΦ on screen impedance module normalized to free space characteristic impedance

[00014]$\begin{array}{cc}.Math.\frac{Z_S}{W_0}.Math..Math.\text{:}.Math..Math.\mathrm{\Delta \Phi }=\left(55\pm 5\right).Math..Math.\frac{W_0}{Z_S}.Math.,\mathrm{deg}& \left(F.Math..Math.5\right)\end{array}$

[0097] Expression (F5) is valid in the range of

[00015]$.Math.\frac{Z_S}{W_0}.Math.\ge 0.45.$

[0098] Within this range of the screen impedance module there are phase oscillations of DD with depth ΔΦ=40 . . . 120 deg.

[0099] For the range of impedance module

[00016]$.Math.\frac{Z_S}{W_0}.Math.=0.1.Math..Math.\mathrm{.Math.}.Math..Math.0.45$

expression (F5) is not applicable, since phase DD shows 180 phase slips in this range.

[0100] Artificial obstructions caused 180 phase slips in phase DD are also of interest, as they are similar to strong shading from real obstructions, and result in irregular/dissected amplitude and phase DD.

[0101] A dependence of phase DD oscillations depth ΔΦ in degrees on screen impedance module normalized to free space characteristic impedance

[00017]$.Math.\frac{Z_S}{W_0}.Math.$

obtained from (F5) is shown in FIG. 6).

[0102] Expression (F6) follows from (F5), which enables the required screen impedance module

[00018]$.Math.\frac{Z_S}{W_0}.Math.$

to be determined from the assigned DD phase oscillations ΔΦ:

[00019]$\begin{array}{cc}.Math.\frac{Z_S}{W_0}.Math.=\left(55\pm 5\right).Math.\frac{1}{\Delta .Math..Math.\Phi }& \left(F.Math..Math.6\right)\end{array}$

[0103] Let us consider different examples of the proposed methods to calculate different parameters of the top semi-transparent spherical screen causing needed amplitude and phase distortions, as well as an angular period of DD oscillations.

Example 1

[0104] The task is to create a test installation capable of producing oscillations with period T.sub.θ=3 degrees, and amplitude oscillations depth ΔF=7 dB.

[0105] According to (F2), calculate the required radius of the top screen R:

[00020]$\frac{R}{\lambda }=50.Math.\frac{1}{T_{\theta }}=50.Math.\frac{1}{3}=16.6$

[0106] According to (F4) and considering requirements for amplitude DD oscillations depth, calculate the needed impedance of the top screen Z.sub.S:

[00021]$.Math.\frac{Z_S}{W_0}.Math.=2.Math.{10}^{0.05.Math..Math.\Delta .Math..Math.F}=2.Math.{10}^{0.05.Math.\left(-7\right)}=0.89$

[0107] Then from (F5) for screen impedance module

[00022]$.Math.\frac{Z_S}{W_0}.Math.=0.89$

calculate phase DD oscillations depth:

[00023]$\Delta .Math..Math.\Phi =55.Math..Math.\frac{W_0}{Z_S}.Math.=55.Math.0.89=61.8.Math..Math.\mathrm{deg}$

[0108] Amplitude and phase directional diagrams calculated in example 1 are shown in FIG. 7a).

Example 2

[0109] The task is to create a test installation capable of producing oscillations with period T.sub.θ=7 deg and phase oscillations depth ΔΦ=80 deg.

[0110] According to (F2), calculate the required radius of the top screen R:

[00024]$\frac{R}{\lambda }=50.Math.\frac{1}{T_{\theta }}=50.Math.\frac{1}{7}=7.1$

[0111] According to (F6) and considering requirements for phase DD oscillations depth, calculate the needed impedance of the screen Z.sub.S:

[00025]$.Math.\frac{Z_S}{W_0}.Math.=55.Math.\frac{1}{\Delta .Math..Math.\Phi }=55.Math.\frac{1}{80}=0.69$

[0112] From (F3) calculate amplitude DD oscillations depth for the screen impedance module

[00026]$.Math.\frac{Z_S}{W_0}.Math.=0.69.Math.\text{:}.Math..Math.\Delta .Math..Math.F=20.Math.\lg \left(0.5.Math..Math.\frac{Z_S}{W_0}.Math.\right)=20.Math.\lg \left(0.5.Math.0.69\right)=-9.2.Math..Math.\mathrm{dB}$

[0113] Amplitude and phase directional diagrams calculated in example 2 are shown in FIG. 7b).

Example 3

[0114] The task is to create a test installation capable of producing oscillations with period T.sub.θ=5 deg and 180-degree phase slips.

[0115] According to (F2), calculate the required radius of the top screen R:

[00027]$\frac{R}{\lambda }=50.Math.\frac{1}{T_{\theta }}=50.Math.\frac{1}{5}=10$

[0116] According to (F6) and considering requirements for availability of 180-degree phase slips in phase DD, select an impedance module from the range

[00028]$.Math.\frac{Z_S}{W_0}.Math.=0.1.Math..Math.\mathrm{.Math.}.Math..Math.0.45.Math.\text{:}.Math..Math.\frac{Z_S}{W_0}.Math.=0.4$

[0117] From (F3) one can calculate amplitude DD oscillations depth for impedance module

[00029]$.Math.\frac{Z_S}{W_0}.Math.=0.4.Math.\text{:}.Math..Math.\Delta .Math..Math.F=20.Math.\lg \left(0.2.Math..Math.\frac{Z_S}{W_0}.Math.\right)=20.Math.\lg \left(0.5.Math.0.4\right)=-14.Math..Math.\mathrm{dB}$

[0118] Amplitude and phase directional diagrams calculated in example 3 are shown in FIG. 7c).

Example 4

[0119] This example relates to calculating amplitude and phase DD for a screen with radius R=10λ and impedance of the screen material

[00030]$.Math.\frac{Z_S}{W_0}.Math.=1.1.$

[0120] According to (F3) one calculates that the depth of amplitude drops is within ΔF=−(4.4 . . . 6.1) dB.

[0121] From (5) phase error is within a range of

[00031]$\frac{\Delta .Math..Math.\Phi }{2}=\frac{45.Math..Math.\mathrm{.Math.}.Math..Math.54}{2}=23.Math..Math.\mathrm{.Math.}.Math..Math.27.Math..Math.\mathrm{deg}.$

[0122] The calculated angular oscillations period is T.sub.θ=5 deg.

[0123] Amplitude and phase directional diagrams calculated in example 4 are shown in FIG. 7d.

[0124] This set of parameters for the top screen corresponds to slightly distorted satellite signals.

Example 5

[0125] This example relates to calculating amplitude and phase DD for a screen with radius R=25λ and screen impedance

[00032]$.Math.\frac{Z_S}{W_0}.Math.=0.6.$

[0126] According to (F3) one calculates that the depth of amplitude drops is within ΔF=−(9.6 . . . 11.3) dB.

[0127] From (5) phase error is within a range of

[00033]$\frac{\Delta .Math..Math.\Phi }{2}=\frac{83.Math..Math.\mathrm{.Math.}.Math..Math.100}{2}=41.Math..Math.\mathrm{.Math.}.Math..Math.50.Math.\mathrm{deg}.$

[0128] The calculated angular oscillations period is T.sub.θ=5 deg.

[0129] Amplitude and phase directional diagrams calculated are shown in FIG. 7d.

[0130] Amplitude and phase directional diagrams calculated in example 5 are shown in FIG. 7e.

[0131] This set of parameters for the top screen corresponds to strongly distorted satellite signals with interruptions of separate satellites.

[0132] For manufacturing the top semi-transparent tunnel-shaped screen, taking into account blockage of open sky by the obstruction, angle α between a ray from the antenna at height H to the top upper point of the top screen and the horizon directions is to be no more than 30 deg.

[0133] In this case expressions F1-F6 are still valid.

Calculation of Parameters for Screen Material

[0134] There are known methods of developing surfaces (coatings) with different layer impedance Z.sub.S by applying slot and tape meshes.

[0135] There is no analytic dependence of slot and tape meshes on impedance, hence the parameters of the meshes can be determined only by selecting with the help of expressions (F7, F8), and known dependences of mesh impedance on mesh material parameters.

Slot Mesh

[0136] Slot meshes can have resistive and resistive-capacitive impedance. A possible design of the slot mesh with capacitive impedance is shown in FIG. 8a.

[0137] FIG. 8b presents a possible design of slot mesh with resistive-capacitive impedance. If there are no resistors soldered to slots, impedance Z.sub.S is equal to the self-impedance of the slot structure:

Z.sub.S=Z.sub.S.sup.s  (F7)

[0138] When resistors with resistance R are soldered to slots, impedance Z.sub.S is determined according to:

[00034]$\begin{array}{cc}{Z}_S=\frac{1}{1/Z_S^s+1/R}& \left(F.Math..Math.8\right)\end{array}$

[0139] Impedance of slot mesh for given mesh parameters is determined according to:

[00035]$\begin{array}{cc}.Math.\frac{Z_S^s}{W_0}=\frac{C.Math.\frac{a.Math..Math.\pi }{d}}{1-C.Math.\frac{a.Math..Math.\pi }{d}}.Math..Math..Math.\mathrm{where}.Math.\text{:}.Math..Math.C=\frac{2}{\frac{a.Math..Math.\pi }{d}.Math.\underset{n=-\infty }{\overset{\infty }{.Math.}}.Math..Math.J_0^2\left(\frac{2.Math..Math.\pi .Math..Math.\mathrm{na}}{d}\right).Math.\frac{k_1}{k_{\mathrm{zn}.Math..Math.1}}.Math.\left(1+\frac{\cos .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h-i.Math.\frac{K_{n.Math..Math.1}}{K_{n.Math..Math.2}}.Math.\sin .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h}{\cos .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h-i.Math.\frac{K_{n.Math..Math.1}}{K_{n.Math..Math.2}}.Math.\sin .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h}\right)};.Math..Math..Math.K_{n.Math..Math.1}=W_1.Math.\frac{k_{\mathrm{zn}.Math..Math.1}}{k_1};.Math..Math..Math.K_{n.Math..Math.2}=W_2.Math.\frac{k_{\mathrm{zn}.Math..Math.2}}{k_2};.Math..Math..Math.K_{n.Math..Math.1}=\frac{1}{W_1}.Math.\frac{k_{\mathrm{zn}.Math..Math.1}}{k_1};.Math..Math..Math.K_{n.Math..Math.2}=\frac{1}{W_2}.Math.\frac{k_{\mathrm{zn}.Math..Math.2}}{k_2};.Math..Math..Math.k_{\mathrm{zn}.Math..Math.1}=\sqrt{k_1^2-{\left(\frac{2.Math..Math.\pi .Math..Math.n}{d}\right)}^2};.Math..Math..Math.k_{\mathrm{zn}.Math..Math.2}=\sqrt{k_2^2-{\left(\frac{2.Math..Math.\pi .Math..Math.n}{d}\right)}^2};.Math..Math..Math.k_1=\frac{2.Math..Math.\pi }{\lambda };.Math..Math..Math.k_2=\sqrt{\mathrm{.Math.}}.Math.\frac{2.Math..Math.\pi }{\lambda };.Math..Math..Math.W_1=W_0=120.Math..Math.\pi ;.Math..Math..Math.W_2=\frac{1}{\sqrt{\mathrm{.Math.}}}.Math.W_0=\frac{1}{\sqrt{\mathrm{.Math.}}}.Math.120.Math..Math.\pi ;& \left(F.Math..Math.9\right)\end{array}$

[0140] J.sub.0( ) is the Bessel function of 0.sup.th order; i is the square root of −1; λ is the wavelength; 2a is the slot width; d is the period of the slot mesh; h is the thickness of the dielectric substrate; ∈ is the dielectric permeability of the substrate.

[0141] Let us consider an example of the proposed method to calculate material parameters for the top semi-transparent spherical screen produced of a slot mesh. This screen provides predicted amplitude and phase distortions and angular period of oscillations for directional diagrams.

Example 6

[0142] This example relates to calculating parameters for slot mesh with impedance

[00036]$\frac{Z_S}{W_0}=-0.7.Math.i.Math..Math.\mathrm{at}.Math..Math.\mathrm{frequency}$$f=1390.Math..Math.\mathrm{MHz}\left(\mathrm{at}.Math..Math.\lambda =\frac{3.Math.{10}^8}{f}=\frac{3.Math.{10}^8}{1390.Math.{10}^6}=0.21.Math..Math.m\right).$

[0143] One of possible parameter sets corresponding to the assigned impedance is calculated with (F7) by adjusting parameters: [0144] 2a=1.5 mm; d=19 mm; h=1.5 mm; ∈=3.2

[0145] The value of impedance is

[00037]$\frac{Z_S}{W_0}=\frac{Z_S^s}{W_0}=-0.704.Math.i.$

Tape Mesh

[0146] Mesh tapes can have inductive and resistive-inductive impedance. A possible design of the tape mesh with inductive impedance is shown in FIG. 9a.

[0147] A possible design of the tape mesh with resistive-inductive impedance is shown in FIG. 9b. If there are no resistors soldered to tapes, impedance Z.sub.S is equal to the self-impedance of the tape structure:

Z.sub.S=Z.sub.S.sup.t  (F10)

[0148] When resistors with resistance R are soldered to the tape, impedance Z.sub.S is determined according to:

Z.sub.S=Z.sub.S.sup.t+R  (F11)

[0149] Impedance of the mesh tape for the given mesh parameters is determined according to (F12):

[00038]$\begin{array}{cc}\frac{Z_S^t}{W_0}=-\frac{1}{2}.Math.\left(\frac{1}{R}+1\right).Math..Math.\mathrm{where}.Math.\text{:}.Math..Math.R=\frac{\begin{array}{c}\left(\left(K_{02}^2-K_{01}^2\right)+C.Math.\frac{a.Math..Math.\pi }{d}.Math.K_{01}\right).Math.i.Math..Math.\sin \left(k_{z.Math..Math.02}.Math.h\right)-\\ C.Math.\frac{a.Math..Math.\pi }{d}.Math.K_{02}.Math.\cos \left(k_{z.Math..Math.02}.Math.h\right)\end{array}}{2.Math.K_{01}.Math.K_{02}\left(k_{z.Math..Math.02}.Math.H_1\right)-i\left(K_{02}^2+K_{01}^2\right).Math.\sin \left(k_{z.Math..Math.02}.Math.h\right)}.Math..Math.C=\frac{2.Math.K_{01}.Math.\frac{K_{02}.Math.\cos .Math..Math.k_{z.Math..Math.02}.Math.h-{\mathrm{iK}}_{01}.Math.\sin .Math..Math.K_{z.Math..Math.02}.Math.h}{2.Math.K_{01}.Math.K_{02}.Math.\cos .Math..Math.k_{z.Math..Math.02}.Math.h-i.Math..Math.\sin .Math..Math.k_{z.Math..Math.02}.Math.h\left(K_{02}^2+K_{01}^2\right)}}{\frac{a.Math..Math.\pi }{d}.Math.\underset{n=-\infty }{\overset{\infty }{.Math.}}.Math.{\left(J_0\left(\frac{2.Math..Math.\mathrm{an}.Math..Math.\pi }{d}\right)\right)}^2.Math..Math.\frac{\begin{array}{c}{K}_{n.Math..Math.2}.Math.\cos .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h-\\ {\mathrm{ik}}_{n.Math..Math.1}.Math.\sin .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h\end{array}}{\begin{array}{c}2.Math.K_{n.Math..Math.1}.Math.K_{n.Math..Math.2}.Math.\cos .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h-\\ i\left(K_{n.Math..Math.2}^2+K_{n.Math..Math.1}^2\right).Math.\sin .Math..Math.k_{\mathrm{zn}.Math..Math.2}.Math.h\end{array}}};.Math..Math.K_{n.Math..Math.1}=\frac{1}{W_1}.Math.\frac{k_{\mathrm{zn}.Math..Math.1}}{k_1};.Math..Math.K_{n.Math..Math.2}=\frac{1}{W_2}.Math.\frac{k_{\mathrm{zn}.Math..Math.2}}{k_2};.Math..Math.K_{01}=\frac{1}{W_1};.Math..Math.K_{02}=\frac{1}{W_2};.Math..Math.k_{\mathrm{zn}.Math..Math.1}=\sqrt{k_1^2-{\left(\frac{2.Math..Math.\pi .Math..Math.n}{d}\right)}^2};.Math..Math.k_{\mathrm{zn}.Math..Math.2}=\sqrt{k_2^2-{\left(\frac{2.Math..Math.\pi .Math..Math.n}{d}\right)}^2};.Math..Math.k_{z.Math..Math.01}=k_1;.Math..Math.k_{z.Math..Math.02}=k_2;.Math..Math.k_1=\frac{2.Math..Math.\pi }{\lambda };.Math..Math.k_2=\sqrt{\mathrm{.Math.}}.Math.\frac{2.Math..Math.\pi }{\lambda };.Math..Math.W_1=W_0=120.Math..Math.\pi ;.Math..Math.W_2=\frac{1}{\sqrt{\mathrm{.Math.}}}.Math..Math.W_0=120.Math..Math.\pi & \left(\mathrm{F12}\right)\end{array}$

[0150] J.sub.0( ) is a Bessel function of 0.sup.th order; i is the square root of −1; λ is the wavelength; 2a is the tape width; d is the period of the tape mesh; h is the thickness of the dielectric substrate; ∈ is the dielectric permeability of the substrate.

[0151] Let us consider an example of the proposed method to calculate material parameters for the top semi-transparent spherical screen produced of a mesh tape. This screen provides predicted amplitude and phase distortions and angular period of oscillations for directional diagrams.

Example 7

[0152] This example relates to calculating parameters for mesh tape with impedance

[00039]$\frac{Z_S}{W_0}=0.7.Math.i$

at frequency f=1390 MHz (at the wavelength of

[00040]$\lambda =\frac{3.Math.{10}^8}{f}=\frac{3.Math.{10}^8}{1390.Math.{10}^6}=0.21.Math..Math.m).$

[0153] One of possible parameter sets corresponding to the assigned impedance is calculated with (F10) by adjusting parameters: [0154] 2a=1 mm; d=42 mm; h=1.5 mm; ∈=3.2

[0155] The value of tape impedance is equal to

[00041]$\frac{Z_S}{W_0}=\frac{Z_S^t}{W_0}=0.69.Math.i.$

The proposed test installation can be additionally used along with an anechoic chamber.

[0156] FIG. 10 presents an embodiment of the test installation with an anechoic chamber.

[0157] The installation with the anechoic chamber is used as follows.

[0158] A receiving antenna (1006) is placed in an anechoic chamber with absorbing walls and ceiling (1001), and reflecting floor (1002).

[0159] Above the receiving antenna there is a top screen (1003).

[0160] The floor of the anechoic chamber (1002) optionally with an additional reflecting coating is served as a bottom reflecting screen,

[0161] Outside the chamber in the line-of-sight of GNSS satellites there is a receiving antenna (1004) connected to a radiating antenna (1005) via a cable (1012).

[0162] Satellite signals are received from directions (1007, 1008, 1109), are transmitted to the radiating antenna (1005) via cable (1012) and being received by receiving antenna (1006).

[0163] Radiating antenna (1005) during reception-transmission process is moved along trajectory (1011) around screen (1003).

[0164] In this test installation all satellite signals will come to receiving antenna (1106) from direction to radiating antenna (1010), the signals having the same amplitude-phase distortions caused by screen (1003) effects.

[0165] This embodiment enables to have the same amplitude-phase distortions for signals from all satellites, these distortions being dependent upon previously known angular characteristics of amplitude and phase DD for an obstruction and a position of radiating antenna (1005).

[0166] Therefore, expressions (F1-F8) on the basis of assigned parameters of amplitude and phase distortions and angular oscillations periods for DD allow calculation of parameters for the test installation (dimensions of screen and parameters of its material) needed for simulating natural obstructions and debugging positioning algorithms, as well as facilitate buildup of such a test installation and tests and measurements.

[0167] This attains the aim of the present invention directed to building test installations simulating natural obstructions which cause multipath reflections and distortions of satellites signals.

[0168] As an alternative embodiment, the top screen may be shaped seen in FIG. 11, where the top semitransparent screen is shaped as a semi-cylindrical tunnel, the antenna is mounted on a movable platform and is oriented such that angle α between a ray from the antenna towards a point of the top screen and a horizon is no more than 30 degrees.

[0169] FIG. 12 shows a photograph of test installation with a top “tunnel”-shaped screen of a length of about 30 meters.

[0170] Having thus described a preferred embodiment, it should be apparent to those skilled in the art that certain advantages of the described method and apparatus have been achieved. In particular, those skilled in the art would appreciate that the proposed system and method provide for convenient uploading of the digital pictures and accompanying data.

[0171] It should also be appreciated that various modifications, adaptations and alternative embodiments thereof may be made within the scope and spirit of the present invention. The invention is further defined by the following claims.