SYSTEM AND METHOD FOR POSITIONING AND NAVIGATION OF AN OBJECT

Abstract

A positioning system and method for determination of location data of an object are described. The positioning system includes one or more transmitting units configured to transmit a multi-frequency signal that comprises at least two different signal frequency components. The positioning system also includes a receiver system mounted on the object, and configured to receive the multi-frequency signals from the transmitting units, and to determine phases of each signal frequency component of the multi-frequency signal. The positioning system also includes a processing system configured to receive the phases of each signal frequency component of the multi-frequency signal, and to determine a distance between the transmitting units and the object, and the location data of the object.

Claims

1-20. (canceled)

21. A positioning system for determination of location data of an object comprising: at least one transmitting unit configured to transmit a multi-frequency signal comprising at least two different signal frequency components; a receiver system mounted on the object and configured to receive the multi-frequency signals from said at least one transmitting unit, and to determine phases of each signal frequency component of the multi-frequency signal; and a processing system being in data communication with the receiver system, and configured to receive the phases of each signal frequency component of the multi-frequency signal, and to determine a distance D between said at least one transmitting unit and the object, and the location data of the object; wherein the receiver system is configured for: receiving the multi-frequency signals provided by said at least one transmitting unit; analyzing the multi-frequency signals, wherein the multi-frequency signal includes a sum of a predetermined number L of signal frequency components f.sub.i, where i is a number index of the signal frequency components, i=1, 2, . . . , L; wherein the signal frequency components f are mutually prime numbers; and determining said number L of the signal frequency components f.sub.i of each of said multi-frequency signals.

22. The positioning system of claim 21, wherein the distance D between said at least one transmitting unit and the object is determined by D=cΔt, where c is the light speed, and Δt is the time of propagation of the multi-frequency signals between said at least one transmitting unit and the object, the time is determined from an equation: $\Delta t=\frac{{\varphi }_i+2\pi N_i}{2\pi f_i}$ where ϕ.sub.i is the phase of an i-th signal frequency component determined by the receiver system, N.sub.i is a number of wave cycles of an i-th signal frequency component spanned on the distance D, and where a number i of the signal frequency component f.sub.i is selected from 0, 1, 2 and 3.

23. The positioning system of claim 22, wherein a number of the signal frequency components f.sub.i transmitted by said at least one transmitting unit is four, f.sub.0, f.sub.1, f.sub.2, and f.sub.3, and wherein the processing system is configured for determining a number N.sub.0 of cycles of the first signal frequency component f.sub.0 by using any one of the following equations: $N_0=-\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{2\pi \left(f_0-f_1\right)}$ $N_0=-\frac{f_0{\varphi }_2-f_2{\varphi }_0+2\pi M_1{f}_0}{2\pi \left(f_0-f_2\right)}$ $\mathrm{and}$ $N_0=-\frac{f_0{\varphi }_3-f_1{\varphi }_0+2\pi M_2{f}_0}{2\pi \left(f_0-f_3\right)},$ where M.sub.0, M.sub.1, and M.sub.2 are additives to the number of cycles N.sub.0 for the signal frequency components f.sub.1, f.sub.2, f.sub.3, correspondingly.

24. The positioning system of claim 23, wherein M.sub.0 and M.sub.1 are determined by using the following algorithm: for each M.sub.0 selected from 0 to (M.sub.0max−1) and for each M.sub.1 selected from M.sub.0 to (M.sub.1max−1), the processing system calculates integer numbers corresponding to M.sub.0 and M.sub.1 so as to satisfy an equation: $\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_2-f_2{\varphi }_0+2\pi M_1{f}_0}{f_0-f_2},$ where M.sub.0max=round[2π(f.sub.i−f.sub.0)T.sub.s] and where M.sub.1max=[2π(f.sub.2−f.sub.1)T.sub.s] where T.sub.s, is the measurement rate.

25. The positioning system of claim 23, wherein M.sub.0 and M1 are determined from an equation: $\Delta p_{\mathrm{mx}}:=.Math.\mathrm{floor}\left[-\frac{f0.Math.\mathrm{\varphi 1}-f1.Math.\mathrm{\varphi 0}+2.Math.\pi .Math.\mathrm{mod}\left(\mathrm{mx},\mathrm{Ma}0\right).Math.f0}{2\pi .Math.\left(f0-f1\right)}\right]-\mathrm{floor}\left[-\frac{f0.Math.\mathrm{\varphi 2}-f2.Math.\mathrm{\varphi 0}+2.Math.\pi .Math.\mathrm{floor}\left(\frac{\mathrm{mx}}{\mathrm{Ma}0}\right).Math.f0}{2\pi .Math.\left(f0-f2\right)}\right].Math.$ by calculating integer numbers satisfying a condition Δp.sub.mx=0 for each mx selected from 0 to (M.sub.0max.Math.M.sub.1max)−1, where M.sub.0max=round[2π(f.sub.1−f.sub.0T.sub.s] and where M.sub.1max=round[2π(f.sub.2−f.sub.1)T.sub.s] where T.sub.s is the measurement rate, and Ma0=M.sub.0max or M.sub.1max.

26. The positioning system of claim 24, wherein the processing system is configured to calculate M.sub.2 by solving an equation: $\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_3-f_3{\varphi }_0+2\pi M_2{f}_0}{f_0-f_3}.$

27. The positioning system of claim 25, wherein the processing system is configured to calculate M.sub.2 by solving an equation: $\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_3-f_3{\varphi }_0+2\pi M_2{f}_0}{f_0-f_3}.$

28. The positioning system of claim 22, wherein the processing system is further configured to receive the phase data ϕ.sub.i each signal frequency component for each of the multi-frequency signals from the receiver system, and to determine kinematic data based on the phase data ϕ.sub.i, said kinematic data selected from velocity and acceleration of the object.

29. The positioning system of claim 21, wherein the positioning system comprises three transmitting units having coordinates (x.sub.a, y.sub.a, z.sub.a), (x.sub.b, y.sub.b, z.sub.b) and (x.sub.c, y.sub.c, z.sub.c), correspondingly, and the determination of the location data includes calculating three location coordinates x(t), y(t) and z(t) of the object at time t; and wherein the processing system is configured to determine the three location coordinates x(t), y(t) and z(t) of the object (11) by using the following equations:
D.sub.a=√{square root over ((x(t)−x.sub.a).sup.2+(y(t)−y.sub.a).sup.2+(z(t)−z.sub.a).sup.2)}
D.sub.b=√{square root over ((x(t)−x.sub.b).sup.2+(y(t)−y.sub.b).sup.2+(z(t)−z.sub.b).sup.2)}
D.sub.c=√{square root over ((x(t)−x.sub.c).sup.2+(y(t)−y.sub.c).sup.2+(z(t)−z.sub.c).sup.2)} where D.sub.a, D.sub.b and D.sub.c are distances from said three transmitting units to the receiver system, correspondingly.

30. The positioning system of claim 21, wherein the positioning system comprises four transmitting units having coordinates (x.sub.a, y.sub.a, z.sub.a), (x.sub.b, y.sub.b, z.sub.b), (x.sub.c, y.sub.c, z.sub.c) and (x.sub.d, y.sub.d, z.sub.d), correspondingly, and wherein the processing system is configured to determine three location coordinates x(t), y(t) and z(t) of the object and system time T by solving the following system of equations:
c(T−Δt.sub.a)=√{square root over ((x(t)−x.sub.a).sup.2+(y(t)−y.sub.a).sub.2+(z(t)−z.sub.a).sup.2)}
c(T−Δt.sub.b)=√{square root over ((x(t)−x.sub.b).sup.2+(y(t)−y.sub.b).sub.2+(z(t)−z.sub.b).sup.2)}
c(T−Δt.sub.c)=√{square root over ((x(t)−x.sub.c).sup.2+(y(t)−y.sub.c).sub.2+(z(t)−z.sub.c).sup.2)}
c(T−Δt.sub.d)=√{square root over ((x(t)−x.sub.d).sup.2+(y(t)−y.sub.d).sub.2+(z(t)−z.sub.d).sup.2)} where T is the system time which is common to said four transmitting units, and where c(T−Δt.sub.a), c(T−Δt.sub.b), c(T−Δt.sub.c) and c(T−Δt.sub.d) are the distances between said transmitting units and said receiver system mounted on the object, correspondingly.

31. A positioning method for determining location data of an object, comprising: providing the positioning system of claim 21; transmitting a multi-frequency signal comprising at least two different frequencies; and measuring the phases of each signal frequency component of the multi-frequency signal; determining a distance D between said at least one transmitting unit and the object, and the location data of the object; wherein the receiver system of the positioning system is configured for: receiving the multi-frequency signals provided by said at least one transmitting unit; analyzing the multi-frequency signals, wherein the multi-frequency signal includes a sum of a predetermined number L of signal frequency components f.sub.i, where i is a number index of the signal frequency components, i=1, 2, . . . , L; wherein the signal frequency components f.sub.i are mutually prime numbers; and determining said number L of the signal frequency components f.sub.i of each of said multi-frequency signals.

32. The positioning method of claim 31, wherein the distance D between said at least one transmitting unit and the object is determined by D=cΔt, where c is the light speed, and Δt is the time of propagation of the multi-frequency signals between said at least one transmitting unit and the object, the time is determined from an equation: $\Delta t=\frac{{\varphi }_i+2\pi N_i}{2\pi f_i}$ where ϕ.sub.i is the phase of an i-th signal frequency component determined by the receiver system, and N.sub.i is a number of wave cycles of an i-th signal frequency component spanned on the distance D, and where a number i of the signal frequency component f.sub.i is selected from 0, 1, 2 and 3.

33. The positioning method of claim 32, wherein a number of the signal frequency components f.sub.i transmitted by said at least one transmitting unit is four, f.sub.0, f.sub.1, f.sub.2, and f.sub.3, and wherein the method includes determining a number N.sub.0 of cycles of the first signal frequency component f.sub.0 by using any one of the equations: $N_0=-\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{2\pi \left(f_0-f_1\right)}$ $N_0=-\frac{f_0{\varphi }_2-f_2{\varphi }_0+2\pi M_1{f}_0}{2\pi \left(f_0-f_2\right)}$ $\mathrm{and}$ $N_0=-\frac{f_0{\varphi }_3-f_1{\varphi }_0+2\pi M_2{f}_0}{2\pi \left(f_0-f_3\right)}$ where M.sub.0, M.sub.1, and M.sub.2 are additives to the number of cycles N.sub.0 for the signal frequency components f.sub.1, f.sub.2, f.sub.3, correspondingly.

34. The positioning method of claim 33, comprising determining M.sub.0 and M.sub.1 by using the following algorithm: for each M.sub.0 selected from 0 to (M.sub.0max−1) and for each M.sub.1 selected from 0 to (M.sub.1max−1), calculating, by the processing system, integer numbers corresponding to M.sub.0 and M.sub.1, which satisfy an equation: $\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_2-f_2{\varphi }_0+2\pi M_1{f}_0}{f_0-f_2}$ where M.sub.0max=round[2π(f.sub.1+f.sub.0)T.sub.s] and where M.sub.1max=[2π(f.sub.2−f.sub.1)T.sub.s] where T.sub.s is the measurement rate.

35. The positioning method of claim 33, comprising determining M.sub.0 and M.sub.1 from an equation: $\Delta p_{\mathrm{mx}}:=.Math.\mathrm{floor}\left[-\frac{f0.Math.\mathrm{\varphi 1}-f1.Math.\mathrm{\varphi 0}+2.Math.\pi .Math.\mathrm{mod}\left(\mathrm{mx},\mathrm{Ma}0\right).Math.f0}{2\pi .Math.\left(f0-f1\right)}\right]-\mathrm{floor}\left[-\frac{f0.Math.\mathrm{\varphi 2}-f2.Math.\mathrm{\varphi 0}+2.Math.\pi .Math.\mathrm{floor}\left(\frac{\mathrm{mx}}{\mathrm{Ma}0}\right).Math.f0}{2\pi .Math.\left(f0-f2\right)}\right].Math.$ by calculating integer numbers satisfying a condition Δp.sub.mx=0 for each mx selected from 0 to (M.sub.0max.Math.M.sub.1max)−1, where M.sub.0max=round[2π(f.sub.1−f.sub.0)T.sub.s] and where M.sub.1max=round[2π(f.sub.2−f.sub.1)T.sub.s] where T.sub.s is the measurement rate, and Ma0=M.sub.0max or M.sub.1max.

36. The positioning method of claim 34, comprising calculating M.sub.2 by solving an equation: $\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_3-f_3{\varphi }_0+2\pi M_2{f}_0}{f_0-f_3}.$

37. The positioning method of claim 35, comprising calculating M.sub.2 by solving an equation: $\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_3-f_3{\varphi }_0+2\pi M_2{f}_0}{f_0-f_3}.$

38. The positioning method of claim 31, wherein determining of kinematic data includes receiving the phase data ϕ.sub.i of each signal frequency component for each of the multi-frequency signals from the receiver system and to determining the kinematic data based on the phase data ϕ.sub.i, said kinematic data selected from velocity and acceleration of the object.

39. The positioning method of claim 31, wherein the positioning system comprises three transmitting units having coordinates (x.sub.a, y.sub.a, z.sub.a), (x.sub.b, y.sub.b, z.sub.b) and (x.sub.c, y.sub.c, z.sub.c), correspondingly, the method includes determining location data, and includes calculating three location coordinates x(t), y(t) and z(t) of the object at time t, correspondingly; and wherein the processing system of the positioning system is configured to determine the three location coordinates x(t), y(t) and z(t) of the object by using equations:
D.sub.a=√{square root over ((x(t)−x.sub.a).sup.2+(y(t)−y.sub.a).sup.2+(z(t)−z.sub.a).sup.2)}
D.sub.b=√{square root over ((x(t)−x.sub.b).sup.2+(y(t)−y.sub.b).sup.2+(z(t)−z.sub.b).sup.2)}
D.sub.c=√{square root over ((x(t)−x.sub.c).sup.2+(y(t)−y.sub.c).sup.2+(z(t)−z.sub.c).sup.2)} where D.sub.a, D.sub.b and D.sub.c are distances from said three transmitting units to the receiver system, correspondingly.

40. The positioning method of claim 31, wherein the positioning system comprises four transmitting units having coordinates (x.sub.a, y.sub.a, z.sub.a), (x.sub.b, y.sub.b, z.sub.b), y.sub.c, y.sub.c, z.sub.c) and (x.sub.d, y.sub.d, z.sub.d), correspondingly, the method includes determining location data and system time T; and wherein the processing system of the positioning system is configured to determine the three location coordinates x(t), y(t) and z(t) of the object and the system time T by solving the following system of equations:)
c(T−Δt.sub.a)=√{square root over ((x(t)−x.sub.a).sup.2+(y(t)−y.sub.a).sup.2+(z(t)−z.sub.a).sup.2)}
c(T−Δt.sub.b)=√{square root over ((x(t)−x.sub.b).sup.2+(y(t)−y.sub.b).sup.2+(z(t)−z.sub.b).sup.2)}
c(T−Δt.sub.c)=√{square root over ((x(t)−x.sub.c).sup.2+(y(t)−y.sub.c).sup.2+(z(t)−z.sub.c).sup.2)}
c(T−Δt.sub.d)=√{square root over ((x(t)−x.sub.d).sup.2+(y(t)−y.sub.d).sup.2+(z(t)−z.sub.d).sup.2)} wherein T is the system time which is common to said four transmitting units, and where c(T−Δt.sub.a), c(T−Δt.sub.b), c(T−Δt.sub.c) and c(T−Δt.sub.d) are the distances between said transmitting unit and said receiver system mounted on the object, correspondingly.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

[0032] FIG. 1 illustrates a schematic block diagram of a positioning system, according to an embodiment of the present invention;

[0033] FIG. 2 illustrates a schematic block diagram of a positioning system, according to another embodiment of the present invention; and FIG. 3 illustrates a schematic block diagram of a positioning system, according to a further embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

[0034] The principles and operation of the positioning system and method for determining location data of an object according to the present invention may be better understood with reference to the drawings and the accompanying description, it being understood that these drawings and examples in the description are given for illustrative purposes only and are not meant to be limiting. The same reference Roman numerals and alphabetic characters will be utilized for identifying those components which are common in the positioning system and its components shown in the drawings throughout the present description of the invention. It should be noted that the blocks in the drawings illustrating various embodiments of the present invention are intended as functional entities only, such that the functional relationships between the entities are shown, rather than any physical connections and/or physical relationships.

[0035] Some portions of the detailed descriptions, which follow hereinbelow, are presented in terms of algorithms and/or symbolic representations of operations on data represented as physical quantities within registers and memories of a computer system. An algorithm is here conceived to be a sequence of steps requiring physical manipulations of physical quantities and leading to a desired result. Usually, although not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. In the present description, these signals can be referred to as values, elements, symbols, terms, numbers, or the like.

[0036] Unless specifically stated otherwise, throughout the description, utilizing terms such as “computing” or “calculating” or “determining” or “obtaining” or the like, refer to the action and processes of a computer system, or similar electronic processing device, that manipulates and transforms data.

[0037] Referring to FIG. 1, a schematic block diagram of a positioning system 10 configured for determination of location data of an object 11 is illustrated, according to an embodiment of the present invention. The positioning system 10 includes a transmitting unit 12 and a receiver system 111 mounted on the object 11. According to this embodiment, the object 11 and the receiver system 111 constitute a unitary body.

[0038] The positioning system 10 also includes a processing system 13 in data communication with the receiver system 111. The processing system 13 communicates with the receiver system 111 via a communication network, using any known suitable wired and/or wireless communication techniques and data protocols.

[0039] According to an embodiment, the processing system 13 can be integrated with and be a part of the receiver system 111. Alternatively, the processing system 13 can be a stand-alone unit separate from the receiver system 111. When desired, the processing system 13 can include a display, printer and/or other monitoring devices (not shown).

[0040] In operation, the transmitting unit 12 is located at a certain distance D from the object 11. Generally, a positioning method for determining the distance D and the location data of the object 11 by using the positioning system 10 includes transmitting a multi-frequency signal comprising at least two different signal frequency components and measuring the phases of each signal frequency component of the multi-frequency signal. Then the processing system 13 calculates distance D between the transmitting unit 12 and the object 11, and the location data of the object 11.

[0041] According to an embodiment, the transmitting unit 12 is configured and operable for transmitting multi-frequency signals having a predetermined number L (at least two) of signal frequency components having frequencies f such that all the different signal frequency components are originated at the same time, where i is the number index of the signal frequency component, i=0, 1, . . . , L. The frequencies f.sub.i are selected from a predetermined set of frequencies.

[0042] The multi-frequency signal may be transmitted via the transmitting unit 12 with a certain time pattern, for example, as a sequence of periodic pulses, each pulse having a number L of signal frequency components. Alternatively, the multi-frequency signal may be a continuous signal having a number L of signal frequency components.

[0043] Upon arrival of the multi-frequency transmitted signal to the receiver system 111, each signal frequency component has a certain phase that can be measured. Accordingly, the receiver system 111 is configured and operable to receive the multi-frequency signals including the signal frequency components having frequencies f.sub.i originated from the transmitting unit 12, and to determine the phase ϕ.sub.i of each signal frequency component of the multi-frequency signal at the time of arrival to the transmitting unit 12. To this end, the receiver system 111 includes a phase measuring unit 120, which is adapted to receive the signal frequency components as an input data and to measure the phase ϕ.sub.i of each signal frequency component.

[0044] According to some embodiments of the present invention, the receiver system 111 is configured to receive multi-frequency signals provided by the transmitting unit 12, to analyze the multi-frequency signals and to determine a number L of the signal frequency components f.sub.i of each multi-frequency signal.

[0045] According to an embodiment of the present invention, the processing system 13 is in data communication with the receiver system 111, and is configured to receive the phase data ϕ.sub.i of each signal frequency component of the multi-frequency signal provided by the phase measuring 120 unit, and to calculate the distance D between the transmitting unit 12 and the object 11.

[0046] According to an embodiment of the present invention, the receiver system 111 includes a time clock unit coupled to the phase measuring unit 120 for activation of measurements of the phases ϕ.sub.i with a predetermined measurement rate T.sub.s. The measurements of the phases ϕ.sub.i can be carried out with a predetermined measurement rate T.sub.s, that can, for example, be in the range of 10 microseconds to 100 microseconds.

[0047] In operation, upon receiving the phase data ϕ.sub.i of each signal frequency component, the processing system 13 calculates the time of propagation Δt of the multi-frequency signals from the transmitting unit 12 to the receiver system 111 mounted on the object 11.

[0048] According to an embodiment of the present invention, the time of propagation Δt of the signal frequency components from the transmitting unit 12 to the receiver system 111 is determined by:

[00006]$\begin{array}{cc}\Delta t=\frac{{\varphi }_i+2\pi N_i}{2\pi f_i},& \left(1\right)\end{array}$

where N.sub.i is the number of wave cycles of an i-th signal frequency component spanned on the distance D between the transmitting unit 12 and the object 11. This number of cycles is denoted by N.sub.i=N.sub.0+M.sub.i, where N.sub.0 is the number of cycles of the first signal frequency component and M.sub.i is the additive number to the number of cycles N.sub.0 for the i-th signal frequency component.

[0049] Generally, the number of cycles N.sub.0 of the first signal frequency component can be calculated by:

[00007]$\begin{array}{cc}{N}_0=\mathrm{floor}\left(\frac{2\pi f_0\mathrm{dt}-{\varphi }_0}{2\pi }\right).& \left(2\right)\end{array}$

[0050] According to an embodiment of the present invention, the multi-frequency signal includes four signal frequency components having frequencies f.sub.0, f.sub.1, f.sub.2, and f.sub.3. In this case, N.sub.0 which is a number of cycles of the first signal frequency component f.sub.0 can be obtained by using any one of the following equations:

[00008]$\begin{array}{cc}{N}_0=-\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{2\pi \left(f_0-f_1\right)}& \left(3a\right)\end{array}$$\begin{array}{cc}{N}_0=-\frac{f_0{\varphi }_2-f_2{\varphi }_0+2\pi M_1{f}_0}{2\pi \left(f_0-f_2\right)}& \left(3b\right)\end{array}$$\mathrm{and}$$\begin{array}{cc}{N}_0=-\frac{f_0{\varphi }_3-f_1{\varphi }_0+2\pi M_2{f}_0}{2\pi \left(f_0-f_3\right)},& \left(3c\right)\end{array}$

where M.sub.0, M.sub.1, and M.sub.2 are additives to the number of cycles N.sub.0 for the signal frequency components having frequencies f.sub.1, f.sub.2, and f.sub.3, correspondingly.

[0051] According to an embodiment of the present invention, for determination of the values of the additives M.sub.0 and M.sub.1, the processing system 13 executes the following algorithm.

[0052] The additives M.sub.0 and M.sub.1 are selected from 1 to their corresponding maximum value. Specifically, M.sub.0 is selected from 0 to (M.sub.0max−1), where M.sub.0max=[2π(f.sub.1−f.sub.0)T.sub.s] and M.sub.1 is selected from 0 to (M.sub.1max−1), where M.sub.1max=[2π(f.sub.2−f.sub.1)T.sub.s], where T.sub.s is the measurement rate.

[0053] The processing system 13 calculates integer values of M.sub.0 and M.sub.1 such that M.sub.0 and M.sub.1 satisfy the following equation:

[00009]$\begin{array}{cc}\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_2-f_2{\varphi }_0+2\pi M_1{f}_0}{f_0-f_2}& \left(4\right)\end{array}$

[0054] According to another embodiment of the present invention, for determination of the values of the additives M.sub.0 and M.sub.1 by the processing system 13, the following relationship can be used:

[00010]$\begin{array}{cc}\Delta p_{\mathrm{mx}}:=.Math.\mathrm{floor}\left[-\frac{f0.Math.\mathrm{\varphi 1}-f1.Math.\mathrm{\varphi 0}+2.Math.\pi .Math.\mathrm{mod}\left(\mathrm{mx},\mathrm{Ma}0\right).Math.f0}{2\pi .Math.\left(f0-f1\right)}\right]-\mathrm{floor}\left[-\frac{f0.Math.\mathrm{\varphi 2}-f2.Math.\mathrm{\varphi 0}+2.Math.\pi .Math.\mathrm{floor}\left(\frac{\mathrm{mx}}{\mathrm{Ma}0}\right).Math.f0}{2\pi .Math.\left(f0-f2\right)}\right].Math..& \left(5\right)\end{array}$

In this case, the integer values of M.sub.0 and M.sub.1 can be selected so as to satisfy the condition Δp.sub.mx=0. Specifically, mx can be selected from 0 to (M.sub.0max.Math.M.sub.1max)−1, where M.sub.0max=round[2π(f.sub.1−f.sub.0)T.sub.s] and where M.sub.1max=round [2π(f.sub.2−f.sub.1)T.sub.s] and T.sub.s is the measurement rate and Ma0=M.sub.0max or M.sub.1max.

[0055] After determining M.sub.0 and M.sub.1, the processing system 13 can calculate the additive M.sub.2, for example, by solving the equation:

[00011]$\begin{array}{cc}\frac{f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0}{f_0-f_1}=\frac{f_0{\varphi }_3-f_3{\varphi }_0+2\pi M_2{f}_0}{f_0-f_3}& \left(6\right)\end{array}$

[0056] Accordingly, the additive M.sub.2 can be calculated by:

[00012]$\begin{array}{cc}{M}_2=\frac{f_0-f_3}{2{\mathrm{\pi f}}_0\left(f_0-f_1\right)}\left(f_0{\varphi }_1-f_1{\varphi }_0+2\pi M_0{f}_0\right)-\frac{f_0{\varphi }_3+f_3{\varphi }_0}{2{\mathrm{\pi f}}_0}.& \left(6a\right)\end{array}$

[0057] After determination of all the additives M.sub.0, M.sub.1, and M.sub.2 the processing system 13 can determine N.sub.0 and Δt by using the abovementioned equations (3a)-(3c) and (1), accordingly.

[0058] Upon determination of the time of propagation Δt, the processing system 13 can determine the distance D between the transmitting unit 12 and the object 11 by using the equation D=c Δt, where c is the speed of propagation of the electromagnetic radiation.

[0059] The proposed technique has been checked by simulation for the multi-frequency signal including four signal frequency components satisfying the following relationships: f.sub.0=0.65 GHz, f.sub.1−f.sub.0=0.112 MHz, f.sub.2−f.sub.0=0.241 MHz, f.sub.3−f.sub.0=2.671 MHz, and for the phases measured by the phase measuring unit 120 set to: ϕ.sub.0=66.3745 deg, ϕ.sub.1=339.2858 deg, ϕ.sub.2=348.2641 deg, and ϕ.sub.3=40.1806 deg.

[0060] In this example, the maximal values for the additives M.sub.0, M.sub.1 and M.sub.1, calculated by the processing system 13 by using the algorithms described above and the equations (4) or (5) have been obtained as: M.sub.0max=30, M.sub.1max=35, M.sub.2max=685. In turn, the number of the cycles N.sub.0 of the first signal frequency component has been obtained as N.sub.0=1.0203×10.sup.4. Accordingly, the calculated distance D between the transmitting unit 12 and the object 11 has been obtained as 158.18 km.

[0061] According to another aspect of the present technique, the processing system 13 is configured for determining location data of the object 11. This location data, in general, may include various parameters associated with three location coordinates (spatial coordinates) x(t), y(t) and z(t) of the object at time t and a system time T.

[0062] Referring to FIG. 2, a schematic block diagram of a positioning system 10 configured for determining location data of an object 11 is illustrated, according to an embodiment of the present invention. According to this embodiment, the positioning system 100 includes four transmitting units 12a-12d. Each transmitting unit has a predetermined location characterized by a set of corresponding spatial location coordinates. In particular, the transmitting unit 12a has coordinates (x.sub.a, y.sub.a, z.sub.a), the transmitting unit 12b has coordinates (x.sub.b, y.sub.b, z.sub.b), the transmitting unit 12c has coordinates x.sub.c, y.sub.c, z.sub.c) and the transmitting unit 12d has coordinates (x.sub.d, y.sub.d, z.sub.d). It should be noted that clocks of the transmitting units 12a-12d can be synchronized or unsynchronized with the clock of the receiver system 111. When the clocks of transmitting units 12a-12d are unsynchronized, each clock operates with its corresponding time t.sub.a, t.sub.b, t.sub.c, and t.sub.d, which is different from the time of the receiver system 111.

[0063] The positioning system 100 also includes a receiver system 111 mounted on the object 11 having location coordinates (x(t), y(t), z(t)) at time t.

[0064] Each of the transmitting units 12a-12d transmits a multi-frequency signal having a predetermined number L (at least two) of signal frequency components.

[0065] The receiver system 111 is configured to determine the phase data ϕ.sub.i of each signal frequency component for each of the multi-frequency signals upon receiving the multi-frequency signals from all the transmitting units 12a-12d.

[0066] The positioning system 100 also includes a processing system 13 configured to receive the phase data ϕ.sub.i of each signal frequency component for each of the multi-frequency signals from the receiver system 111, and to determine distances D.sub.a, D.sub.b, D.sub.c and D.sub.d from each transmitting unit 12a, 12b, 12c and 12d to the object 11, correspondingly.

[0067] Once the distances D.sub.a, D.sub.b, D.sub.c and D.sub.d are determined, the processing system 13 can calculate the location data coordinates (x(t), y(t), z(t)) of the receiver 111 mounted on the object 11, and when desired can also be synchronized by determining the system time T.

[0068] Accordingly, the processing system 13 can be configured for determining the system time T by solving the following system of equations:

c(T−Δt.sub.a)=√{square root over ((x(t)−x.sub.a).sup.2+(y(t)−y.sub.a).sub.2+(z(t)−z.sub.a).sup.2)}  (7a)

c(T−Δt.sub.b)=√{square root over ((x(t)−x.sub.b).sup.2+(y(t)−y.sub.b).sub.2+(z(t)−z.sub.b).sup.2)}  (7b)

c(T−Δt.sub.c)=√{square root over ((x(t)−x.sub.c).sup.2+(y(t)−y.sub.c).sub.2+(z(t)−z.sub.c).sup.2)}  (7c)

c(T−Δt.sub.d)=√{square root over ((x(t)−x.sub.d).sup.2+(y(t)−y.sub.d).sub.2+(z(t)−z.sub.d).sup.2)}  (7d)

where c(T−Δt.sub.a), c(T−Δt.sub.b), c(T−Δt.sub.c) and c(T−Δt.sub.d) are the distances between the receiver system 111 mounted on the object 11 and the transmitting units 12a, 12b, 12c, and 12d, correspondingly.

[0069] It should be understood that the number of transmitting units can be selected in accordance with the number K of unknown location parameters of the system.

[0070] When desired, the processing system 13 is further configured for determining kinematic data indicative of velocity and acceleration of the object. The determining is based on the location data of the receiver 111 and the system time T. The kinematic data may, for example, be determined by taking time derivatives form the location data coordinates (x(t), y(t), z(t)) of the receiver 111 mounted on the object 11.

[0071] In the cases where the system time T cannot be determined directly (e.g. clocks of the transmitters are not synchronized with the clock of the receiver system 111), the processing system 13 is configured for receiving the phase data ϕ.sub.i of each signal frequency component for each of the multi-frequency signals from the receiver system 111 and determining kinematic data based on the phase data ϕ.sub.i.

[0072] More specifically, the processing system 13 is configure for determining distances and kinematic data in accordance with phase difference of each signal frequency component for each of the multi-frequency signals. The phase difference is measured with a predetermined measurement rate T.sub.s, thereby the distance D between each transmitting unit and the object and kinematic data can be determined at each time t.

[0073] It should be noted that when the system is not synchronized (i.e. clocks of the transmitters are not synchronized with the clock of the receiver system 111), a pseudo-range is determined for each transmitting unit. Such a pseudo-range does not provide the accurate distance between the transmitting unit and the object, however, changes in location of the object (due to the object motion) can still be determined accurately. Upon determining the distance D for each time t, the kinematic data can be determined.

[0074] Referring to FIG. 3, a schematic block diagram of a positioning system 100 is illustrated, according to an embodiment of the present invention.

[0075] For example, as shown in FIG. 3, if the system time T is known, while three other location parameters, (such as location data coordinates (x(t), y(t), z(t)) of the receiver 111 mounted on the object 11) are unknown, the positioning system 100 includes three transmitting units 12a, 12b and 12c. Each transmitting unit has a certain location characterized by a set of corresponding spatial location coordinates. Specifically, the transmitting unit 12a has coordinates (x.sub.a, y.sub.a, z.sub.a), the transmitting unit 12b has coordinates (x.sub.b, y.sub.b, z.sub.b), and the transmitting unit 12c has coordinates (x.sub.c, y.sub.c, z.sub.c).

[0076] Accordingly, the processing system 13 can be configured to determine these three location coordinates x(t), y(t) and z(t) of the object by solving the system of the equations:

D.sub.a=√{square root over ((x(t)−x.sub.a).sup.2+(y(t)−y.sub.a).sup.2+(z(t)−z.sub.a).sup.2)}  (8a)

D.sub.b=√{square root over ((x(t)−x.sub.b).sup.2+(y(t)−y.sub.b).sup.2+(z(t)−z.sub.b).sup.2)}  (8b)

D.sub.c=√{square root over ((x(t)−x.sub.c).sup.2+(y(t)−y.sub.c).sup.2+(z(t)−z.sub.c).sup.2)}  (8c)

where D.sub.a, D.sub.b and D.sub.c are the distances between the object 11 mounted on the receiver system 13 and the transmitting units 12a, 12b and 12c, correspondingly, that can be obtained as described herein above.

[0077] In the case, when one of the location data coordinates (x(t), y(t), z(t)) is known, for example a moving car or a ship, where the altitude z(t) is known and does not change, only two of the transmitting units (for example, transmitting units 12a, 12b) are needed to determine the two remaining data coordinates (x(t), y(t)).

[0078] Accordingly, the processing system 13 can be configured to determine these two location coordinates x(t) and y(t) of the object by solving the system of the equations:

D.sub.a=√{square root over ((x(t)−x.sub.a).sup.2+(y.sub.a).sup.2+(z(t)−z.sub.a).sup.2)}  (8d)

D.sub.b=√{square root over ((x(t)−x.sub.b).sup.2+(y.sub.b).sup.2+(z(t)−z.sub.b).sup.2)}  (8e)

[0079] As such, those skilled in the art to which the present invention pertains, can appreciate that while the present invention has been described in terms of preferred embodiments, the concept upon which this disclosure is based may readily be utilized as a basis for the designing of other structures, systems and processes for carrying out the several purposes of the present invention.

[0080] Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting.

[0081] Finally, it should be noted that the word “comprising” as used throughout the appended claims is to be interpreted to mean “including but not limited to”.

[0082] It is important, therefore, that the scope of the invention is not construed as being limited by the illustrative embodiments set forth herein. Other variations are possible within the scope of the present invention as defined in the appended claims. Other combinations and sub-combinations of features, functions, elements and/or properties may be claimed through amendment of the present claims or presentation of new claims in this or a related application. Such amended or new claims, whether they are directed to different combinations or directed to the same combinations, whether different, broader, narrower or equal in scope to the original claims, are also regarded as included within the subject matter of the present description.