3D and 4D mapping of space using microwave and millimeter wave parallax

Abstract

The distance of an object is determined using two RF transmitters and an RF receiver, or two RF receivers and an RF transmitter. When two RF transmitters are used, the direction of the first transmitter is changed until it reaches a first direction defined by a first angle at which the power of the RF signal transmitted by the first transmitter that is reflected from the object and received by the receiver reaches a maximum. The direction of the second transmitter is also changed until it reaches a second direction defined by a second angle at which the power of the second RF signal transmitted by the second transmitter that is reflected from the object and received by the receiver reaches a maximum. The distance between the object and the first transmitter is defined by the distance between the two transmitters, the second angle, and the difference between the first angle and the second angle.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit under 35 USC 119(e) of U.S. Application No. 62 / 613,704, filed on January 4, 2018, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to position determination using radio frequency signals. Background Art

[0004] Determining the position and movement rate of an object within a limited area can benefit a wide range of applications, such as gaming, human-machine interfaces, security, environmental awareness, health systems, wireless power transfer, service industries, etc. A three-dimensional (3D) map of various entities within an area (e.g., a room) is accomplished by determining the distance from the object to the source in different directions.

[0005] In four-dimensional (4D) imaging systems, in addition to position information, other information is obtained about various targets, such as their speed and direction of movement. In standard LiDAR and radar solutions, the distance from the signal source to a remote target is measured by evaluating the flight time, i.e. the time it takes for the signal to reach the target and return to the signal source. Therefore, timing marks on the detection signal are required to perform this measurement. This can be performed as a pulse radar (i.e. amplitude modulation of the radar signal), where short pulses of the RF signal are emitted towards the target and their flight time is measured.

[0006] When a chirp frequency that increases linearly with time is used as the transmitted signal, frequency modulated continuous wave (FM-CW) radar and phase modulated continuous wave (PM-CW) radar can also be used to determine distance (range) by evaluating the difference between the frequencies of the reflected signal and the transmitted signal.

[0007] However, in such conventional methods, since the range resolution is mainly determined by the bandwidth of the transmitted signal, the modulated signal occupies a considerable bandwidth. Bandwidth limitation affects the range resolution. Summary of the invention

[0008] A method for determining the distance of an object according to one embodiment of the present invention partially includes: transmitting a first RF signal from a first transmitter to the object; changing the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle, at which the power of the first RF signal reflected from the object and received by a receiver reaches a maximum; transmitting a second RF signal from a second transmitter to the object; changing the direction of the second transmitter until the second transmitter reaches a second direction defined by a second angle, at which the power of the second RF signal reflected from the object and received by the receiver reaches a maximum; and determining the distance between the object and the first transmitter using the distance between the two transmitters, the second angle, and the difference between the first angle and the second angle.

[0009] In one embodiment, the method further comprises, in part, determining a distance between the object and the second transmitter using the distance between the two transmitters, the first angle, and a difference between the first angle and the second angle.

[0010] In one embodiment, the method further comprises, in part, determining a distance between the object and the receiver using the distance between the two transmitters, the first angle and the second angle, the difference between the first angle and the second angle, and the distance between the receiver and each of the first transmitter and the second transmitter. In one embodiment, the first transmitter, the second transmitter, and the receiver are positioned along a substantially straight line.

[0011] In one embodiment, the direction of the first transmitter is changed by mechanically rotating the transmitter. In one embodiment, the direction of the first transmitter is changed by changing the phase of multiple transmit / antenna elements of a phased array. In one embodiment, the direction of the first transmitter is changed by changing the phase of multiple transmit / antenna elements of a first sub-array of the phased array, and the direction of the second transmitter is changed by changing the phase of multiple transmit / antenna elements of a second sub-array of the phased array.

[0012] In one embodiment, the method further includes, in part, deactivating the second transmitter while transmitting the first RF signal, and deactivating the first transmitter while transmitting the second RF signal. In one embodiment, the receiver is a Doppler receiver adapted to detect a difference between a frequency of the first RF signal and a frequency of an RF signal reflected by an object to determine a velocity of the object.

[0013] A method for determining the distance of an object according to one embodiment of the present invention partially includes: transmitting an RF signal from a transmitter to the object; changing the direction of a first transmitter until the first transmitter reaches a first direction defined by a first angle, at which the power of the RF signal reflected from the object reaches a first maximum value at a first receiver, and at which the power of the RF signal reflected from the object reaches a second maximum value at a second receiver; and determining the distance between the object and the transmitter using the distance between the transmitter and the first receiver, the distance between the transmitter and the second receiver, and the first angle.

[0014] In one embodiment, the first receiver, the second receiver and the transmitter are positioned along a substantially straight line. In one embodiment, the first receiver is positioned substantially near the transmitter. In one embodiment, the first receiver and the second receiver are Doppler receivers.

[0015] A method for determining the distance of an object according to one embodiment of the present invention partially includes: transmitting a first RF signal from a first transmitter to the object; changing the direction of the first transmitter along the azimuth and elevation until the first transmitter reaches a first direction defined by a first angle and a second angle, at which the power of the first RF signal reflected from the object and received by a receiver reaches a maximum value; transmitting a second RF signal from a second transmitter to the object; changing the direction of the second transmitter along the azimuth and elevation until the second transmitter reaches a second direction defined by a third angle and a fourth angle, at which the power of the second RF signal reflected from the object and received by the receiver reaches a maximum value; and determining the distance between the object and the first transmitter using the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle.

[0016] In one embodiment, the method further comprises, in part, determining a distance between the object and the second transmitter using the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle. In one embodiment, the method further comprises, in part, determining a distance between the object and the receiver using the distance between the two transmitters, the distance between the first transmitter and the receiver, and the first angle, the second angle, the third angle, and the fourth angle.

[0017] In one embodiment, the first transmitter, the second transmitter, and the receiver are positioned along a substantially straight line. In one embodiment, the method further comprises, in part: deactivating the second transmitter while transmitting the first RF signal, and deactivating the first transmitter while transmitting the second RF signal. In one embodiment, the receiver is a Doppler receiver.

[0018] A method for determining the distance of an object according to one embodiment of the present invention partially includes: transmitting a first RF signal from a transmitter to the object; changing the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle and a second angle, at which the power of the first RF signal reflected from the object reaches a first maximum value at a first receiver, and at which the power of the first RF signal reflected from the object reaches a second maximum value at a second receiver; and determining the distance between the object and the transmitter using the distance between the transmitter and the first receiver, the distance between the transmitter and the second receiver, and the first angle and the second angle.

[0019] A mapping system according to one embodiment of the present invention includes, in part: a first transmitter adapted to transmit a first RF signal to an object; a second transmitter adapted to transmit a second RF signal to the object; a receiver; and a controller configured to: change the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle, at which the power of the first RF signal reflected from the object and received by the receiver reaches a maximum. The controller is also configured to change the direction of the second transmitter until the second transmitter reaches a second direction defined by a second angle, at which the power of the second RF signal reflected from the object and received by the receiver reaches a maximum. The controller is also configured to: determine the distance between the object and the first transmitter using the distance between the two transmitters, the second angle, and the difference between the first angle and the second angle.

[0020] In one embodiment, the controller is further configured to determine a distance between the object and the second transmitter using the distance between the two transmitters, the first angle, and a difference between the first angle and the second angle.

[0021] In one embodiment, the controller is further configured to determine the distance between the object and the receiver using the distance between the two transmitters, the first angle and the second angle, the difference between the first angle and the second angle, and the distance between the receiver and each of the first transmitter and the second transmitter.

[0022] In one embodiment, the first transmitter, the second transmitter, and the receiver are positioned along a substantially straight line. In one embodiment, the controller is further configured to change the direction of the first transmitter by mechanically rotating the transmitter. In one embodiment, the first transmitter is a phased array transmitter. In one embodiment, the first transmitter is a first subarray of the phased array transmitter, and the second transmitter is a second subarray of the phased array transmitter. In one embodiment, the controller is further configured to: deactivate the second transmitter while the first transmitter transmits the first RF signal, and deactivate the first transmitter while the second transmitter transmits the second RF signal. In one embodiment, the receiver is a Doppler receiver.

[0023] A mapping system according to one embodiment of the present invention includes, in part: a transmitter adapted to transmit a first RF signal to an object; a first receiver and a second receiver; and a controller configured to change the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle at which the power of the RF signal reflected from the object reaches a first maximum at the first receiver, and at the first angle at which the power of the RF signal reflected from the object reaches a second maximum at the second receiver. The controller is further configured to determine the distance between the object and the transmitter using the distance between the transmitter and the first receiver, the distance between the transmitter and the second receiver, and the first angle.

[0024] In one embodiment, the first receiver, the second receiver and the transmitter are positioned along a substantially straight line. In one embodiment, the first receiver is positioned substantially near the transmitter. In one embodiment, the first receiver and the second receiver are Doppler receivers.

[0025] A mapping system according to one embodiment of the present invention includes, in part: a first transmitter adapted to transmit a first RF signal to an object; a second transmitter adapted to transmit a second RF signal to the object; a receiver; and a controller configured to: change the direction of the first transmitter along an azimuth and an elevation angle until the first transmitter reaches a first direction defined by a first angle and a second angle, at which the power of the first RF signal reflected from the object and received by the receiver reaches a maximum. The controller is also configured to change the direction of the second transmitter along an azimuth and an elevation angle until the second transmitter reaches a second direction defined by a third angle and a fourth angle, at which the power of the RF signal reflected from the object and received by the receiver reaches a maximum. The controller is also configured to determine the distance between the object and the first transmitter using the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle.

[0026] In one embodiment, the controller is further configured to determine the distance between the object and the second transmitter using the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle. In one embodiment, the controller is further configured to determine the distance between the object and the receiver using the distance between the two transmitters, the distance between the first transmitter and the receiver, and the first angle, the second angle, the third angle, and the fourth angle.

[0027] In one embodiment, the first transmitter, the second transmitter and the receiver are positioned along a substantially straight line. In one embodiment, the controller is further configured to: deactivate the second transmitter while the first transmitter transmits the first RF signal, and deactivate the first transmitter while the second transmitter transmits the second RF signal. In one embodiment, the receiver is a Doppler receiver.

[0028] A mapping system according to an embodiment of the present invention includes, in part: a transmitter adapted to transmit an RF signal to an object; a first receiver and a second receiver; and a controller configured to: change the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle and a second angle, at which the power of the RF signal reflected from the object reaches a first maximum at the first receiver, and at which the power of the RF signal reflected from the object reaches a second maximum at the second receiver. The controller is also configured to: determine the distance between the object and the transmitter using the distance between the transmitter and the first receiver, the distance between the transmitter and the second receiver, and the first angle and the second angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1A A surveying and mapping system according to an embodiment of the present invention is shown.

[0030] Figure 1B A surveying and mapping system according to an embodiment of the present invention is shown.

[0031] Figure 2 A surveying and mapping system according to an embodiment of the present invention is shown.

[0032] Figure 3A A surveying and mapping system according to an embodiment of the present invention is shown.

[0033] Figure 3B A surveying and mapping system according to an embodiment of the present invention is shown.

[0034] Figure 4 A surveying and mapping system according to an embodiment of the present invention is shown.

[0035] Figure 5 A surveying and mapping system according to an embodiment of the present invention is shown.

[0036] Figure 6 A surveying and mapping system according to an embodiment of the present invention is shown.

[0037] Figure 7 A surveying and mapping system according to an embodiment of the present invention is shown.

[0038] Figure 8 A Doppler mapping system according to one embodiment of the present invention is shown.

[0039] Fig. 9 A Doppler mapping system according to one embodiment of the present invention is shown.

[0040] Fig. 10A A pair of transmitters are shown transmitting signals to a target to determine the range of the target in accordance with one embodiment of the present invention.

[0041] Fig. 10B A pair of phased arrays are shown transmitting signals to a target to determine the range of the target in accordance with one embodiment of the present invention.

[0042] Fig. 10C A phased array is shown transmitting a signal to a target to determine the range of the target in accordance with one embodiment of the present invention. DETAILED DESCRIPTION

[0043] According to one embodiment of the present invention, continuous wave radio frequency is used to determine the range of stationary and moving objects to form a 3D and / or 4D map while consuming minimal signal bandwidth. To achieve this, embodiments of the present invention use parallax, which is defined in this article as the angular difference resulting from observing an object from different lines of sight. In the context of 3D / 4D mapping and in its simplest case, the angular difference can be obtained by the displacement between at least two receivers (RX) that capture reflected signals at two slightly different angles or between at least two transmitters (TX) whose radiated signals arrive at the target at two slightly different angles.

[0044] Figure 1A A pair of transmitters 10 and 12 are shown transmitting signals at respective angles θ1 and θ2 toward a target 15 to determine the range of the target 15, according to one embodiment of the present invention and as further described below. Figure 1B A pair of receivers 20 and 22 are shown according to another embodiment of the present invention and as further described below, which receive signals from a target 15 at respective angles θ1 and θ2 in order to determine the range of the target 15. Figure 1A and Figure 1B In both, parallax is obtained by the spacing between the transmitters and / or receivers which causes an angular difference.

[0045] Figure 2 A 3D / 4D mapping system 100 is shown in accordance with an exemplary embodiment of the present invention. The mapping system 100 is shown as including, in part, transmitters 10, 12, a receiver 20, and a controller / computer 90. The transmitters 10 and 12 may be components of a dual beam transmitter / scanner that are spaced apart by a distance D. In the exemplary mapping system 100, it is assumed that the receiver 20 is located along a line connecting the transmitters 10, 12 and is located away from the transmitters 10, 12 by respective distances D1 and D2. Thus, in Figure 2 In the embodiment of the present invention, D=D1+D2. It should be understood that the embodiments of the present invention are not limited thereto, and in other embodiments, the transmitters 10, 12 and the receiver 50 may not be positioned in a straight line. The controller / computer 90 is configured in part to control the operation of the transmitter and the receiver, and further perform the calculations described below to determine the range of the target 15.

[0046] In order to determine the range of the target 15 and generate a 3D / 4D map, one transmitter is activated to scan the environment while the other transmitter is deactivated. For example, when the transmitter 10 is activated to scan the environment, the transmitter 12 remains deactivated. Conversely, when the transmitter 12 is activated to scan the environment, the transmitter 10 is deactivated.

[0047] During active scanning of either of the two transmitters, when the beam of the active transmitter is directed toward the target, the strength of the signal reflected by the target 15 and captured (or received) by the receiver 20 is at a maximum. For example, assume that the transmitter 10 is activated to be in a scanning mode to scan the environment while the transmitter 12 is turned off. When the beam radiated from the transmitter 10 is directed directly toward the target 15, the signal received by the receiver 20 caused by the reflection from the target 15 reaches a maximum. Therefore, according to one aspect of the present invention, the beam direction θ1 of the transmitter 10 that causes the maximum received signal of the receiver 20 is used as one of the parameters when determining the range of the target 15.

[0048] Similarly, when the beam radiated from the transmitter 12 is directed toward the target 15, the signal received by the receiver 20 (which is caused by the reflection of the signal transmitted by the transmitter 12 when the transmitter 10 is turned off by the target 15) reaches a maximum. The beam direction of the transmitter 12 that causes the maximum reception signal of the receiver 20 is also used as a parameter when determining the range of the target 15.

[0049] The two angles θ1 and θ2 obtained as described above define the parallax angle Δθ=θ1-θ2. Using the geometry of the arrangement, these two angles are then used to calculate the range of the target 15 from the transmitters 10, 12 and the receiver 20, as further described below. Applying the law of sines to the triangle formed by the transmitters 10, 12 and the target 15 yields the following:

[0050]

[0051] The distances R1 and R2, i.e. the distances from the transmitters 10, 12 to the target, are obtained as:

[0052]

[0053]

[0054] Knowing R1 and R2, the distance R0 between the receiver 20 and the target 15 is calculated by applying the law of cosines to the triangle formed by the receiver 20, the transmitter 10 and the target 15 or the triangle formed by the receiver 20, the transmitter 12 and the target 15:

[0055]

[0056] The distance R0 is thus determined as follows:

[0057]

[0058] In one embodiment, target 15 is an active target that includes circuitry for receiving RF signals transmitted by transmitters 10, 12 and modulating and / or encoding signals that target 15 subsequently transmits to receiver 20 to assist in determining the distance calculated by the computer.

[0059] refer to Figure 1A According to another embodiment of the present invention, the transmitters 10, 12 and the controller / computer 90 form a mapping system 75. In such an embodiment, the target 15, which may be a smart phone or another mobile device, includes power sensing circuitry adapted to sense the power level received by the target 15 from the transmitter, and communication circuitry adapted to transmit the power level sensed by the target 15 to the controller / computer 90, among other components. The controller / computer 90 is configured, in part, to control the operation of the transmitter, perform the calculations described below to determine the range of the target 15, and receive information from the target 15.

[0060] In order to determine the range of the target 15 to generate a 3D / 4D map, one transmitter is activated to scan the environment while the other transmitter is deactivated. For example, when the transmitter 10 is activated to scan the environment, the transmitter 12 remains deactivated. Conversely, when the transmitter 12 is activated to scan the environment, the transmitter 10 is deactivated.

[0061] During active scanning by either of the two transmitters, the signal strength received by the target (or mobile device) 15 is at a maximum when the beam of the active transmitter is directed toward the target. For example, assume that the transmitter 10 is activated to be in a scanning mode to scan the environment while the transmitter 12 is turned off. The signal received by the target 15 reaches a maximum when the beam radiated from the transmitter 10 is directed directly toward the target 15. When the transmitter 10 is in the scanning mode, the target 15 is adapted to transmit the maximum power it receives from the transmitter 10. Therefore, according to one aspect of the present invention, the beam direction θ1 of the transmitter 10 that causes the maximum received signal of the target 15 is used as one of the parameters when determining the range of the target 15.

[0062] Similarly, the signal received by target 15 (which is caused by the transmission of transmitter 12 when transmitter 10 is turned off) reaches a maximum when the beam radiated from transmitter 12 is directed directly at target 15. When transmitter 12 is in scanning mode, target 15 is adapted to receive the maximum power from transmitter 12. The beam direction θ2 of transmitter 12 that causes the maximum received signal at target 20 is also used as a parameter when determining the range of target 15.

[0063] The two angles θ1 and θ2 obtained as described above define the parallax angle Δθ=θ1-θ2. Using the geometry of the arrangement, these two angles are then used to calculate the range of the target 15 from the emitters 10, 12, as further described below. Applying the law of sines to the triangle formed by the emitters 10, 12 and the target 15 yields the following:

[0064]

[0065] The distances R1 and R2, i.e. the distances from the transmitters 10, 12 to the target, are obtained as:

[0066]

[0067]

[0068] Figure 3AA 3D / 4D mapping system 150 is shown according to another exemplary embodiment of the present invention. The mapping system 150 is shown as including, in part, a pair of two-dimensional transmitters 30, 32, a receiver 20, and a controller / computer 90. In the exemplary mapping system 150, it is assumed that the receiver 20 is positioned along a line connecting the transmitters 30, 32, and is positioned away from the transmitters 30, 32 by respective distances D1 and D2. Therefore, in FIG. 3, D=D1+D2. It should be understood that embodiments of the present invention are not limited to this, and in other embodiments, the transmitters 30, 32 and the receiver 20 may not be positioned along a straight line. The controller / computer 90 is configured in part to control the operation of the transmitter and the receiver, and further perform the calculations described below to determine the range of the target 15.

[0069] In order to determine the range of the target 15 and generate a 3D / 4D map, one transmitter is activated to scan the environment while the other transmitter is deactivated. The scanning of the environment by the transmitter is performed in the elevation direction and the azimuth direction. For example, when the two-dimensional transmitter 30 is activated to scan the environment, the transmitter 32 remains deactivated. Conversely, when the transmitter 12 is activated to scan the environment, the transmitter 10 is deactivated.

[0070] During active scanning of any of the transmitters, when the beam of the active transmitter is directed toward the target, the strength of the signal reflected by the target 15 and captured by the receiver 20 is at a maximum. For example, assume that the transmitter 30 is in scanning mode to scan the environment when the transmitter 32 is turned off. As shown, when the beam radiated from the transmitter 30 is directed toward the target, the intensity of the signal reflected by the target 15 and captured by the receiver 20 is at a maximum. When , the signal received by the receiver 20 caused by the reflection from the target 15 reaches a maximum. Similarly, as shown, when the beam radiated from the transmitter 32 is directed to When the transmitter 30 is turned off, the signal received by the receiver 20 caused by the reflection of the signal transmitted by the transmitter 32 by the target 15 reaches a maximum. Using these measurements and using the positions of the transmitter and receiver, the values ​​of sinα1, cosα1, sinα2, cosα2 and sin(α1-α2) can be calculated as follows:

[0071]

[0072]

[0073]

[0074] Therefore, the distances R1, R2, and R0 can be determined using the following expressions:

[0075]

[0076]

[0077]

[0078] In one embodiment, target 15 is an active target that includes circuitry for receiving RF signals transmitted by transmitters 30, 32 and modulating and / or encoding signals that target 15 subsequently transmits to receiver 20 to assist in determining the range calculated by the computer.

[0079] Figure 3B A 3D / 4D mapping system 95 is shown in accordance with another exemplary embodiment of the present invention. The mapping system 95 is shown as including, in part, a pair of two-dimensional transmitters 30, 32 and a controller / computer 90. In such an embodiment, a target 15, which may be a smart phone or another mobile device, includes power sensing circuitry adapted to sense the power level received by the target 15 from the transmitter, and communication circuitry adapted to transmit the power level sensed by the target 15 to the controller / computer 90, among other components. The controller / computer 90 is configured, in part, to control the operation of the transmitter, perform the calculations described below to determine the range of the target 15, and receive information from the target 15.

[0080] In order to determine the range of the target 15 and generate a 3D / 4D map, one transmitter is activated to scan the environment while the other transmitter is deactivated. The scanning of the environment by the transmitter is performed in the elevation direction and the azimuth direction. For example, when the two-dimensional transmitter 30 is activated to scan the environment, the transmitter 32 remains deactivated. Conversely, when the transmitter 12 is activated to scan the environment, the transmitter 10 is deactivated.

[0081] During active scanning of any of the transmitters, when the beam of the active transmitter is directed toward the target, the strength of the signal reflected by the target 15 is at a maximum. For example, assume that the transmitter 30 is in a scanning mode to scan the environment while the transmitter 32 is in an off state. As shown, when the beam radiated from the transmitter 30 is directed toward the target, the intensity of the signal reflected by the target 15 is at a maximum. , the signal received by target 15 reaches a maximum value. Target 15 is adapted to transmit the maximum power received from transmitter 30 when transmitter 30 is in scanning mode. Similarly, as shown, when the beam radiated from transmitter 32 is directed to The signal received by the target 15 reaches a maximum value when the target 15 is in the scanning mode. The target 15 is adapted to transmit the maximum power it receives from the transmitter 32 when the transmitter 32 is in the scanning mode. Therefore, it is determined that the power radiated by the transmitter 30 and determined by the angle The direction of the beam of maximum power is defined and corresponds to that received by the target 15 and transmitted back to the transmitter 30. Similarly, the direction of the beam radiated by the transmitter 32 and transmitted by the angle The direction of the beam of maximum power is defined and corresponds to that received by the target 15 and transmitted back to the transmitter 32. Using these measurements and taking advantage of the position of the transmitter, the values ​​of sinα1, cosα1, sinα2, cosα2 and sin(α1-α2) can be calculated as follows:

[0082]

[0083]

[0084]

[0085] Therefore, the distances R1 and R2 can be determined using the following expressions:

[0086]

[0087]

[0088] Figure 4 A 3D / 4D mapping system 200 is shown according to another exemplary embodiment of the present invention. The mapping system 200 is shown as including, in part, a transmitter 10, receivers 20, 22, and a controller / computer 90. In the exemplary mapping system 200, it is assumed that the transmitter 10 is located along a line connecting the receivers 20, 22 and is located at respective distances D1 and D2 away from the receivers 20, 22. Figure 4 In the embodiment of the present invention, D=D1+D2. It should be understood that the embodiments of the present invention are not limited thereto, and in other embodiments, the transmitter 10 and the receivers 20, 22 may not be positioned in a straight line. The controller / computer 90 is configured in part to control the operation of the transmitter and the receiver, and further perform the calculations described below to determine the range of the target 15.

[0089] To determine the range of the target 15, when the transmitter 10 scans the area by sweeping the angle θ, when the angle θ reaches Figure 4 The signals received by both receivers 20 and 22 are at their maximum values ​​at the specific values ​​shown. The scan determines the angular direction of the target, but the signal reflection from target 15 reaches the two receivers at slightly different angles, namely angle θ1 associated with receiver 20 and angle θ2 associated with receiver 22. Assuming that the two receivers 20 and 22 have similar gain patterns, G RX (θ), the difference in angle and range can be calculated by the difference in the signal strengths received by the two receivers. Using the well-known radar equation, the measured signal power at the receiver unit 20, i.e. and the measured signal power at the receiver unit 22, namely can be defined as follows:

[0090]

[0091]

[0092] Among them, P TX represents the power of the signal transmitted by the transmitter 10, G TX (θ) represents the gain pattern of the antenna of the transmitter 10 , and σ(θ) represents the radar cross section of the target 15 .

[0093] Assuming R0>>D, both θ1 and θ2 can be approximated by θ0 and σ(θ1)=σ(θ2)=σ(θ0). Figure 4 From the arrangement of the receiver, transmitter, and target shown, it can be seen that R0cosθ0=R1cosθ1=R2cosθ2. Therefore, the parameters and The sum can be defined as:

[0094]

[0095]

[0096] By using G RX (θ)cos 2 Taylor expansion of θ around θ = θ0 gives the following:

[0097]

[0098] Therefore, the two received signals and The difference between can be defined as:

[0099]

[0100] The two received signals and The mean value of is defined as:

[0101]

[0102] In the above equation, represents the signal strength received by a hypothetical receiver located at the same location as the transmitter 10.

[0103] Assuming that the position of the target 15 is far enough from the surveying and mapping system to satisfy the condition (R0>>D), if |D1-D2|<<D, then (θ1-θ0)≈(θ0-θ2), thus obtaining the following expression:

[0104]

[0105] Therefore, by taking the difference of these two measured signals Divide by the average of these two signals You can see:

[0106]

[0107] The only unknown is the parallax angle difference Δθ = θ1-θ2. Therefore, the above equation directly relates the measured power of the reflected signals received by the two receivers to the parallax angle. Therefore, by determining Δθ, the range R0 of the target from the transmitter 10 can be easily determined using the following equation:

[0108]

[0109] If D1=D2=D / 2, the above formula can be simplified to:

[0110]

[0111] In one embodiment, target 15 is an active target that includes circuitry for receiving RF signals transmitted by transmitter 10 and modulating and / or encoding signals that target 15 subsequently transmits to receivers 20, 22 to assist in determining distances calculated by the computer.

[0112] Figure 5 A 3D / 4D mapping system 250 is shown according to another exemplary embodiment of the present invention. The mapping system 250 is similar to the mapping system 200, except that in the mapping system 250, the transmitter 10 and the receiver 20 are substantially located near the same point, so that D1=0 and D2=D. Therefore, in the system 250, θ1=θ0 is known, while θ2 and the target range (R1=R0) from the transmitter 10 or the receiver 20 are unknown parameters determined by the controller / computer 90.

[0113] The parameter P0 defined above can be calculated as:

[0114]

[0115] Therefore θ2 and Δθ=θ1-θ2 can be calculated as follows:

[0116]

[0117] Accordingly, the range, R1=R0, can be obtained as follows:

[0118]

[0119] Figure 63D / 4D mapping system 300 according to another exemplary embodiment of the present invention is shown. The mapping system 300 is shown to include, in part, a pair of receivers 40, 42 adapted to change azimuth and elevation (to enable the acquisition of images at θ and 4D). In the exemplary surveying system 300, it is assumed that the transmitter 10 is located along the line connecting the receivers 40, 42 and is located at respective distances D1 and D2 away from the receivers. Figure 6 In the embodiment of the present invention, D=D1+D2. It should be understood that the embodiments of the present invention are not limited thereto, and in other embodiments, the receivers 40, 42 and the transmitter 10 may not be positioned along a straight line. The controller / computer 90 is configured in part to control the operation of the transmitter and the receiver, and further perform the calculations described below to determine the range of the target 15.

[0120] When the beam radiated from the transmitter 10 is directed toward the target, the signal received at the receivers 40, 42, i.e., the signal and is at its maximum value. Therefore, when the transmitter is at θ and While scanning in both directions, the received power levels at the receivers are recorded. The angles θ and θ at which the received power levels at the two receivers 40 and 42 reach their maximum values ​​are Corresponding to the angle θ0 and

[0121] By replacing the variables θ and Transformed into new variables α and β, such as Figure 6 As shown, the same process as described above can be used to obtain the parallax angle and thus detect the range based on the power levels of the reflected signals received at the two receivers.

[0122] As from Figure 6 It can be seen that:

[0123]

[0124] These equations can be used to convert the gain pattern of the receiver element (at angle θ, Definition) is transformed into a gain pattern (defined by angles α and β). Using this transformation, we obtain the following:

[0125]

[0126] This equation provides the parallax angle, Δα=α1-α2, which in turn provides the range as follows:

[0127]

[0128] If the transmitter 10 is placed exactly at the midpoint between the receivers 40, 42, that is, D1 = D2 = D / 2, the above equation can be simplified to:

[0129]

[0130] In one embodiment, target 15 is an active target that includes circuitry for receiving RF signals transmitted by transmitter 10 and modulating and / or encoding signals that target 15 subsequently transmits to receivers 40, 42 to assist in determining distances calculated by the computer.

[0131] Figure 7 A 3D / 4D mapping system 350 is shown according to another exemplary embodiment of the present invention. The mapping system 350 is similar to the mapping system 300, except that in the mapping system 350, the transmitter 10 and the receiver 40 are substantially located near the same point, thereby eliminating the need for approximation. In the mapping system 350, the parameters Δα and R0 can be calculated as follows:

[0132]

[0133]

[0134] Conventional CW radars typically use Doppler shift to detect the radial velocity of a moving target. As described above, embodiments of the present invention may also be used to determine the range of a moving object by measuring the reflected signal while also using Doppler shift to detect velocity.

[0135] Figure 8 A 3D / 4D Doppler mapping system 400 suitable for detecting the range of a moving target is shown in accordance with an exemplary embodiment of the present invention. The Doppler mapping system 400 is shown as including, in part, Doppler receivers 20, 22, a transmitter 10, and a controller / computer 90. For simplicity, the following description is made with reference to the transmitter being a one-dimensional transmitter / scanner. However, it should be understood that, as described above, the transmitter 10 can be a two-dimensional scanner. In the exemplary mapping system 400, it is assumed that the transmitter 10 is located along a line connecting the receivers 20, 22 and is located at respective distances D1 and D2 away from the receivers. Therefore, in Figure 8 In the embodiment of the present invention, D=D1+D2. It should be understood that the embodiments of the present invention are not limited thereto, and in other embodiments, the receivers 20, 22 and the transmitter 10 may not be positioned along a straight line. The controller / computer 90 is configured in part to control the operation of the transmitter and the receiver, and further perform the calculations described below to determine the range of the target 15.

[0136] Similar to the above reference Figure 6The described embodiment 300 can be expressed as follows (wherein the signal and , respectively representing the power levels of the Doppler signals received by receivers 20, 22, the range of the target 15 from the transmitter is determined by first calculating the parallax angle by measuring the strength of the signals received by the Doppler receivers (referred to herein alternatively as the Doppler signals) at the two receiving units:

[0137]

[0138] The range of the target from the transmitter can then be obtained using the following expression:

[0139]

[0140] In one embodiment, target 15 is an active target that includes circuitry for receiving RF signals transmitted by transmitter 10 and modulating and / or encoding signals that target 15 subsequently transmits to receivers 20, 22 to assist in determining distances calculated by the computer.

[0141] Fig. 9 A 3D / 4D Doppler mapping system 450 suitable for detecting the range of a moving target according to another exemplary embodiment of the present invention is shown. The Doppler mapping system 450 is shown as including, in part, transmitters 10, 12, a Doppler receiver 20, and a controller / computer 90. For simplicity, the following description refers to transmitters 10, 12, each of which is a one-dimensional transmitter / scanner and is suitable for scanning along one dimension. However, it should be understood that, as described above, the transmitters 10, 12 can be two-dimensional scanners. In addition, in the exemplary mapping system 450, it is assumed that the receiver 20 is positioned along the line connecting the transmitters 10, 12, and is positioned away from the receiver at respective distances D1 and D2. Therefore, in Fig. 9 In the embodiment of the present invention, D=D1+D2. It should be understood that the embodiments of the present invention are not limited thereto, and in other embodiments, the transmitters 10, 12 and the receiver 20 may not be positioned along a straight line. The controller / computer 90 is configured in part to control the operation of the transmitter and the receiver, and further perform the calculations described below to determine the range of the target 15.

[0142] Each transmitter scans the area while the other transmitter is off and finds the direction in which the receiver captures the maximum Doppler signal, thereby determining the angles θ1 and θ2 as shown. The range can then be determined as follows:

[0143]

[0144]

[0145]

[0146] In one embodiment, target 15 is an active target that includes circuitry for receiving RF signals transmitted by transmitters 10, 12 and modulating and / or encoding signals that target 15 subsequently transmits to receiver 20 to assist in determining distance calculated by the computer.

[0147] A variety of techniques can be used to form the emitter / scanner and achieve the desired displacement between the two emitter units. Fig. 10A In one embodiment shown, each transmitter / scanner may be a unit transmitter antenna that uses an angle encoder to mechanically rotate and radiate its beam in a specific direction, thereby scanning a desired area to determine the range of the target 15. Fig. 10A As shown, two such emitters / scanners 10, 12 may be physically spaced apart by a distance D to create parallax.

[0148] In another embodiment, each transmitter / scanner may be a phased array having multiple transmitting elements / antennas that electronically steers the direction of the radiation beam by varying the relative phase of each antenna element to scan the entire desired area. Fig. 10B Two phased arrays 10 and 12 are shown, each having a two-dimensional array of 3 x 3 radiating elements / antennas. The two phased arrays are physically spaced a distance D from their respective centers to create parallax.

[0149] According to yet another embodiment, each transmitter / scanner may be a subarray of a phased array having multiple transmitting elements / antennas. Each subarray steers its beam electronically and independently of the other subarrays. The effective displacement required for parallax is equal to the distance between the centers of the subarrays. Fig. 10C An exemplary phased array 60 is shown having a two-dimensional array of 3×14 radiating elements / antennas. Phased array 60 is shown divided into two sub-arrays 62 and 64, each having a two-dimensional array of 3×7 radiating elements / antennas. The distance between the centers of the two sub-arrays is shown to be equal to D.

[0150] The above embodiments of the present invention are exemplary and non-limiting. Other additions, subtractions or modifications are obvious based on this disclosure and are intended to fall within the scope of the appended claims.

Claims

1. A method for determining the distance of an object, the method comprising: transmitting a first RF signal from a first transmitter to the object; changing the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle at which a power of a first reflected RF signal reflected from the object and received by a receiver reaches a maximum value; transmitting a second RF signal from a second transmitter to the object; changing the direction of the second transmitter until the second transmitter reaches a second direction defined by a second angle at which a power of a second reflected RF signal reflected from the object and received by the receiver reaches a maximum value; and determining a distance between the object and the first transmitter based on the distance between the two transmitters, the second angle, and a difference between the first angle and the second angle; The method further comprises: deactivating the second transmitter while transmitting the first RF signal; and The first transmitter is deactivated while the second RF signal is transmitted.

2. The method according to claim 1, further comprising: The distance between the object and the second transmitter is determined based on the distance between the two transmitters, the first angle, and the difference between the first angle and the second angle.

3. The method according to claim 2, further comprising: The distance between the object and the receiver is determined based on the distance between the two transmitters, the first angle and the second angle, the difference between the first angle and the second angle, and the distance between the receiver and each of the first transmitter and the second transmitter.

4. The method according to claim 3, wherein: The first transmitter, the second transmitter, and the receiver are positioned along a straight line.

5. The method according to claim 1, wherein: Changing the direction of the first transmitter includes mechanically rotating the transmitter.

6. The method according to claim 1, wherein: Changing the direction of the first transmitter includes changing the phase of a plurality of transmit / antenna elements of a phased array.

7. The method according to claim 1, wherein: Changing the direction of the first transmitter includes changing the phase of multiple transmit / antenna elements of a first subarray of a phased array, and changing the direction of the second transmitter includes changing the phase of multiple transmit / antenna elements of a second subarray of the phased array.

8. The method according to claim 1, wherein: The receiver is a Doppler receiver adapted to detect a difference between a frequency of the first RF signal and a frequency of the first reflected RF signal to determine a velocity of the object.

9. The method according to claim 1, wherein: The first reflected RF signal and the second reflected RF signal are modulated signals.

10. A method for determining the distance of an object, the method comprising: transmitting a first RF signal from a transmitter to the object; changing the direction of the transmitter until the transmitter reaches a first direction defined by a first angle at which a power of a reflected RF signal reflected from the object reaches a first maximum at a first receiver and at which a power of the reflected RF signal reaches a second maximum at a second receiver; and determining a distance between the object and the transmitter based on a distance between the transmitter and the first receiver, a distance between the transmitter and the second receiver, and the first angle; Wherein, the first receiver is positioned near the transmitter.

11. The method according to claim 10, wherein: The first receiver, the second receiver, and the transmitter are positioned along a straight line.

12. The method according to claim 10, wherein: The first receiver and the second receiver are Doppler receivers.

13. The method according to claim 10, wherein: The reflected RF signal is a modulated signal.

14. A method for determining the distance of an object, the method comprising: transmitting a first RF signal from a first transmitter to the object; changing the direction of the first transmitter along the azimuth and elevation until the first transmitter reaches a first direction defined by a first angle and a second angle at which a power of a first reflected RF signal reflected from the object and received by a receiver reaches a maximum value; transmitting a second RF signal from a second transmitter to the object; changing the direction of the second transmitter along the azimuth and elevation until the second transmitter reaches a second direction defined by a third angle and a fourth angle at which a power of a second reflected RF signal reflected from the object and received by the receiver reaches a maximum value; and determining a distance between the object and the first transmitter according to the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle; The method further comprises: deactivating the second transmitter while transmitting the first RF signal; and The first transmitter is deactivated while the second RF signal is transmitted.

15. The method according to claim 14, further comprising: The distance between the object and the second transmitter is determined according to the distance between the two transmitters and the first angle, the second angle, the third angle and the fourth angle.

16. The method according to claim 15, further comprising: The distance between the object and the receiver is determined based on the distance between the two transmitters, the distance between the first transmitter and the receiver, and the first angle, the second angle, the third angle, and the fourth angle.

17. The method according to claim 16, wherein: The first transmitter, the second transmitter, and the receiver are positioned along a straight line.

18. The method according to claim 14, wherein: The receiver is a Doppler receiver.

19. A method for determining the distance of an object, the method comprising: transmitting a first RF signal from a transmitter to the object; changing the direction of the transmitter until the transmitter reaches a first direction defined by a first angle and a second angle at which a power of a reflected RF signal reflected from the object reaches a first maximum at a first receiver, and at which a power of the reflected RF signal reaches a second maximum at a second receiver; and determining a distance between the object and the transmitter based on a distance between the transmitter and the first receiver, a distance between the transmitter and the second receiver, and the first angle and the second angle; Wherein, the first receiver is positioned near the transmitter.

20. The method according to claim 19, wherein: The RF signal reflected at the first angle and the RF signal reflected at the second angle are modulated signals.

21. A surveying and mapping system, comprising: a first transmitter adapted to transmit a first RF signal to the object; a second transmitter adapted to transmit a second RF signal toward the object; Receiver; and A controller configured to: changing the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle at which a power of a first reflected RF signal reflected from the object and received by the receiver reaches a maximum value; changing the direction of the second transmitter until the second transmitter reaches a second direction defined by a second angle at which a power of a second reflected RF signal reflected from the object and received by the receiver reaches a maximum value; and determining a distance between the object and the first transmitter based on the distance between the two transmitters, the second angle, and a difference between the first angle and the second angle; The controller is also configured to: deactivating the second transmitter while the first transmitter transmits the first RF signal; and The first transmitter is deactivated while the second transmitter is transmitting the second RF signal.

22. The surveying and mapping system according to claim 21, wherein: The controller is also configured to: The distance between the object and the second transmitter is determined based on the distance between the two transmitters, the first angle, and the difference between the first angle and the second angle.

23. The surveying and mapping system according to claim 22, wherein: The controller is also configured to: The distance between the object and the receiver is determined based on the distance between the two transmitters, the first angle and the second angle, the difference between the first angle and the second angle, and the distance between the receiver and each of the first transmitter and the second transmitter.

24. The surveying and mapping system according to claim 23, wherein: The first transmitter, the second transmitter, and the receiver are positioned along a straight line.

25. The mapping system according to claim 21, wherein: The controller is configured to: The direction of the first emitter is changed by mechanically rotating the emitter.

26. The mapping system according to claim 21, wherein: The first transmitter is a phased array transmitter.

27. The mapping system according to claim 21, wherein: The first transmitter is a first subarray of a phased array transmitter, and the second transmitter is a second subarray of the phased array transmitter.

28. The mapping system according to claim 21, wherein: The receiver is a Doppler receiver adapted to detect a difference between a frequency of the first RF signal and a frequency of the first reflected RF signal to determine a velocity of the object.

29. The mapping system according to claim 21, wherein: The first reflected RF signal and the second reflected RF signal are modulated signals.

30. A surveying and mapping system, comprising: a transmitter adapted to transmit a first RF signal to the object; a first receiver; a second receiver; and A controller configured to: changing the direction of the transmitter until the transmitter reaches a first direction defined by a first angle at which the power of a reflected RF signal reflected from the object reaches a first maximum at the first receiver and at which the power of the reflected RF signal reaches a second maximum at the second receiver; and determining a distance between the object and the transmitter based on a distance between the transmitter and the first receiver, a distance between the transmitter and the second receiver, and the first angle; Wherein, the first receiver is positioned near the transmitter.

31. The mapping system according to claim 30, wherein: The first receiver, the second receiver, and the transmitter are positioned along a straight line.

32. The mapping system according to claim 30, wherein: The first receiver and the second receiver are Doppler receivers.

33. The mapping system according to claim 30, wherein: The reflected RF signal is a modulated signal.

34. A surveying and mapping system, comprising: a first transmitter adapted to transmit a first RF signal to the object; a second transmitter adapted to transmit a second RF signal toward the object; Receiver; and A controller configured to: changing the direction of the first transmitter in azimuth and elevation until the first transmitter reaches a first direction defined by a first angle and a second angle at which a power of a first reflected RF signal reflected from the object and received by the receiver reaches a maximum value; changing the direction of the second transmitter in azimuth and elevation until the second transmitter reaches a second direction defined by a third angle and a fourth angle at which a power of a second reflected RF signal reflected from the object and received by the receiver reaches a maximum value; and determining a distance between the object and the first transmitter according to the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle; The controller is also configured to: deactivating the second transmitter while the first transmitter transmits the first RF signal; and The first transmitter is deactivated while the second transmitter is transmitting the second RF signal.

35. The mapping system of claim 34, wherein: The controller is also configured to: The distance between the object and the second transmitter is determined according to the distance between the two transmitters and the first angle, the second angle, the third angle and the fourth angle.

36. The mapping system of claim 35, wherein: The controller is also configured to: The distance between the object and the receiver is determined based on the distance between the two transmitters, the distance between the first transmitter and the receiver, and the first angle, the second angle, the third angle, and the fourth angle.

37. The mapping system of claim 36, wherein: The first transmitter, the second transmitter, and the receiver are positioned along a straight line.

38. The mapping system of claim 34, wherein: The receiver is a Doppler receiver.

39. A surveying and mapping system comprising: a transmitter adapted to transmit a first RF signal to the object; a first receiver and a second receiver; and A controller configured to: changing the direction of the transmitter until the transmitter reaches a first direction defined by a first angle and a second angle at which a power of a reflected RF signal reflected from the object reaches a first maximum at the first receiver, and at which a power of the reflected RF signal reaches a second maximum at the second receiver; and determining a distance between the object and the transmitter based on a distance between the transmitter and the first receiver, a distance between the transmitter and the second receiver, and the first angle and the second angle; Wherein, the first receiver is positioned near the transmitter.

40. The mapping system of claim 39, wherein: The RF signal reflected at the first angle and the RF signal reflected at the second angle are modulated signals.

41. A method of determining a distance of a device, the method comprising: transmitting a first RF signal from a first transmitter to the device; changing the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle at which a power of the first RF signal received by the device reaches a first maximum value; transmitting a second RF signal from a second transmitter toward the object; changing the direction of the second transmitter until the second transmitter reaches a second direction defined by a second angle at which the power of the second RF signal received by the device reaches a second maximum value; and determining a distance between the device and the first transmitter based on the distance between the two transmitters, the second angle, and a difference between the first angle and the second angle; The method further comprises: deactivating the second transmitter while transmitting the first RF signal; and The first transmitter is deactivated while the second RF signal is transmitted.

42. The method of claim 41 further comprising: The distance between the object and the second transmitter is determined based on the distance between the two transmitters, the first angle, and the difference between the first angle and the second angle.

43. A surveying and mapping system, comprising: a first transmitter adapted to transmit a first RF signal; a second transmitter adapted to transmit a second RF signal; and A controller configured to: changing the direction of the first transmitter until the first transmitter reaches a first direction defined by a first angle at which the power of the first RF signal received by the device reaches a first maximum value, the device being configured to wirelessly communicate the power received by the device from the first transmitter to the controller; changing the direction of the second transmitter until the second transmitter reaches a second direction defined by a second angle at which the power of the second RF signal received by the device reaches a second maximum value, the device being configured to wirelessly communicate the power received by the device from the second transmitter to the controller; and determining a distance between the device and the first transmitter based on the distance between the two transmitters, the second angle, and a difference between the first angle and the second angle; The controller is also configured to: deactivating the second transmitter while the first transmitter transmits the first RF signal; and The first transmitter is deactivated while the second transmitter is transmitting the second RF signal.

44. The mapping system of claim 43, wherein: The controller is also configured to: The distance between the device and the second transmitter is determined based on the distance between the two transmitters, the first angle, and the difference between the first angle and the second angle.

45. A method of determining a distance of a device, the method comprising: transmitting a first RF signal from a first transmitter to the device; changing the direction of the first transmitter in azimuth and elevation until the first transmitter reaches a first direction defined by a first angle and a second angle at which a power of the first RF signal received by the device reaches a first maximum value; transmitting a second RF signal from a second transmitter toward the object; changing the direction of the second transmitter in azimuth and elevation until the second transmitter reaches a second direction defined by a third angle and a fourth angle at which the RF signal received by the device reaches a second maximum; and determining a distance between the device and the first transmitter according to the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle; The method further comprises: deactivating the second transmitter while transmitting the first RF signal; and The first transmitter is deactivated while the second RF signal is transmitted.

46. ​​The method of claim 45, further comprising: The distance between the device and the second transmitter is determined according to the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle.

47. A surveying and mapping system, comprising: a first transmitter adapted to transmit a first RF signal and change direction in azimuth and elevation; a second transmitter adapted to transmit a second RF signal and to redirect in azimuth and elevation; and A controller configured to: changing the direction of the first transmitter in azimuth and elevation until the first transmitter reaches a first direction defined by a first angle and a second angle at which a power of the first RF signal received by a device reaches a first maximum value, the device being configured to wirelessly communicate the power received by the device from the first transmitter to the controller; changing the direction of the second transmitter in azimuth and elevation until the second transmitter reaches a second direction defined by a third angle and a fourth angle at which the second RF signal received by the device reaches a second maximum value, the device being configured to wirelessly communicate power received by the device from the second transmitter to the controller; and determining a distance between the device and the first transmitter according to the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle; The controller is also configured to: deactivating the second transmitter while the first transmitter transmits the first RF signal; and The first transmitter is deactivated while the second transmitter is transmitting the second RF signal.

48. The mapping system of claim 47, wherein: The controller is also configured to: The distance between the device and the second transmitter is determined according to the distance between the two transmitters and the first angle, the second angle, the third angle, and the fourth angle.

Images