# US 11,112,484 B2 · System and method for establishing relative distance and position of a transmitting antenna > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,112,484 B2 - Document ID: US11112484B2 - Status: Granted - Kind: B2 - Application number: 16/412,826 - Filed: 2019-05-15 - Published: 2020-11-19 - Granted: 2021-09-07 - Earliest claimed: 2019-05-15 - Assignees: Nanning Fugui Precision Industrial Co., Ltd. - Applicants: Nanning Fugui Precision Industrial Co., Ltd. - Inventors: Wen-Jen Lin; Ming-Chieh Cheng - Web page: https://patentgrep.com/patent/US11112484B2 ## CPC - G01S 5/04: Position of source determined by a plurality of spaced direction-finders - G01S 5/12: by co-ordinating position lines of different shape, e.g. hyperbolic, circular, elliptical or radial - G01S 3/30: derived directly from separate directional systems - G01S 11/06: using intensity measurements - G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES ## Abstract A system and method for a second wireless device to establish distance and location of a first device which is transmitting radio waves includes the first and second devices. Each second device includes two or more (N in number) receiving antennas. An angle between the directions in which adjacent receiving antennas receive the strongest signals is 360°/N. The second device obtains a received signal strength indicator (RSSI) of each receiving antenna receiving signals from the first device, and from the two strongest receiving antennas, calculation of an angle between the first device and one of the adjacent receiving antennas can be performed. The distance between the first device and the second device can also be calculated. ## Claims ### Claim 1 A positioning system comprising: a first device comprising at least two receiving antennas, wherein a number of the at least two receiving antennas is defined as N, an angle between the directions in which adjacent two of the receiving antennas receive the strongest signals is 360°/N; and a second device having a transceiving function; wherein the first device obtains a received signal strength indicator (RSSI) of each of the receiving antenna receiving signals from the second device, determines which of the two receiving antennas is closest to the second device according to received signal strength indicator (RSSI) , calculates an angle between the second device according to RSSIs of the two closest receiving antennas and the receiving antenna which is determined closest to the second device, and calculates a distance between the second device and the first device according to the angle, a gain of the closest receiving antennas, an output power of the second device and a gain of one of the transmitting antennas. ### Claim 2 (depends on 1) The positioning system of claim 1, wherein the first device further calculates an angle between the second device and the closest receiving antennas according to a following formula AntI RSSI - AntIV RSSI = 10 ⁢ log ⁡ ( 4 ⁢ π sin 2 ⁢ θ ⁢ 1 ) - 10 ⁢ ⁢ log ( 4 ⁢ π sin 2 ⁡ ( 360 ⁢ ° N - θ ⁢ ⁢ 1 ) ) , wherein, θ1 represents the angle between the second device and the closest receivings antenna, AntIRSSI and AntIVRSSI represents RSSIs of the two closest receiving antennas. ### Claim 3 (depends on 2) The positioning system of claim 2, wherein the first device calculates a gain of one of the closest receiving antennas according to a following formula Gt ⁢ ⁢ 1 ⁢ ( dB ) = 1 ⁢ 0 ⁢ log ⁡ ( 4 ⁢ π sin 2 ⁢ θ ⁢ 1 ) , wherein Gt1(θ1) represents the gain of the closest receiving antennas, the first device further calculates the distance between the second device and the first device according to a following formula d ⁢ ⁢ 1 = 1 2 ⁢ 0 ⁢ In ⁡ ( AntI RSSI + Pt + Gt ⁡ ( θ1 ) + Gr + 20 ⁢ ⁢ log ⁢ ⁢ λ ) , wherein Pt represents an output power of the second device, Gr represents a gain of one of the transmitting antennas, and λ represents a wavelength. ### Claim 4 (depends on 3) The positioning system of claim 3, wherein the first device obtains a preset number of RSSIs of each of the receiving antennas, and uses an average value of the RSSIs as the RSSI of each of the receiving antennas. ### Claim 5 (depends on 1) The positioning system of claim 1, wherein the first device identifies the second device according to physical information of the second device, wherein the physical information is a Media Access Control (MAC) address. ### Claim 6 (depends on 1) The positioning system of claim 1, wherein N is equal to four, an angle between the directions of the strongest received signals between adjacent receiving antennas is 90°, the first device calculates the angle between the second device and the closest receiving antennas according to a following formula θ ⁢ 1 = 1 2 ⁢ cos - 1 ( 1 In ⁡ ( AntI RSSI - AntIV RSSI 1 ⁢ 0 ) + 1 - 1 ) , wherein, θ1 represents the angle between the second device and the closest receiving antennas, AntIRSSI and AntIVRSSI represents RSSIs of the two closest receiving antennas. ### Claim 7 A positioning method, used for a first device to determine at least one second device, each of the second device comprising at least two receiving antennas, wherein a number of the at least two receiving antennas is defined as N, an angle between the directions in which adjacent two of the receiving antennas receive the strongest signals is 360°/N, the positioning method comprising: (a) establishing a connection between the first device and the second device; (b) obtaining a received signal strength indicator (RSSI) of each of the receiving antennas received signals from the second device; (c) determining which of the two receiving antennas is positioned closest to the second device according to received signal strength indicator (RSSI); and (d) calculating an angle between the second device and the closest receiving antennas according to RSSIs of the two closest receiving antennas, and calculating a distance between the second device and the first device according to the angle, a gain of the closest receiving antennas, an output power of the second device and a gain of one of the transmitting antennas. ### Claim 8 (depends on 7) The positioning method of claim 7, wherein the step (d) comprises: calculating the angle between the second device and the closest receiving antennas according to a following formula AntI RSSI - AntIV RSSI = 10 ⁢ log ⁡ ( 4 ⁢ π sin 2 ⁢ θ ⁢ 1 ) - 10 ⁢ ⁢ log ( 4 ⁢ π sin 2 ⁡ ( 360 ⁢ ° N - θ ⁢ ⁢ 1 ) ) , wherein, θ1 represents the angle between the second device and the closest receiving antennas AntIRSSI and AntIVRSSI represents RSSIs of the two a closest receiving antennas. ### Claim 9 (depends on 8) The positioning method of claim 8, wherein the step (d) comprises: calculating a gain of one of the closest receiving antennas according to a following formula Gt ⁢ ⁢ 1 ⁢ ( dB ) = 1 ⁢ 0 ⁢ log ⁡ ( 4 ⁢ π sin 2 ⁢ θ ⁢ 1 ) , wherein Gt1(θ1) represents the gain of one of the closest receiving antennas; calculating a distance between the second device and the first device according to a following formula d ⁢ ⁢ 1 = 1 2 ⁢ 0 ⁢ In ⁡ ( AntI RSSI + Pt + Gt ⁡ ( θ1 ) + Gr + 20 ⁢ ⁢ log ⁢ ⁢ λ ) , wherein Pt represents an output power of the second device, Gr represents a gain of one of the transmitting antennas, and λ represents a wavelength. ### Claim 10 (depends on 7) The positioning method of claim 7, wherein the step (a) comprises: obtaining a preset number of RSSIs of the receiving antenna, and using an average value of the RSSIs as the RSSI of the receiving antenna. ### Claim 11 (depends on 7) The positioning method of claim 7, further comprising: identifying the second device according to physical information of the second device, wherein the physical information is a Media Access Control (MAC) address. ### Claim 12 (depends on 7) The positioning method of claim 7, wherein N is equal to four, an angle between the directions of the strongest received signals between the adjacent receiving antennas is 90°, the step (a) comprises: calculating the angle between the second device and the closest receiving antenna according to a following formula θ1 = 1 2 ⁢ cos - 1 ( 1 In ⁡ ( AntI RSSI - AntIV RSSI 1 ⁢ 0 ) + 1 - 1 ) , wherein, θ1 represents the angle between the second device and the closest receiving antennas, AntIRSSI and AntIVRSSI represents RSSIs of the two closest receiving antennas. ### Claim 13 A positioning system comprising: a first device comprising at least two receiving antennas, wherein a number of the at least two receiving antennas is defined as N, an angle between the directions in which adjacent two of the receiving antennas receive the strongest signals is 360°/N; and a second device having a transceiving function; the first device obtains a received signal strength indicator (RSSI) of each of the receiving antenna receiving signals from the second device, determines which of the two receiving antennas is closest to the second device, calculates an angle between the second device and the receiving antenna which is determined closest to the second device, and calculates a distance between the second device and the first device; wherein the first device further caculates an angle between the second device and the closest receiving antennas according to a folloiwng formula AntI RSSI - AntIV RSSI = 10 ⁢ log ⁡ ( 4 ⁢ π sin 2 ⁢ θ ⁢ 1 ) - 10 ⁢ ⁢ log ( 4 ⁢ π sin 2 ⁡ ( 360 ⁢ ° N - θ ⁢ ⁢ 1 ) ) , wherein, θ1 repersents the angle between the second device and the closest receivings antenna, AntIRSSI and AntIVRSSI represents RSSIs of the two closest receiving antennas; the first device calculates a gain of one of the closest receiving antennas according to a following formula Gt ⁢ ⁢ 1 ⁢ ( dB ) = 1 ⁢ 0 ⁢ log ⁡ ( 4 ⁢ π sin 2 ⁢ θ ⁢ 1 ) , wherein Gt1(θ1) represents the gain of the closest receiving antennas, the first device further calculates the distance between the second device and the first device according to a following formula d ⁢ ⁢ 1 = 1 2 ⁢ 0 ⁢ In ⁡ ( AntI RSSI + Pt + Gt ⁡ ( θ1 ) + Gr + 20 ⁢ ⁢ log ⁢ ⁢ λ ) , wherein Pt represents an output power of the second device, Gr represents a gain of one of the transmitting antennas, and λ represents a wavelength.