A method for two-station positioning based on direction-finding time difference

Abstract

The application provides a double-station positioning method based on a direction-finding time difference, and belongs to the technical field of array signal processing. A plane rectangular coordinate system is constructed with a main station as an origin, and analytic circles are constructed on a target-substation connecting line and a target-main station connecting line respectively with the target-substation distance as a diameter. By using geometric analytic methods such as the analytic circle, the cosine theorem and the Pythagorean theorem, the relationship between the target-substation connecting line distance and the included angle between the target-substation connecting line and the target-main station connecting line is obtained, the target-substation connecting line distance is first calculated, and then the relative coordinates of the target are calculated through the time difference of the target information of two receiving stations and the direction-finding angle obtained by the main station. The application has the advantages of fast calculation speed, relatively flexible station arrangement and good application value.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a bistation positioning method based on direction finding time difference. Background Technology

[0002] Array signal processing is a crucial branch of modern signal processing, and target localization has always been considered a key research area within this field. Traditional time-difference positioning methods require constructing analytical equations regarding time difference and distance. Solving these equations involves not only matrix inversion but also multiple iterations to find the optimal solution, resulting in a massive computational burden. Furthermore, in direction-finding convergence positioning, all receiving station antennas must possess direction-finding capabilities, placing high demands on the antennas, reducing deployment flexibility, and increasing costs. Therefore, the characteristics of traditional positioning algorithms limit the applicability and flexibility of the aforementioned positioning systems in practical applications. Summary of the Invention

[0003] In view of this, the present invention provides a bi-station positioning method based on direction finding time difference, which has fast calculation speed, relatively flexible station deployment, and good application value.

[0004] This invention is achieved through the following technical solutions:

[0005] A bistatic positioning method based on direction-finding time difference includes the following steps:

[0006] Step 1: Given the location coordinates P of the main station S0 and the secondary station S1 S0 (x0,y0),P S1 Given (x1, y1), construct a rectangular coordinate system XOY with the main station as the origin, then:

[0007] P S0 (x0,y0)=P S0 (0,0)

[0008] Step 2: Let the coordinates of the target T to be solved be P. T (x, y), using the direction-finding capability of the main station, the angle between the line connecting the target and the main station and the X-axis is obtained, i.e., the target's azimuth information θ. d ;

[0009] Step 3: Calculate the angle between the line connecting the main station and the secondary station and the X-axis using the coordinates of the main station and the secondary station:

[0010] θ S =atan(y1 / x1)

[0011] In the formula, atan(·) is the arctangent function;

[0012] Next, calculate the angle ∠S1S0T between the line connecting the main station and the secondary station and the line connecting the target station and the main station, denoted as θ1:

[0013] θ1=θ S -θ d

[0014] Step 4: Draw a circle with the midpoint O of the target-sub-station line S1T as the center and the length r1 of S1T as the diameter, intersecting the target-main station line S0T at point Q; take a point S1' on the target-main station line S0T, let TS1' = r1, and draw a circle with the midpoint O' of TS1' as the center and r1 as the diameter, intersecting circle O at point P; obtain the length Δd of S0S1' using geometric relationships:

[0015] Δd=S0T-TS1'=S0T-r1=c·Δt

[0016] In the formula, c is the electromagnetic wave propagation speed, and Δt is the time difference between the arrival of the target signal at the main station and the secondary station;

[0017] Step 5: Let the length of the connection line S0S1 between the main station and the secondary station be L1. Calculate the length d of the connection line S1S1' using the Law of Cosines.

[0018] d = sqrt[(Δd)] 2 +(L1) 2 -2·Δd·L1·cos(θ1)]

[0019] In the formula, sqrt(·) is the square root function;

[0020] Step 6: Calculate the length d' of the line connecting S1 and Q using the Law of Sines:

[0021] d'=L1*sin(θ1)

[0022] Step 7: Let ∠S1'S1Q=β, then we have:

[0023] β = acos(d' / d)

[0024] In the formula, acos(·) is the inverse cosine function;

[0025] Step 8: Let the length of S1'Q be m, then we have

[0026] m = sqrt[(d)] 2 -(d') 2 ]

[0027] Step 9: Let the length of the QT connection be n, then we have:

[0028] n = r1 – m

[0029] Step 10: Let ∠PTS1' = α, where α and β are complementary to ∠S1S1'Q. Then α = β, ∠S1TS1' = 2α. According to the Pythagorean theorem, we have:

[0030] r1*cos(2α)=r1–n

[0031] Calculate the length r1 of the line connecting the target station and the secondary station:

[0032] r1 = n / [1-cos(2α)]

[0033] Step 11: Let the length of the target-main site be L, then we have:

[0034] L=Δd+r1

[0035] Thus, the target's location information can be obtained:

[0036] P T (x,y)=(L*cos(θ d ),L*sin(θ d )).

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. Compared with traditional time difference positioning algorithms, this invention does not require iterative solutions and does not involve complex operations such as matrix inversion, thus reducing the processing difficulty.

[0039] 2. Compared with the traditional direction finding intersection positioning algorithm, the present invention only requires the main station to use an array antenna to receive signals so that it has direction finding capability, making the station deployment more flexible and reducing antenna costs. Attached Figure Description

[0040] Figure 1 This is the overall flowchart of the present invention.

[0041] Figure 2 This is a schematic diagram illustrating the principle of the present invention. Detailed Implementation

[0042] A bistatic positioning method based on direction-finding time difference (TDD) is proposed. The main steps include: constructing a Cartesian coordinate system with the master station as the origin; and constructing analytical circles along the lines connecting the target and the secondary station (r1) and the target and master station (r1) with diameters. Using analytical circles, the law of cosines, and the Pythagorean theorem, the relationship between the distance between the target and the secondary station and the angles between these lines is obtained. First, the distance between the target and the secondary station is calculated. Then, using the time difference between the target information received by the two receiving stations and the direction-finding angle obtained by the master station, the relative coordinates of the target are calculated.

[0043] like Figure 1 and 2As shown, the method specifically includes the following steps:

[0044] Step 1: Given the location coordinates P of the main station S0 and the secondary station S1 S0 (x0,y0),P S1 Given (x1, y1), construct a rectangular coordinate system XOY with the main station as the origin, then:

[0045] P S0 (x0,y0)=P S0 (0,0);

[0046] Step 2: Let the coordinates of the target T to be solved be P. T (x, y), since the main station has direction-finding capabilities, the angle between the line connecting the target and the main station and the X-axis can be obtained, i.e., the target's azimuth information θ. d ;

[0047] Step 3: Using the coordinates of the main station and the secondary station, the angle between the line connecting the main station and the secondary station and the X-axis can be calculated:

[0048] θ S =atan(y1 / x1)

[0049] In the above formula, atan(·) is the arctangent function.

[0050] The angle ∠S1S0T between the line connecting the main station and the secondary station and the line connecting the target station and the main station can be obtained and denoted as θ1:

[0051] θ1=θ S -θ d ;

[0052] Step 4: Draw a circle with the midpoint O of the target-sub-station line S1T as its center and the length r1 of S1T as its diameter, intersecting the target-main station line S0T at point Q; take a point S1' on the target-main station line S0T, let TS1' = r1, and draw a circle with the midpoint O' of TS1' as its center and r1 as its diameter, intersecting circle O at point P. The length Δd of S0S1' can be obtained from geometric relationships:

[0053] Δd=SOT-TS1'=SOT-r1=c·Δt;

[0054] In the above formula, c is the electromagnetic wave propagation speed, and Δt is the time difference between the arrival of the target signal at the main station and the secondary station.

[0055] Step 5: Let the length of the connection line S0S1 between the main station and the secondary station be L1. Then, the length d of the connection line S1S1' can be obtained using the Law of Cosines.

[0056] d = sqrt[(Δd)] 2 +(L1) 2-2·Δd·L1·cos(θ1)];

[0057] In the above formula, sqrt(·) is the square root function.

[0058] Step 6: Since points Q, S1, and T are all on circle O, and S1T is its diameter, ∠S1QT = 90°. Therefore, the length d' of the line connecting S1Q can be found using the Law of Sines.

[0059] d' = L1*sin(θ1);

[0060] Step 7: Let ∠S1'S1Q=β, then we have:

[0061] β = acos(d' / d);

[0062] In the above formula, acos(·) is the inverse cosine function.

[0063] Step 8: Let the length of S1'Q be m, then we have

[0064] m = sqrt[(d)] 2 -(d') 2 ];

[0065] Step 9: Let the length of the QT connection be n, then we have:

[0066] n = r1 – m;

[0067] Step 10: Let ∠PTS1' = α. Since α and β are both complementary to ∠S1S1'Q, then α = β, ∠S1TS1' = 2α. Therefore, according to the Pythagorean theorem, we have:

[0068] r1*cos(2α)=r1–n

[0069] Therefore, the length r1 of the line connecting the target station and the secondary station can be calculated:

[0070] r1 = n / [1-cos(2α)]

[0071] Step 11: Let the length of the target-main site be L, then we have:

[0072] L = Δd + r1;

[0073] Therefore, the target's location information can be obtained:

[0074] P T (x,y)=(L*cos(θ d ), L*sin(θ) d )).

[0075] In summary, this invention requires the deployment of two receiving stations to obtain the time difference between the arrival of the target signal at the two stations. The main station also possesses direction-finding capabilities, enabling the acquisition of the target's azimuth information. Based on the time difference and azimuth information, the target's position can be determined solely through geometric analysis, without involving matrix inversion or other computational operations, further simplifying the data processing complexity of the positioning solution.

Claims

1. A bistation positioning method based on direction-finding time difference, characterized in that, Includes the following steps: Step 1: Given the location coordinates P of the main station S0 and the secondary station S1 S0 (x0,y0),P S1 Given (x1, y1), construct a rectangular coordinate system XOY with the main station as the origin, then: P S0 (x0,y0)= P S0 (0,0) Step 2: Let the coordinates of the target T to be solved be P. T (x, y), using the direction-finding capability of the main station, the angle between the line connecting the target and the main station and the X-axis is obtained, i.e., the target's azimuth information θ. d ; Step 3: Calculate the angle between the line connecting the main station and the secondary station and the X-axis using the coordinates of the main station and the secondary station: θ S =atan(y1 / x1) In the formula, atan(·) is the arctangent function; Next, calculate the angle ∠S1S0T between the line connecting the main station and the secondary station and the line connecting the target station and the main station, denoted as θ1: θ1=θ S -θ d Step 4: Draw a circle with the midpoint O of the target-sub-station line S1T as the center and the length r1 of S1T as the diameter, intersecting the target-main station line S0T at point Q; Take point S1' on the target-main station line S0T, let TS1' = r1, and draw a circle with the midpoint O' of TS1' as the center and r1 as the diameter, intersecting circle O at point P; obtain the length Δd of S0S1' from geometric relationships: Δd = S0T- TS1' = S0T- r1= c·Δt In the formula, c is the electromagnetic wave propagation speed, and Δt is the time difference between the arrival of the target signal at the main station and the secondary station; Step 5: Let the length of the connection line S0S1 between the main station and the secondary station be L1. Calculate the length d of the connection line S1S1' using the Law of Cosines. d= sqrt[ (Δd) 2 +(L1) 2 -2·Δd·L1·cos(θ1) ] In the formula, sqrt(·) is the square root function; Step 6: Calculate the length d' of the line connecting S1 and Q using the Law of Sines. d' = L1·sin(θ1) Step 7: Let ∠S1'S1Q = β, then we have: β = acos(d' / d) In the formula, acos(·) is the inverse cosine function; Step 8: Let the length of S1'Q be m, then we have m= sqrt[ (d) 2 - ( d’) 2 ] Step 9: Let the length of the QT connection be n, then we have: n = r1 – m Step 10: Let ∠PTS1' = α, where α and β are complementary to ∠S1S1'Q. Then α = β, ∠S1TS1' = 2α. According to the Pythagorean theorem: r1·cos(2α) = n Calculate the length r1 of the line connecting the target station and the secondary station: r1 = n / cos(2α) Step 11: Let the length of the target-main site be L, then we have: L = Δd + r1 Thus, the target's location information can be obtained: P T (x,y) = (L·cos(θ d ), L·sin(θ d ))。

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