Method for checking the position of a loran receiver based on the time of arrival

Abstract

This invention discloses a Loran receiver position verification method based on time-of-arrival (TOA) assistance. Specifically, the Loran receiver obtains the arrival times of the main and auxiliary stations of the complete station chain, including the three stations of the complete chain and any additional stations, denoted as TOA0TOA. M TOA X TOA Y Based on the complete station chain TOA information, hyperbolic positioning is used to calculate two locations P1 and P2. The arrival times from P1 and P2 to the additional station are calculated. The arrival times from P1 and P2 to the main station are also calculated. Error factors δ1 and δ2 for P1 and P2 are calculated, compared, and the location with the smaller error factor is retained, while the other location is excluded. In this method, the Loran receiver only needs the arrival time information from one additional station to verify the location, eliminating the multi-valued nature of the positioning results, expanding the positioning range of the Loran receiver in practical applications, and demonstrating good feasibility.

Description

Technical Field

[0001] This invention belongs to the field of digital signal processing technology, specifically relating to a Roland receiver position detection method based on time-of-arrival assistance. Background Technology

[0002] The Loran system is a ground-based long-wave long-range wireless navigation system that uses the hyperbolic positioning principle to achieve two-dimensional positioning based on known station coordinates and the time difference of measurements. However, hyperbolic positioning results are multivalued, and erroneous coordinates need to be discarded to obtain accurate position coordinates.

[0003] Traditional location verification employs a time-difference-assisted verification method. This method uses the time difference information of a complete Loland receiver chain for hyperbolic positioning, obtaining multiple location results. Then, it additionally incorporates the time difference information of two stations from another receiver chain to eliminate erroneous location coordinates. However, this method requires information from five stations in total. Loland receivers may not be able to receive signals from all five stations over a large location range, making the time-difference-assisted verification method unusable due to insufficient resources. Therefore, location verification methods for Loland receivers require further in-depth research. Summary of the Invention

[0004] The purpose of this invention is to provide a location verification method for a Roland receiver based on time of arrival, which allows the Roland receiver to verify its location using only the time of arrival information of an additional station.

[0005] The technical solution adopted in this invention is a Loran receiver position verification method based on time-of-arrival assistance, which is implemented according to the following steps:

[0006] Step 1: The Roland receiver obtains the arrival times of the complete station chain, including all three stations in the chain and any additional stations, denoted as TOA0 TOA. M TOA X TOA Y and TOA0;

[0007] Step 2: Based on the complete TOA information of the platform chain, use hyperbolic positioning to calculate the two positions P1 and P2;

[0008] Step 3: Calculate the arrival times from the two locations P1 and P2 to the additional station;

[0009] Step 4: Calculate the arrival times of the two locations P1 and P2 from the main station;

[0010] Step 5: Calculate the error factors δ1 and δ2 for the two positions P1 and P2, compare them, and keep the position with the smaller error factor while excluding the other position.

[0011] The invention is further characterized in that,

[0012] Step 2 specifically involves:

[0013] The three platforms are denoted as Platform 1, Platform 2, and Platform 3; let the spherical latitude and longitude of Platform 1, Platform 2, and Platform 3 be respectively... The baseline length between station 1 and station 2 is d1, the baseline length between station 3 and station 2 is d3, the azimuth angle from station 2 to station 1 is β1, and the azimuth angle from station 2 to station 3 is β3; the time difference between the receiver receiving the same signal transmitted from the main and auxiliary stations is ΔT. i ξ1 is the difference in ground distance from receiver P to station 2 and to station 1, and ξ2 is the difference in ground distance from receiver P to station 2 and to station 3.

[0014] Receiver point P is an unknown location point on the sphere, and its spherical latitude and longitude coordinates are: ρ1, ρ2, and ρ3 represent the spherical distances from point P to platforms 1, 2, and 3, respectively, and θ represents the azimuth angle from platform 2 to point P. All of these are unknowns.

[0015] Step 2.1: In the spherical triangles formed by station 1, station 2, and receiver P, and the spherical triangles formed by station 3, station 2, and receiver P, establish the spherical hyperbolic positioning equations and solve them, as shown in equation (1):

[0016]

[0017] The above system of equations contains four equations with four unknowns (ρ1, ρ2, ρ3, θ). A unique solution can be found to determine the polar coordinates (ρ2, θ) of receiver point P, which can then be converted into spherical latitude and longitude coordinates.

[0018] Step 2.2, substitute the third and fourth formulas in formula (1) into the first and second formulas respectively to obtain formula (2), and simplify to obtain the spherical distance from point P to platform 2, as shown in formula (3);

[0019]

[0020]

[0021] Step 2.3, rearrange and combine formula (3) into a single equation, resulting in formula (4):

[0022]

[0023] Step 2.4, transform equation (4) into a trigonometric equation containing only the azimuth angle θ from point P to point P, as shown in equation (5):

[0024] Asinθ+Bcosθ+D=0 (5);

[0025] A, B, and D are all auxiliary variables, and the calculation formula is shown in equation (6):

[0026]

[0027] Further transformation of equation (5) yields equation (7);

[0028]

[0029] To simplify the calculation, an auxiliary variable ψ is introduced, as shown in equation (8):

[0030]

[0031] Equation (5) can then be rewritten as equation (9):

[0032]

[0033] From the periodicity of the inverse trigonometric function, we know that θ+ψ has two values, as shown in equation (10):

[0034]

[0035] Further calculations yielded two azimuth angles θ1 and θ2 from platform 2 to point P, as shown in equation (11):

[0036]

[0037] Therefore, the expression for the polar coordinates (ρ2,θ) is shown in equation (12):

[0038]

[0039] According to formula (12), the polar coordinates (ρ2, θ) and spherical coordinates of point P can be obtained. The transformation relationship is shown in equation (13):

[0040]

[0041] Based on this, the spherical coordinates of the two positions P1 and P2 can be obtained. and Convert them into geodetic latitude and longitude coordinates (B1, L1) and (B2, L2).

[0042] In step 3, the arrival times of the two locations P1 and P2 to the additional station are denoted as T. 0-P1 and T 0-P2 As shown in equations (15)-(18);

[0043] T0-P1 =d 0-P1 / c (15);

[0044] T 0-P2 =d 0-P2 / c (16);

[0045]

[0046]

[0047] In the formula, c is the speed of light, d 0-P1 It is the distance from P1 to the additional station, d 0-P2 It is the distance from P2 to the additional station. These are the spherical coordinates of the additional stations. These are the spherical coordinates of P1. These are the spherical coordinates of P2.

[0048] In step 4, the arrival times of the two locations P1 and P2 from the main station are denoted as T. M-P1 and T M-P2 As shown in equations (19)-(22);

[0049] T M-P1 =d M-P1 / c (19);

[0050] T M-P2 =d M-P2 / c (20);

[0051]

[0052]

[0053] In the formula, d M-P1 It is the distance d from P1 to the main station M. M-P2 It is the distance from P2 to the main station M. These are the spherical coordinates of the main stage M.

[0054] The error factors δ1 and δ2 of the two positions P1 and P2 in step 5 are shown in equations (23) and (24);

[0055] δ1=T M-P1 -(T M +T 0-P1 -T0) (23)

[0056] δ2=T M-P2 -(T M +T 0-P2 -T0) (24).

[0057] The beneficial effects of this invention are: the Roland receiver can verify the location using only the arrival time information of an additional station, eliminating the multi-valued nature of the positioning results, expanding the positioning range of the Roland receiver in practical applications, and demonstrating good feasibility. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of hyperbolic positioning in the Roland receiver position verification method based on arrival time assistance of the present invention. Detailed Implementation

[0059] The present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0060] Example 1

[0061] This invention relates to a time-of-arrival-assisted position verification method for a Loran receiver, which is implemented according to the following steps:

[0062] Step 1: The Roland receiver obtains the arrival times of the complete station chain, including all three stations in the chain and any additional stations, denoted as TOA0 TOA. M TOA X TOA Y and TOA0;

[0063] Step 2: Based on the complete TOA information of the platform chain, use hyperbolic positioning to calculate the two positions P1 and P2;

[0064] Step 3: Calculate the arrival times from the two locations P1 and P2 to the additional station;

[0065] Step 4: Calculate the arrival times of the two locations P1 and P2 from the main station;

[0066] Step 5: Calculate the error factors δ1 and δ2 for the two positions P1 and P2, compare them, and keep the position with the smaller error factor while excluding the other position.

[0067] Example 2

[0068] This invention relates to a time-of-arrival-assisted position verification method for a Loran receiver, which is implemented according to the following steps:

[0069] Step 1: The Roland receiver obtains the Time of Arrival (TOA) of the complete station chain, including the three stations of a complete chain and any additional stations, denoted as TOA0TOA respectively. M TOA X TOA Y and TOA0;

[0070] Step 2: Based on the complete TOA information of the platform chain, use hyperbolic positioning to calculate the two positions P1 and P2;

[0071] like Figure 1 As shown, the three platforms are denoted as Platform 1, Platform 2, and Platform 3; let the spherical latitude and longitude of Platform 1, Platform 2, and Platform 3 be respectively... The baseline length between station 1 and station 2 is d1, the baseline length between station 3 and station 2 is d3, the azimuth angle from station 2 to station 1 is β1, and the azimuth angle from station 2 to station 3 is β3; the time difference between the receiver receiving the same signal transmitted from the main and auxiliary stations is ΔT. i ξ1 is the difference in ground distance from receiver P to station 2 and to station 1, and ξ2 is the difference in ground distance from receiver P to station 2 and to station 3.

[0072] Receiver point P is an unknown location point on the sphere, and its spherical latitude and longitude coordinates are: ρ1, ρ2, and ρ3 represent the spherical distances from point P to platforms 1, 2, and 3, respectively, and θ represents the azimuth angle from platform 2 to point P. All of these are unknowns.

[0073] Specifically:

[0074] Step 2.1: In the spherical triangles formed by station 1, station 2, and receiver P, and the spherical triangles formed by station 3, station 2, and receiver P, establish the spherical hyperbolic positioning equations and solve them, as shown in equation (1):

[0075]

[0076] The above system of equations contains four equations with four unknowns (ρ1, ρ2, ρ3, θ). A unique solution can be found to determine the polar coordinates (ρ2, θ) of receiver point P, which can then be converted into spherical latitude and longitude coordinates.

[0077] Step 2.2, substitute the third and fourth formulas in formula (1) into the first and second formulas respectively to obtain formula (2), and simplify to obtain the spherical distance from point P to platform 2, as shown in formula (3);

[0078]

[0079]

[0080] Step 2.3, rearrange and combine formula (3) into a single equation, resulting in formula (4):

[0081]

[0082] Step 2.4, transform equation (4) into a trigonometric equation containing only the azimuth angle θ from point P to point P, as shown in equation (5):

[0083] Asinθ+Bcosθ+D=0 (5);

[0084] A, B, and D are all auxiliary variables, and the calculation formula is shown in equation (6):

[0085]

[0086] Further transformation of equation (5) yields equation (7);

[0087]

[0088] To simplify the calculation, an auxiliary variable ψ is introduced, as shown in equation (8):

[0089]

[0090] Equation (5) can then be rewritten as equation (9):

[0091]

[0092] From the periodicity of the inverse trigonometric function, we know that θ+ψ has two values, as shown in equation (10):

[0093]

[0094] Further calculations yielded two azimuth angles θ1 and θ2 from platform 2 to point P, as shown in equation (11):

[0095]

[0096] Therefore, the expression for the polar coordinates (ρ2,θ) is shown in equation (12):

[0097]

[0098] According to formula (12), the polar coordinates (ρ2, θ) and spherical coordinates of point P can be obtained. The transformation relationship is shown in equation (13):

[0099]

[0100] Based on this, the spherical coordinates of the two positions P1 and P2 can be obtained. and Convert them into geodetic latitude and longitude coordinates (B1, L1) and (B2, L2);

[0101] Position spherical coordinates The transformation relationship for converting to geodetic latitude and longitude coordinates (B, L) is shown in equation (14):

[0102]

[0103] Step 3: Calculate the arrival times from the two locations P1 and P2 to the additional station, and denot them as T. 0-P1 and T 0-P2 As shown in equations (15)-(18);

[0104] T 0-P1 =d 0-P1 / c (15);

[0105] T 0-P2 =d 0-P2 / c (16);

[0106]

[0107]

[0108] In the formula, c is the speed of light, d 0-P1 It is the distance from P1 to the additional station, d 0-P2 It is the distance from P2 to the additional station. These are the spherical coordinates of the additional stations. These are the spherical coordinates of P1. These are the spherical coordinates of P2.

[0109] Step 4: Calculate the arrival times from the two locations P1 and P2 to the main station, and denot them as T. M-P1 and T M-P2 As shown in equations (19)-(22);

[0110] T M-P1 =d M-P1 / c (19);

[0111] T M-P2 =d M-P2 / c (20);

[0112]

[0113]

[0114] In the formula, c is the speed of light, d M-P1 It is the distance d from P1 to the main station M. M-P2 It is the distance from P2 to the main station M. These are the spherical coordinates of the main stage M. These are the spherical coordinates of P1. These are the spherical coordinates of P2.

[0115] Step 5: Calculate the error factors δ1 and δ2 of the two positions P1 and P2, as shown in equations (23) and (24), compare them and keep the position with the smaller error factor, and exclude the other position;

[0116] δ1=T M-P1 -(T M +T 0-P1 -T0) (23)

[0117] δ2=T M-P2 -(T M +T 0-P2 -T0) (24).

[0118] Example 3

[0119] The time-of-arrival-assisted position detection method for Roland receivers is implemented according to the following steps:

[0120] Assuming the location of the Roland receiver is (31.0511047N, 114.4246530E), and the received station signals originate from 6000M (Pucheng), 8390M (Xuancheng), 8390X (Raoping), and 8390Y (Rongcheng), with the speed of light c = 299792458 m / s. Xuancheng, Raoping, and Rongcheng form a complete 8390 station chain, while Pucheng is an additional station. The station coordinates are shown in Table 1.

[0121] Table 1 Coordinates of Luolantai Station

[0122]

[0123]

[0124] Step 1: The Roland receiver obtains the TOA (Transmission of Arrival) from the current location to the main and secondary stations of the station chain and the additional stations, which are T and T respectively. M T X T Y Both T0 and T0 are in seconds:

[0125] T M =1480.0053

[0126] T X =2894.2684

[0127] T Y =3358.8331

[0128] T0 = ​​2198.7334

[0129] Step 2: Based on the complete chain T obtained in Step 1 M T X and T YWe can calculate the two positions P1 and P2 as follows:

[0130] P1=(31.0511047N,114.4246530E)

[0131] P2=(29.1171282N,121.3894472E)

[0132] Step 3: Calculate the TOA from the two locations P1 and P2 to the additional station, respectively. 0-P1 and T 0-P2 The unit is seconds;

[0133] T 0-P1 =2096.3568

[0134] T 0-P2 =4307.6599

[0135] Step 4: Calculate the TOA from the two positions P1 and P2 to the main station, respectively. M-P1 and T M-P2 The unit is seconds.

[0136] T 0-P1 =1420.7002

[0137] T 0-P2 =1081.3699

[0138] Step 5: Calculate error factors δ1 and δ2 according to the formula;

[0139] δ1=0.000043

[0140] δ2 = 0.002507

[0141] Since δ1 < δ2, P1 = (31.0511047N, 114.4246530E) is the true location, so we keep it and exclude P2 = (29.1171282N, 121.3894472E). A total of 8 samples were tested, and the location results are shown in Table 2.

[0142] Table 2 Location test results

[0143]

[0144] As can be seen from this embodiment, the Roland receiver position verification method based on time of arrival is correct and effective.

Claims

1. A Loran receiver position verification method based on time-of-arrival assistance, characterized in that, The specific steps are as follows: Step 1: The Roland receiver obtains the arrival times of the complete station chain, including all three stations in the chain and any additional stations, denoted as... , , and ; Step 2: Based on the complete TOA information of the platform chain, use hyperbolic positioning to calculate two positions P1 and P2; specifically: The three platforms are denoted as Platform 1, Platform 2, and Platform 3; let the spherical latitude and longitude of Platform 1, Platform 2, and Platform 3 be respectively... , , The baseline length between Station 1 and Station 2 is The baseline length between Taiwan Strait 3 and Taiwan Strait 2 is The azimuth angle from Taiwan 2 to Taiwan 1 is The azimuth angle from Taiwan 2 to Taiwan 3 is ; The time difference between the receiver receiving the same signal transmitted from the main and secondary stations is ; Let P be the difference in ground distance from receiver P to station 2 and from receiver P to station 1. This is the difference in ground distance from receiver P to station 2 and station 3; Receiver point P is an unknown location point on the sphere, and its spherical latitude and longitude coordinates are: ; , , These represent the spherical distances from point P to platforms 1, 2, and 3, respectively. The azimuth angle from point 2 to point P is an unknown quantity; Step 2.1: In the spherical triangles formed by station 1, station 2, and receiver P, and the spherical triangles formed by station 3, station 2, and receiver P, establish the spherical hyperbolic positioning equations and solve them, as shown in equation (1): （1）； The above system of equations contains four equations and four unknowns. A unique solution can be found to determine the polar coordinates of receiver point P. And convert it into spherical latitude and longitude coordinates. ; Step 2.2, substitute the third and fourth formulas in formula (1) into the first and second formulas respectively to obtain formula (2). After simplification, the spherical distance from point P to platform 2 can be obtained as shown in formula (3). （2）； （3）； Step 2.3, rearrange and combine formula (3) into a single equation, resulting in formula (4): （4）； Step 2.4, transform equation (4) into an equation containing only the azimuth angle from point P to point 2. The trigonometric equation is shown in equation (5): （5）； , , All are auxiliary variables, and the calculation formula is shown in equation (6): （6）； Further transformation of equation (5) yields equation (7); （7）； Auxiliary variables are introduced to simplify calculations. As shown in equation (8): （8）； Equation (5) can be rewritten as equation (9): （9）； It can be seen from the periodicity of inverse trigonometric functions There are two values ​​for , as shown in equation (10): （10）； Further calculations yielded two azimuth angles from point P to point 2. and As shown in equation (11): （11）； Therefore, polar coordinates The expression is shown in equation (12): （12） The polar coordinates of point P can be obtained according to formula (12). Spherical coordinates of point P The transformation relationship is shown in equation (13): （13）； Based on this, the spherical coordinates of the two positions P1 and P2 can be obtained. and Convert it into geodetic latitude and longitude coordinates. and ; Step 3: Calculate the arrival times from the two locations P1 and P2 to the additional station; Step 4: Calculate the arrival times of the two locations P1 and P2 from the main station; Step 5: Calculate the error factors for the two positions P1 and P2. and The comparison is performed, and the position with the smaller error factor is retained, while the other position is excluded.

2. The Loran receiver position verification method based on time-of-arrival assistance according to claim 1, characterized in that, In step 3, the arrival times of the two locations P1 and P2 to the additional station are denoted as follows: and As shown in equations (15)-(18); （15）； （16）； （17）； （18）； In the formula, At the speed of light, It is the distance from P1 to the additional station. It is the distance from P2 to the additional station. These are the spherical coordinates of the additional stations. These are the spherical coordinates of P1. These are the spherical coordinates of P2.

3. The Loran receiver position verification method based on time-of-arrival assistance according to claim 2, characterized in that, In step 4, the arrival times of the two locations P1 and P2 from the main station are recorded as follows: and As shown in equations (19)-(22); （19）； （20）； （21）； （22）； In the formula, It is the distance from P1 to the main station M. It is the distance from P2 to the main station M. These are the spherical coordinates of the main stage M.

4. The Loran receiver position verification method based on time-of-arrival assistance according to claim 3, characterized in that, The error factors of the two positions P1 and P2 in step 5 and As shown in equations (23) and (24); （23） （24）。

Images