A method for Loran pseudo-range time service positioning based on Vincenty formula

Abstract

The application relates to a Loran pseudo-range time service positioning method based on a Vincenty formula and belongs to the technical field of navigation. The method comprises the following steps: selecting a Loran station chain whose signal range contains the position of a receiver, and obtaining the longitude and latitude coordinates of one main station and two vice stations in the Loran station chain; using the receiver to measure the arrival time of the signals emitted by the three stations to the receiver; according to the longitude and latitude coordinates of the three stations, the arrival time and the initial coordinates of the receiver, calculating the new coordinates and time of the receiver based on the Vincenty ranging formula; and converting the new coordinates of the receiver from the ellipsoid reference surface to the longitude and latitude on the actual earth surface, so that the coordinates and time of the receiver are obtained. Compared with the existing pseudo-range algorithm, the application overcomes the problems of harsh initial value selection range and singular value in calculation, so that the initial value selection range is increased by more than four times, and the calculation speed is increased by nearly one time; the application can be used for the fusion positioning and time service of long wave and satellite signals, and the positioning and time service capability is enhanced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of navigation, and particularly relates to a Loran pseudo-range time service positioning method based on Vincenty formula. BACKGROUND

[0002] The performance indexes of the Beidou satellite navigation system (BDS) in positioning and navigation, time service, satellite-based augmentation, precise point positioning, regional short message communication, global short message communication and international search and rescue service have reached the requirements of the Beidou system. However, like other GNSS systems, the Beidou system is also interfered to various degrees, which can cause the position navigation and space-time service provided by the BDS to be unavailable or unreliable.

[0003] Therefore, it is extremely necessary to build a backup system for the BDS. It is widely recognized internationally that the Loran system is the most suitable backup system for the satellite-based navigation and time service system for the following three reasons: independence, low-frequency signal and high power.

[0004] However, the positioning and time service precision of the traditional Loran system is low, and cannot meet the use requirements. The Loran system usually adopts a hyperbolic time difference method of three two-baseline chains for positioning and solution, however, this method has some limitations, such as that the positioning of a single chain causes the precision to be limited by the station layout mode and measurement error, and although the time delay difference is used to eliminate the clock difference between the Loran receiver and the Loran system, the clock difference of the receiver cannot be directly solved. As for the positioning algorithms of double-chain and multi-chain, although the utilization rate of the chain is improved, the potential of the chain positioning is exerted, but the complexity still exists, and the time service solution is still limited. SUMMARY

[0005] The technical problem to be solved by the application is:

[0006] In order to improve the positioning and time service precision of the Loran system, the application provides a Loran pseudo-range time service positioning method based on Vincenty formula, which is used for the backup system of the Beidou satellite navigation system (BDS).

[0007] In order to solve the above technical problem, the application adopts the following technical scheme:

[0008] A Loran pseudo-range time service positioning method based on Vincenty formula, characterized in that it comprises:

[0009] A Loran chain whose signal range contains the position of the receiver is selected, and the longitude and latitude coordinates of a main station and two auxiliary stations in the Loran chain are obtained;

[0010] The arrival times of the signals emitted by the three stations to the receiver are measured by the receiver.

[0011] According to the latitude and longitude coordinates of the three stations, the time of arrival and the initial coordinates of the receiver, the coordinates and time of the new receiver are solved based on the Vincenty distance formula;

[0012] The coordinates of the new receiver are converted from the ellipsoid reference surface to the latitude and longitude of the actual earth surface, that is, the receiver coordinates and time are obtained.

[0013] The further technical solution of the application: if the three stations are selected from different Loran chains, time synchronization needs to be completed.

[0014] The further technical solution of the application: according to the latitude and longitude coordinates of the three stations, the time of arrival and the initial coordinates of the receiver, the coordinates and time are solved based on the Vincenty distance formula; including:

[0015] The initial coordinates of the receiver are obtained;

[0016] The latitude and longitude coordinates of the three stations are used to express the Vincenty distance formula, and the differential equation set is constructed based on the Vincenty distance formula;

[0017] The differential equation set is first-order Taylor expanded at the initial coordinates to obtain the partial differential equation set;

[0018] The iteration convergence threshold is set, and the receiver position and time are obtained by iteratively solving the partial differential equation set.

[0019] The further technical solution of the application: the hyperbolic positioning method is used to obtain the initial value of the receiver, and the convergence threshold of the latitude and longitude is set to be not greater than ±10 degrees.

[0020] The further technical solution of the application: the differential equation set, specifically:

[0021]

[0022] Wherein, ρ i represents the pseudo-range measured by the receiver, represents the Vincenty distance formula, t i represents the receiver time difference, δ i represents other error terms, and c is the speed of light.

[0023] The further technical solution of the application: the partial differential equation set, specifically:

[0024]

[0025] Wherein, D i is the true distance, and is the product of the time of arrival and the speed of light, ρ i0Pseudo range from the Loran station to the receiver, Pseudo range from the Loran station to the receiver, Partial derivative of lambda and t at rho i0 Partial derivative of lambda and t at rho Delta lambda and Delta t are Delta lambda and Delta t are

[0026] The further technical solution of the present application is that the iterative convergence threshold is less than 10 -6 radian.

[0027] A computer system, characterized by comprising: one or more processors, a computer readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0028] A computer readable storage medium, characterized by storing computer executable instructions, the instructions when executed are used to implement the above method.

[0029] A computer program product, characterized by comprising computer executable instructions, the instructions when executed are used to implement the above method.

[0030] The beneficial effects of the present application are:

[0031] The Loran pseudo range time service positioning method based on Vincenty formula provided by the present application can support the Loran receiver to simultaneously solve the positioning and time service results when working. When there is no observation error in the pseudo range, the positioning error can reach the millimeter level, and the time service error can reach the 10-4ns level. When there is random noise with a standard deviation of 100ns, the latitude and longitude error is less than 10 meters, and the time service error is less than 10-4ns.

[0032] Compared with the existing pseudo range algorithm, the Loran pseudo range time service positioning method based on Vincenty formula overcomes the problems of harsh initial value selection range and easy to appear singular value in solving, so that the initial value selection range is increased by more than four times, and the solving speed is increased by nearly one time.

[0033] In addition, the Loran pseudo range time service positioning method based on Vincenty formula is consistent in form with the pseudo range equation set of Beidou satellite positioning and time service calculation, and can be used for long wave and satellite signal fusion positioning and time service, and enhances the positioning and time service capability. BRIEF DESCRIPTION OF DRAWINGS

[0034] The accompanying drawings are included to provide a further understanding of embodiments and are incorporated in and constitute a part of this specification, illustrate embodiments, and together with the description serve to explain the principles of the present application. The same reference numerals in the drawings identify the same elements.

[0035] Figure 1A flowchart of a Loran pseudo-range time service positioning method based on Vincenty formula. DETAILED DESCRIPTION

[0036] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.

[0037] The present application provides a Loran pseudo-range time service positioning method based on Vincenty formula, as shown in Figure 1 The method comprises the following steps:

[0038] Step one: obtaining the coordinates of three Loran stations of the same chain in advance Wherein represents the latitude, λ i represents the longitude, i=1, 2, 3.

[0039] Step two: using the receiver to measure the arrival time td1, td2, td3 of the signals transmitted by the three stations to the receiver

[0040] Step three: inputting the initial coordinates and the parameters obtained in step one and step two, substituting them into the partial differential equation set based on Vincenty formula, and solving the new coordinates and the time t n .

[0041] Step four: repeating step three until the set convergence threshold and Δλ=λ n -λ n-1 < 10 -6 .

[0042] Step five: converting the final coordinates from the ellipsoid reference surface to the latitude and longitude on the actual earth surface, i.e. obtaining the receiver coordinates and time.

[0043] The above process comprises the following specific steps:

[0044] Step one, positioning and time service calculation flow:

[0045] Firstly, select the Loran station chain whose signal range contains the receiver position, and obtain the longitude and latitude coordinates of a main station and two sub-stations in the chain; if the selected stations are not in the same chain, time synchronization is needed; then use the Loran receiver to measure the signal arrival time of each station to the receiver, input the coordinates of the three stations and the corresponding arrival time into the solving program, input the initial value of the receiver, and set the convergence threshold, then the longitude and latitude of the receiver position and the time of the solving moment can be solved;

[0046] Step two: solving method:

[0047] Let the latitude of the unknown reference ellipsoid be σ , the longitude be λ, and the time be t:

[0048]

[0049] Where, ρ i represents the pseudo-range measured by the receiver, represents the Vincenty distance formula, t i represents the receiver time difference, δ i represents other error terms. Perform first-order Taylor expansion of the equation group at the initial value t=t0, to obtain the partial differential equation group:

[0050]

[0051] Where, D i is the true distance, i.e. the measured value without error terms. Express the equation group in matrix form:

[0052] B=A·X (3)

[0053]

[0054] Where,

[0055]

[0056] Next, calculate each partial differential term.

[0057] To calculate the partial derivative of σ with respect to λ, let u=sinσ and v=cosσ,

[0058] Where,

[0059]

[0060] Find the partial derivative of A and B with respect to λ:

[0061] ​

[0062] wherein,

[0063]

[0064]

[0065] the partial derivative of Δσ with respect to λ is:

[0066] Let:

[0067]

[0068] wherein,

[0069]

[0070] Substitute formula (4)-(27) into formula (3), and solve the receiver position and time by iterative calculation according to formula (28).

[0071] The initial value selection method of step one is:

[0072] The hyperbolic positioning method is used to obtain the initial value of the receiver, and the convergence threshold of the latitude and longitude of the hyperbolic positioning method is set to be not greater than ±10 degrees.

[0073] The convergence threshold setting method of step one is:

[0074] The iterative convergence threshold is set to be less than 10 -6 (radian), that is, Δλ<10 -6 At this time, the latitude and longitude distance error is less than 7 meters. It should be noted that the convergence threshold can be continuously reduced, but this will increase the number of iterations.

[0075] The application proposes a Loran pseudo-range time service positioning method based on Vincenty formula. In terms of algorithm, the positioning and time service solving method of the Loran system is improved from the original "three stations and two baseline hyperbolic time difference method" to the "Loran pseudo-range solving method based on vincenty distance formula", which overcomes the problem that the positioning of a single chain is limited by the station layout method and measurement error and cannot directly solve the receiver clock error, and also makes the Loran positioning and time service solving equation have the same form as the satellite positioning and time service solving equation. In terms of algorithm accuracy, the positioning and time service error of the Loran pseudo-range solving method based on vincenty distance formula is close to 0, and has high accuracy. When there is random noise with a standard deviation of 100ns, the latitude and longitude error is less than 10 meters, the time service error is less than 10-4ns, and high latitude and longitude can be provided to meet the demand of Loran positioning and time service. ​

[0076] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application.

Claims

1. A Loran pseudo-range timing positioning method based on the Vincenty formula, characterized in that: include: Select a Loran station chain whose broadcast signal range includes the receiver location, and obtain the longitude and latitude coordinates of a primary station and two secondary stations in the Loran station chain; Use a receiver to measure the arrival time of the signals transmitted by the three stations to the receiver; Based on the latitude and longitude coordinates of the three stations, the arrival time, and the initial coordinates of the receiver, the new receiver coordinates and time are calculated using the Vincenty ranging formula; this includes: Get the initial coordinates of the receiver; The latitude and longitude coordinates of the three stations are used to express the Vincenty ranging formula, and a differential equation system is constructed based on the Vincenty ranging formula; the differential equation system is specifically: in, represents the pseudorange measured by the receiver, L ( , ) represents the Vincenty distance formula, t i Indicates the receiver time difference, δ i represents other error terms, c is the speed of light; Performing a first-order Taylor expansion on the differential equations at the initial coordinates yields a partial differential equation system; the partial differential equation system is specifically: in ，D i is the true distance, the product of the arrival time and the speed of light, is the pseudorange from the Loran station to the receiver, for right The partial derivative of The value of for The amount of change; Set the iterative convergence threshold and iteratively solve the partial differential equations to obtain the receiver position and time; The coordinates of the new receiver are converted from the ellipsoid reference surface to the latitude and longitude of the actual earth surface to obtain the receiver coordinates and time.

2. The Loran pseudorange timing and positioning method based on the Vincenty formula according to claim 1, wherein: It also includes that if the three stations select different Loran stations, time synchronization must be completed.

3. The Loran pseudorange timing and positioning method based on the Vincenty formula according to claim 1, characterized in that: The hyperbola positioning method is used to obtain the initial value of the receiver. The hyperbola positioning method sets the convergence threshold of the longitude and latitude to be no greater than ±10 degrees.

4. The Loran pseudorange timing and positioning method based on the Vincenty formula according to claim 1, wherein: The iterative convergence threshold is less than 10 -6 radian.

5. A computer system, characterized in that include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method of claim 1.

6. A computer-readable storage medium, characterized in that Computer-executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 1.

7. A computer program product, characterized in that The invention comprises computer executable instructions, which are used to implement the method of claim 1 when the instructions are executed.

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