Bearings-only target positioning method and device based on angle measurement error constraint optimization estimation

Abstract

The present invention belongs to the technical field of passive positioning, and specifically discloses a pure bearing target positioning method and device based on angular measurement error constraint optimization estimation, and then improves the positioning accuracy of the target by improving the measurement accuracy. The method includes: constructing an objective function in a global coordinate system and obtaining an equation constraint condition of the angular measurement error, and then constructing a Lagrangian equation; performing first-order and second-order partial derivative calculations on the Lagrangian equation, and then obtaining a KKT equation about the angular measurement error and the Lagrangian multiplier; solving the equation and cyclically iterating the above KKT equation until the detection condition is less than a preset threshold, and then obtaining an estimated value of the angular measurement error; subtracting the estimated value of the angular measurement error from the measurement to obtain a new measurement, which is applied to the corresponding positioning algorithm to effectively improve the positioning accuracy of the target.

Description

Technical Field

[0001] The present invention belongs to the technical field of passive positioning, and more specifically, relates to a bearing-only target positioning method and device based on angular error constraint optimization estimation. Background Art

[0002] Passive positioning technology has the advantages of good concealment, long range, and strong anti-interference ability compared with active positioning due to the lack of electromagnetic radiation. It is widely used in military and civilian scenarios such as radar countermeasures, communication countermeasures, infrared, and sonar. In the bearing-only (BO) passive positioning technology, the current research direction is more concentrated on positioning algorithms and performance analysis. The former is to analyze and compare performance indicators such as the unbiasedness, consistency, and effectiveness of the algorithm, and improve the positioning accuracy by improving the performance of the algorithm. The latter is to analyze and compare the estimation results of the positioning algorithm using positioning accuracy measurement indicators such as circular error probable (CEP) and error ellipse (EE), and improve the positioning accuracy through track optimization or optimal configuration.

[0003] Although the above two directions can significantly improve the positioning accuracy of the target, they ignore a basic fact, that is, in BO passive positioning, the angle measurement error can also be used as an estimated object. When the system error is not considered and according to the central limit theorem, the angle measurement error can be considered as a random variable that obeys the Gaussian white noise distribution. Similar to the estimation of the random variable of the target position by the positioning algorithm, the corresponding algorithm can be used in theory to estimate the angle measurement error. After obtaining the estimated value of the angle measurement error, the approximate true angle value can be obtained by subtracting the estimated value of the angle measurement error from the angle measurement value. Applying this true value to the above positioning algorithm or performance analysis can effectively improve the positioning accuracy of the target. Summary of the invention

[0004] Based on the above defects or improvement needs of the prior art, the present invention aims at the fact that there is little estimation of angle measurement error in the existing BO passive positioning to improve the positioning accuracy, and proposes a sequential quadratic programming (SQP) equality constraint angle measurement error optimization estimation method, which improves the positioning accuracy of the target by improving the measurement quality. Therefore, it is particularly suitable for BO positioning scenarios such as multiple fixed sensors to a single mobile target, a single mobile sensor to a single fixed target, or joint positioning scenarios related to BO.

[0005] To achieve the above object, according to one aspect of the present invention, a bearings-only target positioning method based on angle measurement error constraint optimization estimation is proposed, comprising the following steps:

[0006] Step 1: construct the objective function in the global coordinate system and obtain the equality constraint conditions of the angle measurement error, and then construct the Lagrangian equation;

[0007] Step 2, calculating the first-order and second-order partial derivatives of the Lagrange equation respectively, and then obtaining the KKT equation about the angle measurement error and the Lagrange multiplier;

[0008] Step 3, solving the equation and iterating the KKT equation in a loop until the detection condition is less than a preset threshold, thereby obtaining an estimated value of the angle measurement error;

[0009] Step 4: subtract the angle measurement error estimate from the measurement to obtain a new high-precision measurement.

[0010] As further preferred, in step 1, constructing the objective function in the global coordinate system includes:

[0011] (101) Assume that in the global coordinate system Sensors , or 1 sensor in If the direction is measured at different positions, the tilt angle between each sensor or each sensor position is:

[0012]

[0013] in, For sensor The coordinate value in the global coordinate system, For sensor The coordinate value in the global coordinate system, ;

[0014] (102) Assume that the sensor The azimuth measurement is , then:

[0015]

[0016] in, is the true value of the azimuth, is the angle measurement error;

[0017] (103) Assume that the angle measurement errors are independent of each other and have a mean of 0 and a variance of Gaussian distribution, then in the two-dimensional positioning scene, the following objective function is constructed:

[0018]

[0019] in, .

[0020] As further preferred, in step 1, the equality constraint condition of the angle measurement error includes:

[0021] (111) Assume that the sensor , The baseline distance between , then:

[0022]

[0023] in, For sensor The coordinate value in the global coordinate system, For sensor Coordinate values ​​in the global coordinate system;

[0024] (112) In sensor ~ The sine theorem is used to construct angle constraints:

[0025]

[0026] Or a baseline constraint:

[0027]

[0028] in, It is called the angle constraint; This is called a baseline constraint.

[0029] As a further preferred embodiment, in step 1, the Lagrangian equation includes:

[0030]

[0031] or

[0032]

[0033] in, , is the angle measurement error; is the Lagrange multiplier; is the angle constraint; is the baseline constraint.

[0034] As further preferred, step 2 comprises the following steps:

[0035] (201) Based on the Lagrange equation, we solve the equations about , The first-order partial derivative of , and then obtain the first-order gradient vector in the KKT equation;

[0036] (202) Based on the Lagrange equation, we solve the equations about , The second-order partial derivative of , and then obtain the second-order Hessian matrix in the KKT equation;

[0037] (203) According to the first-order gradient vector and the second-order Hessian matrix, the following KKT equation is constructed:

[0038]

[0039] or

[0040]

[0041] in, , They are , The increment of ;and

[0042]

[0043]

[0044] or

[0045]

[0046]

[0047] As further preferred, step three comprises the following steps:

[0048] (301) is obtained from the KKT equation , The increment is:

[0049]

[0050] or

[0051]

[0052] (302) , The updated value of is:

[0053]

[0054] in, , Respectively represent The loop iteration , The value of

[0055] (303) The following detection conditions are constructed:

[0056]

[0057] in, Represents 2-norm; sets detection threshold , then when , and then loop through steps 2 to 3 until the equation is no longer true. as an estimate of the angle measurement error.

[0058] As further preferred, step 4 includes the following steps:

[0059] (401) After obtaining After that, the new measurement can be expressed as:

[0060]

[0061] in, For new measurements; ; is the estimated value of the angle measurement error;

[0062] (402) Applying the new measurement to a positioning algorithm to obtain an estimate of the target position; preferably, the positioning algorithm is a least squares positioning algorithm.

[0063] According to another aspect of the present invention, there is also provided a bearings-only target positioning system based on angle measurement error constraint optimization estimation, comprising:

[0064] The first main control module is used to construct the objective function in the global coordinate system and obtain the equality constraint conditions of the angle measurement error, and then construct the Lagrange equation;

[0065] The second main control module is used to calculate the first-order and second-order partial derivatives of the Lagrange equation, and then obtain the KKT equation about the angle measurement error and the Lagrange multiplier;

[0066] The third main control module is used to solve the equation and iterate the KKT equation until the detection condition is less than a preset threshold, thereby obtaining an estimated value of the angle measurement error;

[0067] The fourth main control module is used to subtract the angle measurement error estimate from the measurement to obtain a new high-precision measurement.

[0068] According to another aspect of the present invention, there is also provided an electronic device, comprising:

[0069] At least one processor, at least one memory and a communication interface; wherein,

[0070] The processor, memory and communication interface communicate with each other;

[0071] The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a bearing-only target positioning method based on angle measurement error constraint optimization estimation according to any of the above embodiments or a combination of multiple embodiments.

[0072] According to another aspect of the present invention, a non-transitory computer-readable storage medium is also provided, wherein the non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions enable the computer to execute a pure bearing target positioning method based on angular error constraint optimization estimation according to any embodiment or a combination of multiple embodiments described above.

[0073] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0074] The present invention improves the positioning accuracy of the target by improving the measurement quality, and the indirect beneficial effect is to further improve the benefits of the positioning algorithm and performance analysis. As mentioned above, the positioning algorithm is improved by improving the performance indicators such as the unbiasedness, consistency and effectiveness of the algorithm, while the performance analysis is to optimize the track of a single sensor or the position of multiple sensors through specific positioning accuracy measurement indicators, both of which are to improve the positioning accuracy of the target.

[0075] The present invention estimates the measurement error of the sensor, and then subtracts the estimated value of the measurement error from the measured value to obtain an approximate measurement true value. Applying the true value to the positioning algorithm can enable the algorithm to obtain an approximate unbiased and consistent estimate and improve the effectiveness of the algorithm, thereby improving the positioning accuracy of the algorithm; applying the true value to performance analysis can further improve the optimization space of a single sensor track or multi-sensor configuration, thereby improving the positioning accuracy of the target. Therefore, the results of the present invention can be applied to research directions in all BO technologies such as positioning algorithms and performance analysis. The core is to improve the positioning accuracy of the target by improving the measurement quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of a method for bearings-only target positioning based on angle measurement error constraint optimization estimation according to an embodiment of the present invention;

[0077] Figure 2 is a schematic diagram of positioning of four sensors in an embodiment when there is no angle measurement error;

[0078] Figure 3 is a schematic diagram of sensor positions and target tracks in an embodiment;

[0079] Figure 4The sensor in the embodiment Schematic diagram of RMS comparison results during positioning;

[0080] Figure 5 The sensor in the embodiment Schematic diagram of RMS comparison results during positioning. DETAILED DESCRIPTION

[0081] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0082] Example 1

[0083] In this embodiment, Figure 1 As shown, the left side is the angle measurement error estimation method using SQP for optimization estimation, and the right side is the positioning method after the measurement is updated. In the angle measurement error estimation method, it is first necessary to construct the objective function and obtain the equality constraints of the angle measurement error, and then establish the Lagrange equation; then solve the first-order gradient vector and the second-order Hessian matrix of the equation respectively, and then construct the KKT equation; finally, solve the equation, and iterate when the detection condition is greater than the preset threshold, otherwise stop the iteration and output the estimated value of the angle measurement error. In the positioning method, the estimated value of the angle measurement error is first used to update the original measurement to obtain a new measurement; then the new measurement is applied to any existing positioning algorithm to obtain an estimated value of the target position.

[0084] The specific steps are as follows:

[0085] Step 1: Construct the Lagrange equation

[0086] (1) Calculate the tilt angle between sensors: Figure 2 As shown, assuming that there are Sensors ,in , or 1 sensor in If the direction is measured at different positions, the tilt angle between each sensor or each sensor position is:

[0087] (1)

[0088] In particular, when When Parallel to the horizontal axis of the coordinate system; Figure 2 middle shown.

[0089] (2) Constructing the objective function: Assuming that the sensor The azimuth measurement is , then:

[0090] (2)

[0091] in, is the true value of the azimuth; is the angle measurement error. Assuming that are independent of each other and have a mean of 0 and a variance of Gaussian distribution. In the two-dimensional positioning scenario, the following objective function can be constructed:

[0092] (3)

[0093] in, .

[0094] (3) Obtaining constraints: Sensor , The baseline distance between , then:

[0095] (4)

[0096] when hour, With the goal The distance between . Figure 2 in Using the sine theorem, we can construct the following two equality constraints:

[0097] (5)

[0098] (6)

[0099] Among them, equation (5) is called the angle constraint relationship; equation (6) is called the baseline constraint relationship. Similarly, for For each sensor, they can be constructed as follows Constraints:

[0100] (7)

[0101] (8)

[0102] In practical applications, only one of equations (7) and (8) is used. The following content of this embodiment only takes equation (7) as an example, that is, the angle constraint relationship is explained.

[0103] (4) Construct the Lagrange equation: Assume that the Lagrange multiplier is , then the following Lagrange equation can be constructed:

[0104] (9)

[0105] At this time, it is necessary to give , The initial value of .

[0106] Step 2: Construct the KKT equation

[0107] (1) Obtain the first-order gradient vector: Calculate (9) , The partial derivative of

[0108] (10)

[0109] (11)

[0110] in,

[0111] (12)

[0112] for about The gradient of

[0113] (13)

[0114] for about gradient.

[0115] (2) Obtain the second-order Hessian matrix: For equation (10), calculate , The partial derivative of

[0116] (14)

[0117] (15)

[0118] in,

[0119] (16)

[0120] for about The Hessian matrix of

[0121] (17)

[0122] in,

[0123] (18)

[0124] for about The Hessian matrix of .

[0125] For (11), we can calculate , The partial derivatives of are:

[0126] (19)

[0127] (20)

[0128] (3) Constructing KKT equation: Combining equations (14), (15), (19) and (20), we can construct the following KKT equation:

[0129] (twenty one)

[0130] in, , They are , The increment of .

[0131] Step 3: Solve the KKT equation

[0132] (1) Obtaining the increment: From formula (21), we can know that:

[0133] (twenty two)

[0134] (2) Obtaining the updated value: From formula (22), we can see that , The updated value of is:

[0135] (twenty three)

[0136] in, , Respectively represent The loop iteration , The value of .

[0137] (3) Constructing detection conditions: Use formula (23) to construct the following detection conditions:

[0138] (twenty four)

[0139] in, represents the 2-norm.

[0140] (4) Loop iteration: setting detection threshold , then when:

[0141] (25)

[0142] , execute (10) to (24) repeatedly until equation (25) fails to hold; and replace equation (23) with As an estimate of the angle measurement error.

[0143] Step 4: Solve for the target position

[0144] (1) Obtaining new measurements: After that, the new measurement can be expressed as:

[0145] (26)

[0146] in, Combining (2) we can know:

[0147] (27)

[0148] in, Equation (27) shows that the new measurement is equivalent to the true value of the measurement.

[0149] (2) Algorithm solution: Applying equation (26) to a specific positioning algorithm can obtain an estimated value of the target position. The present invention adopts the least square (LS) positioning algorithm.

[0150] Example 2

[0151] In this embodiment, the method for bearing-only target positioning is described using a baseline constraint relationship, wherein the steps before constructing the constraint conditions are the same as those in Embodiment 1. The steps starting from constructing the Lagrangian equation are as follows:

[0152] (4) Construct the Lagrange equation: Assume that the Lagrange multiplier is , then the following Lagrange equation can be constructed:

[0153] (9)

[0154] At this time, it is necessary to give , The initial value of .

[0155] Step 2: Construct the KKT equation

[0156] (1) Obtain the first-order gradient vector: Calculate (9) , The partial derivative of

[0157] (10)

[0158] (11)

[0159] in,

[0160] (12)

[0161] for about The gradient of

[0162] (13)

[0163] for about gradient.

[0164] (2) Obtain the second-order Hessian matrix: For equation (10), calculate , The partial derivative of

[0165] (14)

[0166] (15)

[0167] in,

[0168] (16)

[0169] for about The Hessian matrix of

[0170] (17)

[0171] in,

[0172] (18)

[0173] for about The Hessian matrix of .

[0174] For (11), we can calculate , The partial derivatives of are:

[0175] (19)

[0176] (20)

[0177] (3) Constructing KKT equation: Combining equations (14), (15), (19) and (20), we can construct the following KKT equation:

[0178] (twenty one)

[0179] in, , They are , The increment of .

[0180] Step 3: Solve the KKT equation

[0181] (1) Obtaining the increment: From formula (21), we can know that:

[0182] (twenty two)

[0183] (2) Obtaining the updated value: From formula (22), we can see that , The updated value of is:

[0184] (twenty three)

[0185] in, , Respectively represent the loop iteration , The value of .

[0186] (3) Constructing detection conditions: Use formula (23) to construct the following detection conditions:

[0187] (twenty four)

[0188] in, represents the 2-norm.

[0189] (4) Loop iteration: setting detection threshold , then when:

[0190] (25)

[0191] , execute (10) to (24) repeatedly until equation (25) fails to hold; and replace equation (23) with As an estimate of the angle measurement error.

[0192] like Figure 2 and Figure 3 As shown in the figure, the position relationship between the four sensors and the target track is marked when there is no angle measurement error. Figure 3 middle, , , , The target motion equation is ,and , the sampling interval is 1km. Figure 4 It is used RMS comparison results during positioning. Implementation conditions: Standard deviation of the angle measurement error of each sensor ; The initial value of the angle measurement error of each sensor is ; Initial value of the multiplier ; Detection threshold ; Monte Carlo simulation 2000 times. The root mean square error (RMS) is used to measure the positioning accuracy. In the figure, "modified LS" means that the angle measurement error is estimated by the angle measurement error estimation method of the present invention, and then the updated measurement is applied to the LS algorithm. It can be seen from the figure that the positioning accuracy of the "modified LS" algorithm is significantly better than that of the LS algorithm. Figure 5 It is used RMS comparison results during positioning. Implementation conditions: The initial value of the angle measurement error of each sensor is ; Initial value of the multiplier ; Other conditions are the same Figure 4 As can be seen from the figure, the positioning accuracy of the "modified LS" algorithm is significantly better than that of the LS algorithm.

[0193] The implementation basis of each embodiment of the present invention is to implement programmed processing by a device with a processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present invention can be encapsulated into various modules. Based on this reality, on the basis of the above embodiments, the embodiment of the present invention provides a pure bearing target positioning system based on the optimization estimation of the angle measurement error constraint, which is used to execute a pure bearing target positioning method based on the optimization estimation of the angle measurement error constraint in any embodiment or a combination of multiple embodiments involved in the above method. The system includes: a first main control module, which is used to construct an objective function in a global coordinate system and obtain the equality constraint condition of the angle measurement error, and then construct the Lagrangian equation; a second main control module, which is used to calculate the first-order and second-order partial derivatives of the Lagrangian equation respectively, and then obtain the KKT equation about the angle measurement error and the Lagrangian multiplier; a third main control module, which is used to solve the equation and iterate the KKT equation until the detection condition is less than the preset threshold, and then obtain the estimated value of the angle measurement error; a fourth main control module, which is used to subtract the estimated value of the angle measurement error from the measurement to obtain a new high-precision measurement.

[0194] The method of the embodiment of the present invention is implemented by relying on electronic devices, so it is necessary to introduce the relevant electronic devices. For this purpose, an embodiment of the present invention provides an electronic device, which includes: at least one processor, a communication interface, at least one memory, and a communication bus, wherein at least one processor, a communication interface, and at least one memory communicate with each other through the communication bus. At least one processor can call the logic instructions in at least one memory to execute all or part of the steps of the method provided by the aforementioned method embodiments.

[0195] In addition, the logic instructions in the at least one memory mentioned above can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each method embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0196] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Those of ordinary skill in the art may understand and implement it without creative work.

[0197] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0198] The flowcharts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present invention. Based on this understanding, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, a program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and sometimes they can be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or the flowchart, and the combination of the boxes in the block diagram and / or the flowchart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0199] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for bearings-only target positioning based on angle measurement error constraint optimization estimation, characterized in that: The following steps are involved: Step 1: construct the objective function in the global coordinate system and obtain the equality constraint conditions of the angle measurement error, and then construct the Lagrangian equation; The equality constraints of the angle measurement error include: (111) Assume that the sensor , The baseline distance between , then: in, For sensor The coordinate value in the global coordinate system, For sensor Coordinate values ​​in the global coordinate system; (112) In sensor ~ The sine theorem is used to construct angle constraints: Or a baseline constraint: in, It is called the angle constraint; It is called the baseline constraint; The Lagrange equations include: or in, , is the angle measurement error; is the Lagrange multiplier; is the angle constraint; is the baseline constraint; Step 2, calculating the first-order and second-order partial derivatives of the Lagrange equation respectively, and then obtaining the KKT equation about the angle measurement error and the Lagrange multiplier; Step 3, solving the equation and iterating the KKT equation in a loop until the detection condition is less than a preset threshold, thereby obtaining an estimated value of the angle measurement error; Step 4: subtract the angle measurement error estimate from the measurement to obtain a new high-precision measurement.

2. The method for bearings-only target positioning based on angle measurement error constraint optimization estimation according to claim 1, characterized in that: In step 1, constructing the objective function in the global coordinate system includes: (101) Assume that in the global coordinate system Sensors , or 1 sensor in If the direction is measured at different positions, the tilt angle between each sensor or each sensor position is: in, For sensor The coordinate value in the global coordinate system, For sensor The coordinate value in the global coordinate system, ; (102) Assume that the sensor The azimuth measurement is , then: in, is the true value of the azimuth, is the angle measurement error; (103) Assume that the angle measurement errors are independent of each other and have a mean of 0 and a variance of Gaussian distribution, then in the two-dimensional positioning scene, the following objective function is constructed: in, .

3. The method for bearings-only target positioning based on angle measurement error constraint optimization estimation according to claim 1, characterized in that: Step 2 includes the following steps: (201) Based on the Lagrange equation, we solve the equations about , The first-order partial derivative of , and then obtain the first-order gradient vector in the KKT equation; (202) Based on the Lagrange equation, we solve the equations about , The second-order partial derivative of , and then obtain the second-order Hessian matrix in the KKT equation; (203) According to the first-order gradient vector and the second-order Hessian matrix, the following KKT equation is constructed: or in, , They are , The increment of ;and or 。 4. The method for bearings-only target positioning based on angle measurement error constraint optimization estimation according to claim 1, characterized in that: Step three includes the following steps: (301) is obtained from the KKT equation , The increment is: or (302) , The updated value of is: in, , Respectively represent The loop iteration , The value of (303) The following detection conditions are constructed: in, Represents 2-norm; sets detection threshold , then when , and then loop through steps 2 to 3 until the equation is no longer true. as an estimate of the angle measurement error.

5. The method for bearings-only target positioning based on angle measurement error constraint optimization estimation according to claim 4, characterized in that: Step 4 includes the following steps: (401) After obtaining After that, the new measurement can be expressed as: in, For new measurements; ; is the estimated value of the angle measurement error; (402) The new measurement is applied to a positioning algorithm to obtain an estimate of the target location.

6. The method for bearings-only target positioning based on angle measurement error constraint optimization estimation according to claim 5, characterized in that: The positioning algorithm is a least squares positioning algorithm.

7. A bearings-only target positioning system based on angle measurement error constraint optimization estimation, characterized in that: A method for bearings-only target positioning based on angle measurement error constraint optimization estimation for implementing any one of claims 1 to 6, comprising: The first main control module is used to construct the objective function in the global coordinate system and obtain the equality constraint conditions of the angle measurement error, and then construct the Lagrange equation; The second main control module is used to calculate the first-order and second-order partial derivatives of the Lagrange equation, and then obtain the KKT equation about the angle measurement error and the Lagrange multiplier; The third main control module is used to solve the equation and iterate the KKT equation until the detection condition is less than a preset threshold, thereby obtaining an estimated value of the angle measurement error; The fourth main control module is used to subtract the angle measurement error estimate from the measurement to obtain a new high-precision measurement.

8. An electronic device, characterized in that: include: At least one processor, at least one memory and a communication interface; wherein, The processor, memory and communication interface communicate with each other; The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a bearing-only target positioning method based on angle measurement error constrained optimization estimation as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method for bearings-only target positioning based on angle measurement error constrained optimization estimation as described in any one of claims 1 to 6.

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