Unmanned aerial vehicle arrival angle positioning method based on improved star-graffiti optimization algorithm

Abstract

The invention relates to an unmanned aerial vehicle (AOA) arrival angle positioning method based on an improved star-graffiti optimization algorithm, and aims to solve the problems that in traditional AOA positioning, precision is insufficient due to error nonlinear accumulation, and an existing optimization algorithm is prone to falling into local optimum. The method comprises the following steps of: designing a staged optimization framework based on an observation sequence according to an error propagation characteristic of a pod attitude, inhibiting a nonlinear cumulative effect of an error, and then realizing optimal distribution and compensation of an error source by combining an improved star-graffiti optimization algorithm and introducing Cubic chaotic mapping and a spiral search strategy. Monte Carlo simulation experiments show that the positioning error distance of the improved algorithm is improved by 73.29% compared with AOA positioning precision, the precision of the improved algorithm is improved by 58.12% compared with an original star graffiti optimization algorithm, the improved algorithm is obviously superior to other comparison algorithms, and it is proved that the method can effectively correct the nonlinear disturbance of the photoelectric system.

Description

Technical Field

[0001] This invention relates to the field of UAV positioning methods, specifically a UAV angle of arrival positioning method based on an improved Star Raven optimization algorithm. Background Technology

[0002] With its high stealth, low risk, small size, and ability to flexibly carry various sensors according to mission requirements, the UAV has become an important carrier in the modern flight field. At the same time, monocular vision sensors have advantages such as high accuracy and low cost. Therefore, combining monocular vision with UAVs for target localization has become a widely studied subject by scholars [3]. Traditional UAV target localization methods are mainly divided into active localization and passive localization. Active localization uses the measured distance and angle information between the target point and the photoelectric platform to locate the target. However, when using and radiating electromagnetic waves, the UAV will also expose its position. Passive localization relies solely on passively measuring the electromagnetic signals radiated by the target to achieve localization, which makes up for the shortcomings of active localization. However, the localization accuracy is highly correlated with the noise of the sensor. With the rapid development of UAVs, optimizing passive localization of UAVs has become a new way to improve localization accuracy.

[0003] Passive positioning can be categorized based on different positioning principles into direction-finding cross-positioning (CLO) based on angle of arrival, time difference of arrival (TDOA) based on time difference of arrival (TDOA), frequency difference of arrival (FDOA) based on frequency difference of arrival (FDOA), received signal strength (RSS) based on frequency difference of arrival (FDOA), and various hybrid positioning systems. Among these, CLO is the earliest and most mature passive positioning system, characterized by its simple positioning principle and low computational cost. However, its positioning accuracy is limited by factors such as sensor precision, resulting in insufficient accuracy and requiring optimization from multiple aspects. John A. Fawcett first introduced CRLB into the accuracy evaluation system of passive positioning and derived the CRLB formula for pure azimuth target positioning and tracking. Yaakov Oshman et al. first established the relationship between the estimation error covariance matrix, CRLB, and Fisher information matrix. Ye et al. proposed a method based on signal fitting and direct data acquisition angle estimation algorithm from the transmitter to address the problem of GPS positioning being impossible indoors. As research deepens, scholars have discovered that the main challenge in AOA (Aspect-of-Arrival) positioning lies in the nonlinear correlation between measurement data and target position. Hua et al. developed an efficient closed-loop self-localization algorithm based on AOA using an auxiliary variable-based method. Wang et al. proposed a position bias maximum likelihood estimator (LPML) for azimuth target localization only, improving the accuracy of AOA positioning in two-dimensional planes. Wen et al. proposed a novel UAV AOA positioning framework suitable for three-dimensional scenes. Zhao et al. proposed an ultraviolet hybrid positioning method by combining RSSI (Real-Side Target Injection) and AOA positioning algorithms for collaborative ultraviolet communication positioning among UAV swarms. Du et al. proposed a passive positioning algorithm based on UAV aerial imagery and angle of arrival (AOA) to address the passive target localization problem, ensuring stable target tracking. XU et al. achieved high-precision target localization by using two UAVs and corresponding AOA measurement methods to passively locate unknown targets. However, these AOA positioning algorithms do not consider the sensor's own positioning error; therefore, effectively processing and allocating these errors is crucial for improving the accuracy of UAV AOA positioning. If the standard deviation of the error source is used as a variable for optimization, the error allocation problem can be transformed into a parameter optimization problem and solved by an optimization algorithm. Metaheuristic algorithms in optimization are based on principles found in nature, simulating the biological evolution process to find the optimal solution. These algorithms do not rely on specific mathematical formulas and gradually approach the optimal solution through iterative search and optimization. They have certain advantages in handling nonlinear problems. In recent years, many metaheuristic algorithms have been proposed, such as Particle Swarm Optimization (PSO), Sparrow Algorithm (SSA), and Grey Wolf Algorithm (GWO).NOA (Novel Optimization Algorithm) is a novel intelligent optimization algorithm proposed by Mohamed Abdel-Basset et al. in 2023. This algorithm simulates two different behaviors exhibited by the raven at different stages, demonstrating excellent performance and powerful global search capabilities, and has been widely applied to problems such as path planning. However, when dealing with corresponding problems, the algorithm also suffers from problems such as uneven population initialization and susceptibility to local optima. To address these shortcomings, an improved raven optimization algorithm is proposed. By introducing Cubic chaotic mapping and a spiral search strategy, the algorithm is effectively prevented from getting trapped in local optima, enhancing its exploration capabilities and accelerating its convergence speed. Simulation and flight experiments demonstrate that the improved raven optimization algorithm performs better. Summary of the Invention

[0004] This invention addresses the problems of insufficient accuracy caused by nonlinear accumulation of errors in traditional UAV angle of arrival (AOA) positioning and the tendency of existing optimization algorithms to get trapped in local optima. It proposes a positioning error optimization method that integrates staged correction and improved Star Raven optimization algorithm.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for UAV angle-of-arrival localization based on an improved Star Raven optimization algorithm includes the following steps:

[0007] Step 1: Continuously acquire images of the moving UAV using n observation points at different locations to obtain n frames of UAV image data. Divide the UAV image set obtained from the n observations into n-1 adjacent subsequences, each subsequence containing images from the i-th and i-1th observations.

[0008] Step 2: Calculate the UAV coordinates in the world coordinate system for each subsequence. The calculation method is as follows:

[0009] Projecting the positional relationship between the images obtained from the i-th and i-1th observations and the UAV target P onto the two-dimensional xoy plane yields a pseudo-linear equation regarding the actual two-dimensional coordinates of the target. This equation is then used to calculate the UAV coordinates in the world coordinate system corresponding to each subsequence. ;

[0010] Step 3: After optimizing the world coordinate system coordinates of the n-1 subsequences and converting them to geodetic coordinate system coordinates, input the improved Star-Raven Optimization Algorithm. The improved Star-Raven Optimization Algorithm outputs the UAV coordinates in the world coordinate system. Shaft error ;

[0011] Step 4: Assign the drones to the world coordinate system corresponding to each subsequence. Add the corresponding error to all axis coordinates The optimized UAV coordinate subsequences corresponding to each observation point are obtained. The improved star raven optimization algorithm introduces Sine chaotic mapping to generate the initial population and introduces a spiral search strategy to update the star raven positions of the storage strategy and cache search.

[0012] Step 5: Arrange the optimized UAV coordinate subsequences corresponding to each observation point according to time to obtain the UAV coordinate position sequence.

[0013] Furthermore, in step 2, the pseudo-linear equation is:

[0014]

[0015] make , Then the least squares solution is:

[0016]

[0017] It can be obtained through the arithmetic mean, i.e.:

[0018]

[0019] In the formula, Let be the azimuth angle of the UAV in the geographic coordinate system at the (i-1)th observation. Let be the azimuth angle of the UAV in the geographic coordinate system at the i-th observation. , Let be the translation vector from the origin of the camera coordinate system to the origin of the body coordinate system during the (i-1)th observation. , Let be the translation vector from the origin of the camera coordinate system to the origin of the body coordinate system during the i-th observation.

[0020] Furthermore, the objective function and constraints of the improved star-raven optimization algorithm are as follows:

[0021] in: For the Earth's radius, and Let these represent the average latitude and longitude values ​​obtained from n observations, respectively. The total error to be allocated. To be assigned to the world coordinate system The shaft error is constrained by conditions that the error to be assigned cannot exceed the total error.

[0022] and This represents the latitude and longitude of the UAV obtained from the i-th observation, derived from the UAV coordinates in the world coordinate system corresponding to the i-th subsequence. , , After error optimization and coordinate system transformation, the following is obtained:

[0023] ;

[0024]

[0025] In the formula, ( , , ( ) represents the optimized coordinates. , and Let x, y, and z represent the average values ​​of the x-axis, y-axis, and z-axis coordinates in the world coordinate system obtained from n observations, where a is the major radius of the Earth ellipsoid and b is the minor radius of the Earth ellipsoid. For the second eccentricity, This is the first eccentricity.

[0026] Furthermore, in the improved Star Raven optimization algorithm, coefficients are multiplied before the variable parameter terms in the storage strategy and caching strategy formulas. Introducing a spiral search strategy; where: b represents a random number between -1 and 1. Indicates the maximum number of iterations. This indicates the current iteration number, where e is the natural base.

[0027] The beneficial effects of this invention are as follows:

[0028] This invention linearizes errors using Taylor series and constructs a multi-source error propagation model using the Jacobian matrix, achieving linearization and quantification analysis of positioning errors. Targeted optimizations are made to address the shortcomings of the original Star Raven algorithm. A Cubic chaotic mapping is introduced to generate the initial population, resolving the uneven population distribution problem of the original algorithm. Simultaneously, a spiral search strategy is incorporated to expand the optimization range, breaking through local optima bottlenecks and improving search space coverage.

[0029] This invention designs a phased error correction method based on observation sequences, which, unlike the problem of error accumulation caused by traditional single least squares solutions, suppresses the nonlinear accumulation effect of errors.

[0030] This invention introduces Cubic chaotic mapping and spiral search strategy, which increases the search space of the algorithm, enhances the algorithm's exploration ability, and accelerates its convergence speed.

[0031] The improved AOA positioning method was applied to UAV target positioning, and better positioning results were achieved.

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0033] Figure 1 A schematic diagram of the world coordinate system;

[0034] Figure 2 This is a schematic diagram of the body coordinate system;

[0035] Figure 3 This is a schematic diagram of the image's physical coordinate system and pixel coordinate system;

[0036] Figure 4 This is a schematic diagram of three-dimensional azimuth positioning;

[0037] Figure 5 For the improved NOA flowchart;

[0038] Figure 6 This is a schematic diagram of the drone's flight path;

[0039] Figure 7 This is a graph showing the average fitness rate.

[0040] Figure 8 This is a simulated scatter plot of latitude and longitude.

[0041] Figure 9 A schematic diagram of the average circular error curve for target localization under different terrain conditions;

[0042] Figure 10 This is a schematic diagram of a drone platform.

[0043] Figure 11 This is a schematic diagram of the target area;

[0044] Figure 12 A comparison chart of latitude and longitude results obtained by different algorithms with the true values;

[0045] Figure 13 A comparison chart showing the error distance between data obtained from different algorithms and the ground truth. Detailed Implementation

[0046] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0047] 1. Error propagation theory

[0048] 1.1 Definition of Coordinate System

[0049] Define the coordinate systems needed in the UAV target localization process: geodetic coordinate system, world coordinate system, geographic coordinate system, aircraft coordinate system, camera coordinate system, image physical coordinate system, and pixel coordinate system.

[0050] (1) Geodetic coordinate system

[0051] The WGS84 coordinate system is used, with the origin located at the geometric center of the Earth's ellipsoid and coinciding with the Earth's center of mass. The three-dimensional position of the target point is described using latitude B, longitude L, and altitude H.

[0052] (2) World coordinate system

[0053] The origin of the coordinate system is located at the center of the Earth's ellipsoid. The Z-axis points to the Earth's North Pole and coincides with the axis of rotation. The X-axis points to the intersection of the Prime Meridian and the equator. The Y-axis lies on the equatorial plane, forming a right-handed rectangular coordinate system with the X and Y axes. Figure 1 As shown.

[0054] (3) Geographic coordinate system

[0055] This coordinate system uses the northeast-northeast coordinate system, with the UAV's center of mass as the origin. The X-axis points north to Earth, the Y-axis points east to Earth, and the Z-axis is perpendicular to the Earth's surface and pointing downwards, forming a right-handed coordinate system.

[0056] (4) Body coordinate system

[0057] The origin coincides with the origin of the geographic coordinate system. The X-axis points directly forward of the aircraft, the Y-axis points to the right wing, and the Z-axis is perpendicular to the other two axes and points downward. When the UAV does not change attitude, this coordinate system coincides with the spatial rectangular coordinate system. Figure 2 As shown.

[0058] (5) Camera coordinate system

[0059] The origin of the camera coordinate system is taken as the optical center of the camera. The Z-axis coincides with the optical axis of the camera and the camera direction is taken as the positive direction. When the camera has no attitude angle change, the X-axis points to the right wing of the UAV and the Y-axis points directly below the body of the UAV.

[0060] (6) Image physical coordinate system

[0061] The origin of the image physical coordinate system is located at the intersection of the optical axis and the image plane. The X-axis and Y-axis are parallel to the two perpendicular sides of the image plane, respectively. Figure 3 As shown.

[0062] (7) Pixel coordinate system

[0063] The origin of the coordinate system is located at the top left corner of the image plane, and the X-axis and Y-axis are parallel to the X-axis and Y-axis of the physical coordinate system of the image, respectively. Figure 3 As shown.

[0064] 1.2 Error propagation and synthesis

[0065] For a random vector x undergoing a nonlinear transformation f, the resulting vector y is:

[0066]

[0067] in: For random vectors The mean; The mean is 0 and the covariance is The random error variable. For the above equation... Taylor expansion yields:

[0068]

[0069] The variance of the random error variable after nonlinear coordinate transformation is:

[0070]

[0071] in For function f in The Jacobian matrix at that location.

[0072] The target localization process of a UAV is affected by various errors. Since the UAV's own coordinates serve as the reference anchor point for calculating the target's coordinates, the target's coordinates in the world coordinate system must be derived through the translation relationship between the UAV's geographic coordinate system origin and the world coordinate system. The UAV's attitude angles determine the spatial attitude relationship between the fuselage coordinate system and the geographic coordinate system. The pod angle is the direct measurement source data for AOA positioning, and its measurement accuracy directly determines the accuracy of the target's azimuth calculation. This invention primarily focuses on analyzing UAV position errors, UAV attitude angle errors, and pod azimuth and pitch angle errors. These errors are all random errors, following a normal distribution, and are assumed to be independent of each other. Furthermore, error factors with a small magnitude of impact on positioning accuracy, such as installation alignment errors and vibration damper vibrations, are not included in the analysis framework in this invention due to their low contribution to the final positioning result.

[0073] Assume the coordinates of target point P in the camera coordinate system are pod heading angle With pitch angle error ,in diagonal matrix ,in The standard deviation is given by equation (2), which transforms the target point P into its coordinates in the body coordinate system. Then the error propagation from the camera coordinate system to the body coordinate system is as follows:

[0074]

[0075] in:

[0076]

[0077] For the body coordinate system coordinates UAV attitude angle ,in diagonal matrix After transformation by equation (3), the coordinates of the target point P in the geographic coordinate system can be obtained. Then the error propagation from the body coordinate system to the geographic coordinate system is as follows:

[0078]

[0079] in:

[0080]

[0081] Geographic coordinate system coordinates UAV geodetic coordinates ,in diagonal matrix The world coordinate system coordinates obtained after the geographic coordinate system is transformed can be obtained. .

[0082] The coordinate transformation is as follows:

[0083]

[0084] in: This represents the translation distance from the origin of the world coordinate system to the origin of the geographic coordinate system.

[0085] The error propagation from the world coordinate system to the geographic coordinate system is as follows:

[0086]

[0087] in:

[0088]

[0089] According to equations (11) to (17), the covariance matrix of the target coordinate position in the world coordinate system after coordinate transformation is:

[0090]

[0091] Therefore, the standard deviation of the target positioning error in the world coordinate system is:

[0092]

[0093] in For matrix The sum of the diagonal elements.

[0094] Error in the world coordinate system is caused by The overall effect of errors on each axis is determined by their combined influence; therefore, error allocation can yield individual errors on each axis, allowing for correction of the results. If errors are treated as variables for optimization, the error allocation problem can be transformed into a parameter optimization problem, which can then be solved using optimization algorithms.

[0095] 2. Improved AOA localization method

[0096] To address the error accumulation problem in traditional AOA positioning methods, this section proposes an improved staged positioning method. The classical least squares method, in achieving geometric positioning of the target, suffers from a lack of effective error compensation mechanisms, leading to nonlinear accumulation of errors during coordinate transformation. This ultimately results in a significant deviation between the theoretical coordinates and the actual spatial coordinates of the target point.

[0097] To optimize this problem, this invention designs a phased positioning correction method based on observation sequences. During the observation process of a UAV continuously acquiring n frames of image data, the complete trajectory is divided into... The algorithm constructs a subsequence consisting of several adjacent observation nodes. For each subsequence, least-squares localization is first calculated based on the geometric relationships between adjacent observation nodes. Then, an error propagation model based on the covariance matrix is ​​introduced, and an improved star-raven optimization algorithm is used to compensate for errors in the solution results, effectively suppressing the error accumulation effect during coordinate transformation. Finally, the algorithm... The error-corrected positioning results are used to obtain the estimated coordinates of target point P in the world coordinate system through arithmetic mean. This staged processing mechanism significantly improves positioning accuracy in complex observation environments by reducing the error of a single calculation.

[0098] 2.1 AOA Positioning Principle

[0099] UAVs require two prerequisites for positioning using angle of arrival: the UAV's position in the world coordinate system. The azimuth A and pitch C of the pod in the geographic coordinate system. The UAV's position can be provided by its onboard GPS module, while the azimuth and pitch angles of the pod need to be obtained through coordinate transformation, as shown below.

[0100] Given the coordinates of target point P in the pixel coordinate system Then its coordinates in the physical coordinate system of the image are as shown in equation (13).

[0101]

[0102] in Indicates the center of the image. Let x and y represent the physical dimensions of a single pixel of the camera along the x and y axes, respectively. Therefore, the coordinates of the target point P in the camera coordinate system can be expressed as: ,in This refers to the camera's focal length.

[0103] The transformation from the camera coordinate system to the body coordinate system is shown in equation (14):

[0104]

[0105] in The azimuth angle of the pod in the camera coordinate system. The pitch angle of the pod in the camera coordinate system. , , This is the translation vector from the origin of the camera coordinate system to the origin of the body coordinate system.

[0106] The transformation from the body coordinate system to the geographic coordinate system is shown in equation (15):

[0107]

[0108] in This is the azimuth angle of the drone. For the drone's pitch angle, The roll angle for the drone.

[0109] The azimuth A and pitch C of the pod in the geographic coordinate system are shown in equation (16):

[0110]

[0111] Where azimuth A is positive when turning right, the range is: The pitch angle C is positive upwards, and its range is... .

[0112] During its flight along a predetermined trajectory, the drone takes multiple photos of the target point, acquiring multiple observation images. The position of the i-th drone is... , ,like Figure 4 As shown.

[0113] Projecting the position of the UAV at the i-th measurement point and the position relationship of the target P onto the two-dimensional xoy plane, we obtain a pseudo-linear equation about the actual two-dimensional coordinates of the target, as shown in equation (17).

[0114]

[0115] Right now Its least squares solution is:

[0116]

[0117] It can be obtained through the arithmetic mean, i.e.:

[0118]

[0119] Therefore, the coordinates of the target point P in the world coordinate system are... All the coordinates have been calculated. The coordinates of the target point in the geodetic coordinate system can then be obtained through coordinate transformation. .

[0120] Therefore, the coordinates of the target point P in the world coordinate system are... All the coordinates have been calculated. The coordinates of the target point in the geodetic coordinate system can then be obtained through coordinate transformation. .

[0121]

[0122]

[0123] The calculation results of equations (18) and (19) do not take into account the influence of measurement noise and the position deviation of the UAV itself, and the results obtained deviate significantly from the true values. In the target positioning process of the UAV, the attitude, flight altitude, azimuth angle and elevation angle of the camera corresponding to each measurement point are different. Even if the same camera is used, the above differences will lead to different camera extrinsic parameters at each measurement point, which in turn will result in different contributions of each point to the target positioning error, ultimately causing inconsistent positioning accuracy at different measurement points.

[0124] Traditional angle-of-arrival (AOA) positioning methods rely on continuous observation and overall solution. Because they do not specifically address the error propagation process, nonlinear errors in coordinate transformation accumulate with the number of observations, leading to a gradual increase in the deviation between the positioning result and the true value. To address this issue, this section proposes a staged error correction method based on the observation sequence. Through a process of "segmented solution—error compensation—fusion optimization," the method effectively suppresses the cumulative effect of errors.

[0125] For the n frames of image data continuously collected by the UAV, the complete observation trajectory is divided into n-1 adjacent subsequences. Each subsequence contains two consecutive observation data, i and i-1. The position relationship between the UAV at the i-1 and i-th measurement points and the target P is projected onto the two-dimensional xoy plane to obtain a pseudo-linear equation about the actual two-dimensional coordinates of the target, as shown in equation (20).

[0126] (20)

[0127] make , Its least squares solution is:

[0128] (twenty one)

[0129] It can be obtained through the arithmetic mean, i.e.:

[0130]

[0131] Therefore, it can be calculated that... The coordinates of target point P in the world coordinate system By inputting the parameters of the UAV and camera at each observation point, the total error at that current observation point can be obtained. However, the phased processing does not fundamentally solve the problem of error accumulation caused by coordinate transformation within the sequence. The least squares solution result of each subsequence is still affected by random errors such as UAV parameters and pod angles at that stage, resulting in a deviation between the calculated coordinates and the true values. To further improve positioning accuracy, an efficient optimization algorithm is introduced based on the phased solution to correct and compensate for errors in the positioning results of each subsequence.

[0132] 2.2 Improved Star Raven Optimization Algorithm

[0133] 2.2.1 Target Allocation Model

[0134] The definition of the objective function has a significant impact on the performance and results of the optimization algorithm. Since the precise coordinates of the target point cannot be known during the actual positioning process, the calculated mean point after error correction is taken as the true reference point. Since the target points are relatively close, in order to fully consider the influence of the Earth's curvature on the target positioning results, the Earth is regarded as a sphere and the cosine theorem of the sphere is used as the evaluation index. According to the cosine theorem of the sphere, the distance between the calculated point and the calculated mean point is used as the index for evaluating the positioning accuracy of the UAV. The smaller the difference between the two, the closer the straight distance between the target point and the calculated point is. At the same time, considering that the error to be allocated should not exceed the total allocation error, the objective function and the constraint conditions are as shown in equation (21):

[0135]

[0136]

[0137] in: For the Earth's radius, and This indicates the latitude and longitude of the calculation point. and This represents the average latitude and longitude of the calculation point. The total error to be allocated. To be assigned to the world coordinate system The shaft error is constrained by conditions that the error to be assigned cannot exceed the total error.

[0138] 2.2.2 Star Raven Optimization Algorithm

[0139] The Noah's Raven Optimization Algorithm (NOA), proposed in 2023, is a metaheuristic algorithm with advantages such as strong optimization ability and fast convergence speed. NOA simulates the natural behavior of ravens, which exhibit two different behaviors at different stages: a foraging and storage strategy and a cache search and recovery strategy. A brief description of the original Noah's Raven algorithm principle is as follows:

[0140] (1) Foraging strategy: The jay searches within its search space, first checking the initial location for seeds. If a good seed is found, the jay will transport it to the storage area and bury it. If no good seed is found, it will continue searching for new seeds in different locations on pine trees or other tree species.

[0141]

[0142]

[0143] in: It is based on the random numbers generated by Levi's flight. and These represent the upper and lower bounds of the optimization problem, respectively. , and These are three different Star Crow individuals randomly selected from the population. It is the mean of the current population in the j-th dimension during the t-th iteration. Represents a random number between 0 and 1. These are random numbers generated based on a normal distribution. These are random numbers generated based on Levy flight, where t is the iteration number. Set to 0.05.

[0144] (2) Storage strategy: The Star Raven will first transport the food obtained in the previous stage to a temporary storage location, as shown in equation (23).

[0145]

[0146] in: It is a random number generated by Levi's flight, where l is a linear decreasing factor from 1 to 0.

[0147] There is a balance between the foraging phase and the storage phase:

[0148]

[0149] in, It is a random number between 0 and 1. As the number of iterations decreases linearly from 1 to 0.

[0150] The cache search and retrieval strategy is based on two reference points (RPs) chosen by the individual Star Raven to remember the location of stored food. The two reference points are calculated as follows:

[0151]

[0152]

[0153]

[0154] in: , , It is from 0 to The random radians between them, where A and B are two star jay individuals randomly selected from the population. It is a random vector between 0 and 1. The probability used to determine the percentage of other regions globally explored within the search space, where t represents the current iteration number. It represents the maximum number of iterations.

[0155] (3) Cache search: When the raven searches for stored food, there are two possibilities: the first is that the raven can remember the storage location using equation (25). This behavior is shown in equation (28):

[0156]

[0157] The second scenario is that the Raven doesn't remember using equation (25), so it will use equation (26) to search. In NOA, assuming the Raven uses equation (26) to find its storage area, the position update formula according to equation (26) is:

[0158]

[0159] in: Represents a random number between 0 and 1.

[0160] Whether a raven remembers the location of stored food using formula (25) is determined by comparing it using formula (30):

[0161]

[0162] in: Represents a random number between 0 and 1.

[0163] (4) Recovery strategy: The location update method when food is retrieved is as follows:

[0164]

[0165]

[0166] The location update strategy is selected using the following formula:

[0167]

[0168] There is a balance between cache search and recovery strategies:

[0169]

[0170] 2.2.3 Improved Star Raven Algorithm

[0171] The original Star Raven algorithm uses random numbers to generate the initial population position, which easily leads to uneven distribution of the population in the search space, causing the algorithm to get stuck in local optima. Therefore, this invention introduces the Sine chaotic map. Compared with traditional uniformly distributed random numbers, the Sine chaotic map has the characteristic of deterministic traversal, which can uniformly cover all possible regions in the search space according to the chaotic trajectory, and has the characteristics of fast optimization speed and high accuracy.

[0172] The principle of Sine chaotic mapping is:

[0173]

[0174] Where: a=4 is the control parameter, and the range of chaotic orbital state values ​​is (0, 1).

[0175] The original Star Raven algorithm relies on the random step size and linear decreasing factor of Levy's flight to update the position during the storage strategy and cache search phases. This leads to excessively small step sizes in the later stages, making it prone to searching near local optima and unable to escape. Inspired by the Whale Optimization algorithm, a spiral search strategy is introduced to update the Star Raven positions during the storage strategy and cache search, expanding the search range and preventing the algorithm from converging prematurely to local optima.

[0176] By introducing Sine chaotic mapping and spiral search strategy to improve the Star Raven optimization algorithm, the spiral search guides the population to converge toward the global optimal error distribution scheme through nonlinear spiral trajectory, based on the uniform initial population provided by Sine chaotic mapping.

[0177] The location is improved as follows:

[0178] (1) Storage strategy

[0179]

[0180] (2) Cache search

[0181]

[0182]

[0183] in: b represents a random number between -1 and 1.

[0184] The core computational logic of the improved algorithm focuses on numerical calculations at the coefficient level, without introducing additional iterative loop structures. According to the criteria for analyzing algorithm time complexity, the number of iterations is a key factor affecting time complexity; therefore, the improved algorithm maintains the same time complexity as the original algorithm, with no increase. It should be noted that to improve optimization performance, the improved algorithm introduces exponential and trigonometric function operations (such as the sine function in the golden sine strategy and the exponential decay term in the spiral search strategy). The introduction of these operations slightly increases the computational load in a single iteration, resulting in a minor increase in computational complexity compared to the original algorithm. However, from the perspective of cost-effectiveness in engineering applications, the improved algorithm achieves a significant improvement in positioning accuracy at the cost of this slight increase in computational complexity; the benefit of improved accuracy far outweighs the cost of the increased computational complexity.

[0185] The overall flowchart of the improved Star Raven algorithm is as follows: Figure 5 As shown.

[0186] 3. Simulation Experiment

[0187] To verify the effectiveness of the improved NOA algorithm proposed in this invention in UAV target localization, a Monte Carlo simulation comparison experiment was established. The UAV was set to fly counterclockwise at an altitude of 400 meters with a turning radius of 200 meters, centered at 20°N, 110°E. The UAV roll angle was 30°, the pitch angle was 0°, the pod yaw angle was -90°, and the pod pitch angle was -60°. An average of 100 positioning points were taken on the UAV's flight path. The UAV flight path is shown below. Figure 6 As shown.

[0188] The experiment selected Particle Swarm Optimization (PSO), Sparrow Optimization (SSA), Grey Wolf Optimization (GWO), and the original Star Crow Optimization (NOA) as benchmark comparison algorithms to evaluate the performance of the improved algorithm in terms of global optimization capability and convergence accuracy. The simulation parameters for various UAV errors are shown in Table 1. The experiment set the population size to 30 and the algorithm iterations to 10,000. To verify the reliability of the simulation results, the average value of 100 simulation results was used to plot the fitness change curve, as shown in Table 1. Figure 7 As shown.

[0189] Table 1 Simulation parameters of measurement error

[0190]

[0191] Figure 7 The results show that the improved NOA algorithm can converge quickly when faced with this problem, and finally obtain the global optimal solution with the lowest fitness, which is better than other optimization algorithms.

[0192] To visually demonstrate the improved accuracy of the NOA algorithm in UAV pure orientation localization, one simulation was selected to process the target point. The simulation results are as follows: Figure 8 As shown, (a) represents data without using the algorithm, (b) represents data using the improved NOA algorithm, (c) represents data using the NOA algorithm, (d) represents data using the PSO algorithm, (e) represents data using the GWO algorithm, and (f) represents data using the SSA algorithm.

[0193] The mean of the data after algorithm processing is used as the final positioning result, and the straight-line distance between it and the true value of the target point is calculated. The results are shown in Table 2.

[0194] Table 2 Error Distance

[0195]

[0196] The root mean square error (RMSE) is an indicator that reflects the positioning performance of the algorithm. The calculation formula is as follows:

[0197]

[0198] Where: n is the quantity of target information, and X is the true value of the target information. These are the simulated values ​​for the target information. Based on the above processing method, the root mean square error is calculated for the latitude and longitude of the target point, respectively.

[0199] Table 3 Root Mean Square Error

[0200]

[0201] Table 3 shows that the improved NOA algorithm proposed in this invention has the smallest root mean square error and higher robustness. Table 2 shows that the simulation point accuracy is improved by 73.29%, 58.12%, 61.99%, 9.55%, and 15.57% respectively compared with other results.

[0202] To further investigate the impact of target detection accuracy, average height of the target area, and pod optical axis angular measurement accuracy on the positioning accuracy of the flight test, a photographic area with terrain undulations of 0–40 m and a photographic tilt angle of [missing information]. Quantitative analysis of a single target point was performed under experimental conditions ranging from 40° to 60° and involving 100 trials. Ignoring the influence of target detection accuracy and angular measurement accuracy, the curves showing the variation of the average circular error of positioning with the photographic tilt angle under different terrain undulations in the target area are as follows: Figure 9 As shown.

[0203] from Figure 9 The results show a positive correlation between the camera tilt angle and the positioning error: as the camera tilt angle increases from 40° to 60°, the mean circular error of positioning under different terrain undulations shows a significant upward trend, indicating that the larger the camera tilt angle, the worse the positioning accuracy. Terrain undulations exacerbate positioning errors: at the same tilt angle, the greater the terrain undulation in the target area, the greater the mean circular error of positioning, demonstrating the negative impact of terrain undulations on positioning accuracy. The impact of terrain undulations is amplified as the tilt angle increases: when the tilt angle is small, the corresponding error curves are relatively concentrated; however, when the tilt angle exceeds 55°, the differences between the curves widen significantly, indicating that under large tilt angle scenarios, the sensitivity of positioning errors to terrain undulations is further enhanced.

[0204] IV. Actual Flight Experiment

[0205] The experiment used a CW-25E UAV manufactured by Chengdu Zongheng Automation Co., Ltd., equipped with an MG150E electro-optical pod, employing a fixed rotor layout and vertical takeoff and landing via the rotor. Figure 10 As shown. For the CW-25E UAV, the installation parameters are as follows: This refers to the distance between the optoelectronic pod and the center of mass of the drone.

[0206] During the experiment, the UAV flew at an altitude of approximately 1100 meters, used a GPS positioning system with a positioning accuracy of less than 20 cm, and measured the UAV's roll angle, azimuth angle, and pitch angle with an accuracy of less than 1°. The electro-optical pod also measured the azimuth angle and pitch angle with an accuracy of less than 1°.

[0207] The experiment set up a total of 6 target points, such as Figure 11 As shown in Table 4, the latitude and longitude coordinates of the measurement points were measured using a GPS measuring instrument with a positioning accuracy of 0.1m. Therefore, the measurement results can be used as the true values ​​of the target's geographical location.

[0208] Table 4 Latitude and Longitude of Target Points

[0209]

[0210] The UAV performed 150 measurements of the target point during flight. The measurement data were processed using improved NOA, PSO, GWO, and SSA algorithms according to a phased positioning method. The results were then compared with the ground truth. Figure 9 As shown, (a) is a latitude comparison chart and (b) is a longitude comparison chart.

[0211] The error distances between the six sets of data and the true value are shown in Table 5, and the distance comparison chart is shown below. Figure 13 .

[0212] Table 5 Error Distance

[0213]

[0214] The experimental results show that the improved NOA phased positioning method yields significantly better results than other methods, proving the effectiveness of the proposed method. However, there is a certain gap between the results and the simulation results, which may be due to environmental errors and other systematic errors in actual flight tests.

[0215] V. Conclusion

[0216] This invention addresses the error accumulation problem in traditional UAV AOA positioning methods by proposing an error compensation method based on phased positioning optimization and an improved Star-Raven algorithm. By constructing a coordinate system to analyze the error propagation process, an error propagation model is derived. The impact of UAV attitude angles, pod angles, and GPS position errors on the final positioning result is quantified using the Jacobian matrix. The error propagation model is used to analyze the propagation of errors in each stage of the positioning process, and a phased correction method is designed to suppress the nonlinear accumulation of errors. Cubic chaotic mapping is used to enhance population diversity, and a spiral search strategy is introduced to strengthen global exploration and local exploitation capabilities. The Star-Raven optimization algorithm is improved to achieve optimal error allocation. Monte Carlo simulations show that the improved algorithm significantly reduces positioning deviations caused by random errors and improves the overall accuracy of UAV target positioning. Actual flight experiments also verify the reliability of the simulation results, proving that the proposed method can effectively improve the accuracy of UAV target positioning in practical applications. Future work will focus on exploring more precise error allocation mechanisms, extending the analysis to the mechanism of error source interactions, constructing a time-varying error propagation model including environmental parameters, and further improving positioning reliability in complex scenarios.

[0217] The above description provides examples of the preferred embodiments of the present invention. Parts not detailed herein are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims. Any equivalent modifications based on the technical teachings of the present invention are also within the scope of protection of the present invention.

Claims

1. A method for UAV angle-of-arrival localization based on an improved Star-Raven optimization algorithm, characterized in that, Includes the following steps: Step 1: Continuously acquire images of the moving UAV using n observation points at different locations to obtain n frames of UAV image data. Divide the UAV image set obtained from the n observations into n-1 adjacent subsequences, each subsequence containing images from the i-th and i-1th observations. Step 2: Calculate the UAV coordinates in the world coordinate system for each subsequence. The calculation method is as follows: Projecting the positional relationship between the images obtained from the i-th and i-1th observations and the UAV target P onto the two-dimensional xoy plane yields a pseudo-linear equation regarding the actual two-dimensional coordinates of the target. This equation is then used to calculate the UAV coordinates in the world coordinate system corresponding to each subsequence. ; Step 3: After optimizing the world coordinate system coordinates of the n-1 subsequences and converting them to geodetic coordinate system coordinates, input the improved Star-Raven Optimization Algorithm. The improved Star-Raven Optimization Algorithm outputs the UAV coordinates in the world coordinate system. Shaft error ; Step 4: Assign the drones to the world coordinate system corresponding to each subsequence. Add the corresponding error to all axis coordinates The optimized UAV coordinate subsequences corresponding to each observation point are obtained. The improved star raven optimization algorithm introduces Sine chaotic mapping to generate the initial population and introduces a spiral search strategy to update the star raven positions of the storage strategy and cache search. Step 5: Arrange the optimized UAV coordinate subsequences corresponding to each observation point according to time to obtain the UAV coordinate position sequence.

2. The UAV angle-of-arrival positioning method based on the improved Star Raven optimization algorithm according to claim 1, characterized in that, In step 2, the pseudo-linear equation is: ； make , Then the least squares solution is: ； It can be obtained through the arithmetic mean, i.e.: ； In the formula, Let be the azimuth angle of the UAV in the geographic coordinate system at the (i-1)th observation. Let be the azimuth angle of the UAV in the geographic coordinate system at the i-th observation. , Let be the translation vector from the origin of the camera coordinate system to the origin of the body coordinate system during the (i-1)th observation. , Let be the translation vector from the origin of the camera coordinate system to the origin of the body coordinate system during the i-th observation.

3. The UAV angle-of-arrival positioning method based on the improved Star Raven optimization algorithm according to claim 1, characterized in that, The objective function and constraints of the improved Star Raven optimization algorithm are as follows: ； in: For the Earth's radius, and Let these represent the average latitude and longitude values ​​obtained from n observations, respectively. The total error to be allocated. To be assigned to the world coordinate system The shaft error is constrained by conditions that the error to be assigned cannot exceed the total error. and This represents the latitude and longitude of the UAV obtained from the i-th observation, derived from the UAV coordinates in the world coordinate system corresponding to the i-th subsequence. , , After error optimization and coordinate system transformation, the following is obtained: ； ； In the formula, ( , , ( ) represents the optimized coordinates. , and Let x, y, and z represent the average values ​​of the x-axis, y-axis, and z-axis coordinates in the world coordinate system obtained from n observations, where a is the major radius of the Earth ellipsoid and b is the minor radius of the Earth ellipsoid. For the second eccentricity, This is the first eccentricity.

4. The UAV angle-of-arrival positioning method based on the improved Star Raven optimization algorithm according to claim 1, characterized in that, In the improved Star Raven optimization algorithm, coefficients are multiplied before the variable parameter terms in the storage strategy and caching strategy formulas. Introducing a spiral search strategy; where: b represents a random number between -1 and 1. Indicates the maximum number of iterations. This indicates the current iteration number, where e is the natural base.

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