A radar error correction method based on improved sparrow search algorithm

Abstract

The invention discloses a radar error correction method based on an improved sparrow search algorithm, comprising the following steps: S1: establishing a radar observation error model; S2: initializing the improved sparrow search algorithm, randomly generating a candidate population, and expanding the population range by using chaotic mapping and reverse learning, sorting the individuals in the population according to fitness values, and selecting a new initial population; S3: adaptively adjusting the number of explorers and followers according to the iteration progress; S4: updating the explorer position according to the osprey global search strategy, and updating the positions of followers and sentinels according to the sparrow search mechanism; S5: accelerating the convergence speed by using a dynamically selected adaptive t-distribution perturbation strategy, and further searching for the optimal individual, and calculating the individual position and fitness value after the perturbation; S6: judging whether the algorithm reaches the maximum number of iterations, and outputting the optimal solution if it reaches it, otherwise returning to step S3; S7: correcting the target position measured by the radar.

Description

Technical Field

[0001] The invention relates to the technical field of radar error correction, and in particular to a radar error correction method based on an improved sparrow search algorithm. Background Art

[0002] Radar is the main means of monitoring and early warning of non-cooperative targets at sea. Modern radars represented by phased arrays can detect and track multiple batches of targets at the same time due to their fast beam control speed. However, due to factors such as mechanical structure offset deformation, installation platform tilt, internal electrical component aging and external electromagnetic interference, radar observations often have systematic errors, and the maximum error can even reach the kilometer level, so it is necessary to calibrate the radar regularly.

[0003] Traditional shore-based radar calibration usually uses fixed targets with known positions on the ground or measures the same target in the common observation area of ​​multiple radars to establish a registration model and solve it. This type of method has a limited calibration range and cannot be applied in offshore waters. In addition, in traditional radar calibration methods, the accuracy of radar system error estimation is often not high enough, resulting in poor calibration results. Summary of the invention

[0004] In order to solve the problems raised in the above background technology, the technical solution adopted by the present invention is:

[0005] A radar error correction method based on an improved sparrow search algorithm comprises the following steps:

[0006] S1: Establish a radar observation error model and input radar observation data, GNSS push data and radar station coordinate information;

[0007] S2, improve the initialization of the sparrow search algorithm, randomly generate candidate populations, and use chaotic mapping and reverse learning to expand the population range, sort the individuals in the population according to the fitness value, and select multiple individuals with higher fitness values ​​to form a new initial population;

[0008] S3, adaptively adjust the number of explorers and followers according to the iteration progress;

[0009] S4, update the explorer position according to the Osprey global search strategy, and update the positions of the followers and sentinels according to the sparrow search mechanism;

[0010] S5, using the dynamically selected adaptive t-distribution perturbation strategy to accelerate the convergence speed and further find the optimal individual, and calculate the individual position and fitness value after the perturbation;

[0011] S6, judging whether the algorithm has reached the maximum number of iterations, if so, outputting the optimal solution of the radar observation error model at this time as the estimation result of the radar system error, otherwise returning to step S3;

[0012] S7. Using the estimated result of the radar system error, correct the target position measured by the radar and output the corrected target position.

[0013] Furthermore, in step S1, a radar observation error model is first established, and the cooperative target detected by the radar is used as a reference source. The cooperative target is an aircraft equipped with GNSS and capable of pushing its position in real time through a data link, and the reference source position data measured by the GNSS is associated with the radar observation data, time-aligned, and coordinate-transformed.

[0014] Furthermore, in step S1, when establishing the radar observation error model, the following steps are specifically included:

[0015] First, consider the position deviation caused by communication delay, and set the GNSS data push cycle of the cooperation target to be T G , the radar measurement period is T R , GNSS data push time is The radar measurement time is

[0016] The time difference between the two is The following relationship is obtained:

[0017] Δt2+T G =T R +Δt1 (1)

[0018] The position of the cooperative target is pushed and reconstructed periodically through smoothing and interpolation algorithms, so that T G =T R ,but That is, the communication delay is a constant value Δt. After estimating this value, the position deviation caused by the communication delay is corrected in combination with the speed of the cooperative target aircraft.

[0019] Next, suppose that the geographical location received at time k includes the latitude L G (k), longitude λ G (k) and altitude H G (k), converted to the ECEF coordinate system:

[0020]

[0021] Where e is the eccentricity of the Earth and C is calculated by:

[0022]

[0023] Where E q is the equatorial radius;

[0024] The data measured by the radar at time k contains the radial distance r of the cooperative target m (k), azimuth angle θ m (k), elevation angle η m (k), transform it into the local Cartesian coordinate system with the radar position as the origin coordinate:

[0025]

[0026] Then transform to the ECEF coordinate system with the center of the earth as the origin:

[0027]

[0028] Among them, (x s ,y s ,z s ) is the radar geographic coordinate (L s ,λ s ,H s ) in the ECEF coordinate system can be calculated using formula (2), where T is the rotation matrix:

[0029]

[0030] The transmission of GNSS position information takes Δt, so the position information received at time k is actually the coordinate information of the cooperative target at time k-Δt. During the Δt time, the cooperative target moves a certain distance. Assuming that the cooperative target moves in a uniform linear motion, its actual position (x EGT (k),y EGT (k),z EGT (k)) and GNSS positioning (x EG (k),y EG (k),z EG (k)) have the following relationship:

[0031]

[0032] where v x 、v y 、v z are the velocities of the cooperative target aircraft along the XYZ axes in the radar local coordinate system;

[0033] Next, let the radar system error be β R =[Δr,Δθ,Δη] T , Δr is the ranging system error, Δθ is the azimuth system error, Δη is the elevation system error, and the radar measurement noise is [nr m(k),nθ m (k),nη m (k)] T According to formula (4), the actual position of the cooperative target at time k in the radar local coordinate system is:

[0034]

[0035] Transformed into the ECEF coordinate system:

[0036]

[0037] Both equations (7) and (9) represent the real coordinates of the same reference source in the ECEF coordinate system at a certain moment, so we can get:

[0038]

[0039] Substituting formula (8) into the equation, we get:

[0040]

[0041] At this point, the communication delay and radar system error are combined to establish an integrated error. The integrated system error vector is β = [Δr, Δθ, Δη, Δt] T ;

[0042] Let ψ(k)=[r m (k)-nr m (k),θ m (k)-nθ m (k),η m (k)-nη m (k)] T , then:

[0043]

[0044] Take N measurements of the reference source and construct the objective function:

[0045]

[0046] In the formula, Ω is the definition domain of β. In the subsequent steps, the improved sparrow search algorithm is used to optimize formula (13) to estimate the system error vector β.

[0047] Furthermore, step S2 specifically includes:

[0048] Assume that in the D-dimensional search space consisting of n sparrows, the position of each sparrow is expressed as:

[0049]

[0050] The corresponding sparrow's fitness is expressed as:

[0051]

[0052] The improved sparrow search algorithm is initialized and a candidate initialization population X is randomly generated as shown in formula (14). Then, the chaotic Bernoulli mapping is used to enhance the randomness and diversity of the initial population. The iterative formula of the chaotic Bernoulli mapping is:

[0053]

[0054] Among them, the subscript k is the number of chaotic iterations, λ is a constant, and the generated chaotic sequence z i,j Mapped into the sparrow search space:

[0055] x i,j =x L +(x U -x L )×z i,j (17)

[0056] Where x U and x L are the upper and lower bounds of the search space respectively;

[0057] Substitute X in equation (14) into equation (17) to generate the chaotic population Y;

[0058] On the other hand, the refraction reverse learning mechanism is used to further expand the range of optional solutions. i,j The reverse solution of for:

[0059]

[0060] In the formula, a j and b j They represent the minimum and maximum values ​​of the jth dimension of the current population, respectively, and k is the lens zoom factor;

[0061] Substitute X in equation (14) into equation (18) to generate the reverse learning population Z;

[0062] Then, sort the individuals in populations X, Y, and Z according to their fitness values, and select the first n individuals to form a new initial population, recorded as:

[0063]

[0064] Furthermore, in step S3, in order to expand the search range and increase the proportion of explorers in the population at the beginning of the iteration, when switching to a mode mainly based on local precise search, the number of followers is increased to improve the convergence accuracy and speed of the algorithm;

[0065] In addition, the adaptive adjustment formula for the number of explorers and followers is constructed as follows:

[0066]

[0067] pNum=rn (21)

[0068] fNum=(1-r)n (22)

[0069] In the formula, iter is the number of iterations, iter max is the maximum number of iterations, r is the nonlinear proportional coefficient, which is used to adaptively control the number of explorers pNum and the number of followers fNum, b is a constant coefficient, and l is the disturbance deviation factor.

[0070] Further, in step S4, when updating the explorer position according to the osprey global search strategy, the explorer is regarded as an osprey, and the position set of all candidate prey of the i-th osprey is specified by the following formula:

[0071] FP i ={X k |k∈{1,2,…,n}∧F k <F i}∪{Xbest} (23)

[0072] Among them, Xbest is the best Osprey position;

[0073] At this time, the osprey randomly moves to the location of a candidate prey. In this process, the position update of the j-th dimension of the i-th osprey is described by the following formula:

[0074]

[0075] Among them, SF i,j represents the position of the prey selected by the i-th osprey in the j-th dimension; r i,j is a random number in [0,1]; I is a random number in {1,2}; x i,j and are the positions of the i-th osprey before and after the j-th dimension movement. If the objective function value is better in the new position after the movement, the previous position of the osprey is replaced by the following formula:

[0076]

[0077] Further, in step S4, when the position of the follower is updated according to the sparrow search mechanism, its position is updated as:

[0078]

[0079] in, is the worst position of the sparrow in the j dimension at the iter-th iteration, is the best position of the explorer in the j-dimension at the iter+1th iteration; rand{-1,1} represents a random value in [-1,1], and Q is a random number from a normal distribution;

[0080] When i>n / 2, it means that the i-th follower with lower fitness has not obtained food and will fly to other places to continue foraging;

[0081] When i≤n / 2, the i-th follower will be in the optimal position Searching for food nearby, the corresponding algorithm enters the local search stage.

[0082] Further, in step S4, when the position of the sentinel is updated according to the sparrow search mechanism, its position is updated as:

[0083]

[0084] Where β∈N(0,1) is the step size control parameter; K is a random number in [-1,1]; F i 、F w 、F g They represent the current sparrow fitness value, the global worst fitness value and the best fitness value respectively; ε is a very small constant.

[0085] Furthermore, in step S5, specifically, the number of iterations iter is used as the degree of freedom of the adaptive t distribution, and the perturbation of the position by the adaptive t distribution is as follows:

[0086]

[0087] Where t(iter) represents the adaptive t distribution function with the current iteration number iter as the degree of freedom parameter;

[0088] A dynamic selection rule is set to randomly select some individual positions for perturbation. The basis of the rule is: in the early stage of iteration, the probability of perturbation is relatively high to avoid falling into the local optimum too early and affecting the global search; in the later stage of iteration, the probability of perturbation is relatively low to give full play to the local search performance of the algorithm and improve the convergence speed. Based on this, the probability of perturbation p is set as:

[0089] p=w1-w2×(iter max -iter) / iter max (29)

[0090] Among them, w1 and w2 are the upper limit and variation range of the selection probability respectively, and w1=0.5 and w2=0.1 are set.

[0091] Further, in step S6, it is determined whether the algorithm has reached the maximum number of iterations itermax If it is reached, the optimal solution of the radar observation error model at this time is output as the estimation result of the radar system error, that is, the improved sparrow search algorithm is used to complete the solution of equation (11), otherwise, return to step S3;

[0092] In step S7, the estimated results of the radar system error are substituted into equations (30) and (31) in turn, the target position measured by the radar is corrected, and the corrected target position (x LRc (k),y LRc (k),z LRc (k)),

[0093]

[0094]

[0095] Compared with the prior art, the present invention has the following beneficial effects:

[0096] The radar error correction method based on the improved sparrow search algorithm provided by the present invention transforms the nonlinear model solution problem into a multi-dimensional multi-peak optimization problem, thereby avoiding the introduction of deviations in the linearization process of the nonlinear system; at the same time, multiple strategies are used to improve the convergence speed and solution accuracy of the sparrow search algorithm, so that the radar system error estimation takes into account both accuracy and real-time performance, thereby improving the radar calibration effect and improving the target track accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 A schematic flow chart of a radar error correction method based on an improved sparrow search algorithm provided by the present invention;

[0098] Figure 2a-2d Schematic diagram of the estimation effect of different algorithms on radar system error when the number of observation points is different;

[0099] Figure 3 This is a schematic diagram of the target track comparison before and after correction;

[0100] Figure 4a-4c These are the error correction effect diagrams for the X, Y, and Z axes. DETAILED DESCRIPTION

[0101] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the following further describes how the present invention is implemented in conjunction with the accompanying drawings and specific implementation methods.

[0102] Reference Figure 1 As shown, the present invention provides a radar error correction method based on an improved sparrow search algorithm, comprising the following steps:

[0103] S1: Establish a radar observation error model and input radar observation data, GNSS push data and radar station coordinate information;

[0104] S2, improve the initialization of the sparrow search algorithm, randomly generate candidate populations, and use chaotic mapping and reverse learning to expand the population range, sort the individuals in the population according to the fitness value, and select multiple individuals with higher fitness values ​​to form a new initial population;

[0105] S3, adaptively adjust the number of explorers and followers according to the iteration progress;

[0106] S4, update the explorer position according to the Osprey global search strategy, and update the positions of the followers and sentinels according to the sparrow search mechanism;

[0107] S5, using the dynamically selected adaptive t-distribution perturbation strategy to accelerate the convergence speed and further find the optimal individual, and calculate the individual position and fitness value after the perturbation;

[0108] S6, judging whether the algorithm has reached the maximum number of iterations, if so, outputting the optimal solution of the radar observation error model at this time as the estimation result of the radar system error, otherwise returning to step S3;

[0109] S7. Using the estimated result of the radar system error, correct the target position measured by the radar and output the corrected target position.

[0110] In step S1, when the present invention establishes a radar observation error model, the cooperative target detected by the radar is used as a reference source. The cooperative target is an aircraft equipped with a GNSS (Global Navigation Satellite System) and capable of pushing its position in real time through a data link. The reference source position data measured by the GNSS is associated with the radar observation data, time-aligned, and coordinate-transformed.

[0111] The associated track data can be time-aligned to extrapolate the received GNSS information to keep it in time synchronization with the radar positioning data. However, there is a delay in data link communication, and there is a deviation between the push time of GNSS positioning data and the radar observation time, which is called communication delay. During the delay, the aircraft will still fly forward for a distance. Due to the high speed of the aircraft, the position error caused by the communication delay cannot be ignored, so the radar error correction needs to consider the communication delay.

[0112] Assume that the GNSS data push cycle of the cooperation target is T G , the radar measurement period is T R , GNSS data push time is The radar measurement time is

[0113] The time difference between the two is The following relationship is obtained:

[0114] Δt2+T G =T R +Δt1 (1)

[0115] The position of the cooperative target is pushed and reconstructed periodically through smoothing and interpolation algorithms, so that T G =T R ,but That is, the communication delay is a constant value Δt. After estimating this value, the position deviation caused by the communication delay is corrected in combination with the speed of the cooperative target aircraft.

[0116] The cooperative target position acquired by GNSS is represented by longitude, latitude and altitude in the WGS-84 coordinate system, while the radar point trace is in the polar coordinate system centered on the radar, and the two must be unified; since the commonly used least squares method, Kalman filtering, etc. are linear estimation algorithms, both are transformed into the Cartesian coordinate system. The present invention uses the Earth-Centered, Earth-Fixed (ECEF) coordinate system as a unified coordinate system, takes the cooperative target that can be self-positioned by GNSS within the radar detection range as the reference source, ignores the positioning error of GNSS itself, considers the system errors of radar distance, azimuth, elevation, measurement noise and position deviation caused by communication delay, and establishes an integrated error model of shore-based radar.

[0117] The point data pushed by the cooperative target through the data link is measured by the airborne GNSS. Assume that the geographical location pushed by the cooperative target at time k includes the latitude L G (k), longitude λ G (k) and altitude H G (k), converted to the ECEF coordinate system:

[0118]

[0119] Where e is the eccentricity of the Earth and C is calculated by:

[0120]

[0121] Where E q is the equatorial radius;

[0122] The data measured by the radar at time k contains the radial distance r of the cooperative target m (k), azimuth angle θ m (k), elevation angle η m (k), transform it into the local Cartesian coordinate system with the radar position as the origin coordinate:

[0123]

[0124] Then transform to the ECEF coordinate system with the center of the earth as the origin:

[0125]

[0126] Among them, (x s ,y s ,z s ) is the radar geographic coordinate (L s ,λ s ,H s ) in the ECEF coordinate system can be calculated using formula (2), where T is the rotation matrix:

[0127]

[0128] It takes Δt for GNSS position information to be transmitted through the data link. Therefore, the position information received at time k is actually the coordinate information of the cooperative target at time k-Δt. During the Δt period, the cooperative target moves a certain distance. Assuming that the cooperative target moves in a uniform linear motion, its actual position (x EGT (k),y EGT (k),z EGT (k)) and GNSS positioning (x EG (k),y EG (k),z EG (k)) has the following relationship:

[0129]

[0130] where v x 、v y 、v z They are respectively the speeds of the cooperative target aircraft along the X, Y, and Z axes in the radar local coordinate system, which can be calculated from the aircraft's ground speed through coordinate transformation.

[0131] Assume the radar system error is β R =[Δr,Δθ,Δη] T , Δr is the ranging system error, Δθ is the azimuth system error, Δη is the elevation system error, and the radar measurement noise is [nr m (k),nθ m (k),nη m (k)] T According to formula (4), the actual position of the cooperative target at time k in the radar local coordinate system is:

[0132]

[0133] Transformed into the ECEF coordinate system:

[0134]

[0135] Both equations (7) and (9) represent the real coordinates of the same reference source in the ECEF coordinate system at a certain moment, so we can get:

[0136]

[0137] Substituting formula (8) into the equation, we get:

[0138]

[0139] At this point, the communication delay and radar system error are combined to establish an integrated error. The integrated system error vector is β = [Δr, Δθ, Δη, Δt] T The estimated value of β can be obtained by solving equation (11). Obviously, equation (11) is a nonlinear equation system. The existing algorithms all need to transform equation (11) into a linear equation using a first-order Taylor expansion and ignore the higher-order terms before solving it. This approximate process introduces new deviations, making the estimation result inaccurate.

[0140] The solution of system error is essentially to find a set of estimated values ​​that minimize the Euclidean distance between the corrected radar measurement and the track obtained by GNSS. Therefore, by constructing an objective function and solving it using a nonlinear optimization algorithm, the system error estimation problem is transformed into a multi-dimensional, multi-peak optimization problem, avoiding the deviation caused by the nonlinear system approximation process.

[0141] Let ψ(k)=[r m (k)-nr m (k),θ m (k)-nθ m (k),η m (k)-nη m (k)] T , then:

[0142]

[0143] Take N measurements of the reference source and construct the objective function:

[0144]

[0145] In the formula, Ω is the definition domain of β. The improved sparrow search algorithm is used to optimize formula (13) to estimate the error vector β.

[0146] Estimation of radar system error requires an algorithm that takes into account solution accuracy, convergence speed and stability. Conventional sparrow search algorithms have problems such as poor real-time performance and being extremely prone to falling into local optimality. Therefore, the present invention makes the aforementioned improvements to the sparrow search algorithm to estimate radar system errors: introducing an elite chaos reverse learning strategy to enrich the diversity of the initial population, from which elite individuals are selected to improve the quality of sparrow individuals, and avoiding the randomness of the initial population from affecting the algorithm's search ability and convergence speed; balancing the algorithm's global search ability and convergence accuracy through self-adjustment of the number of explorers and followers; integrating the global exploration strategy of the osprey optimization algorithm to improve the global search ability; and using dynamically selected adaptive t-distribution perturbation variation to coordinate local search and global exploration, thereby improving the convergence speed and jumping out of the local optimal in a timely manner.

[0147] Furthermore, step S2 specifically includes:

[0148] Assume that in the D-dimensional search space consisting of n sparrows, the position of each sparrow is expressed as:

[0149]

[0150] The corresponding sparrow's fitness is expressed as:

[0151]

[0152] The improved sparrow search algorithm is initialized and a candidate initialization population X is randomly generated as shown in formula (14).

[0153] The quality of the initial population of the sparrow search algorithm has a great influence on the convergence speed and solution accuracy. The elite chaos reverse learning strategy uses chaotic mapping and reverse refraction learning to generate candidate solutions in a larger range, and then selects elite individuals with better quality as the initial population through sorting. Chaotic sequences have good non-repetitive traversal and randomness. The present invention uses chaotic Bernoulli mapping to enhance the randomness and diversity of the initial population. The iterative formula of chaotic Bernoulli mapping is:

[0154]

[0155] The subscript k is the number of chaotic iterations, λ is a constant, usually 0.4, and the generated chaotic sequence z i,j Mapped into the sparrow search space:

[0156] x i,j =x L +(x U -x L )×z i,j (17)

[0157] Where x U and xL are the upper and lower bounds of the search space respectively; Substitute X in equation (14) into equation (17) to generate the chaotic population Y.

[0158] On the other hand, the refraction reverse learning mechanism is used to further expand the range of optional solutions. i,j The reverse solution of for:

[0159]

[0160] In the formula, a j and b j They represent the minimum and maximum values ​​of the j-th dimension of the current population respectively, and k is the lens zoom coefficient. Substitute X in formula (14) into formula (18) to generate the reverse learning population Z.

[0161] Then, sort the individuals in populations X, Y, and Z according to their fitness values, and select the first n individuals to form a new initial population, recorded as:

[0162]

[0163] In the sparrow search mechanism, explorers and followers perform global exploration and local search tasks respectively. Under normal circumstances, explorers usually account for 10% to 20% of the entire population. This quantitative limitation will affect the global optimization ability and solution accuracy of the algorithm. Therefore, further, in step S3, at the beginning of the iteration, in order to expand the search range and increase the proportion of explorers in the population, when switching to a mode based on local precise search, the number of followers is increased to improve the convergence accuracy and speed of the algorithm; the adaptive adjustment formula for the number of explorers and followers is constructed as:

[0164]

[0165] pNum=rn (21)

[0166] fNum=(1-r)n (22)

[0167] In the formula, iter is the number of iterations, iter max is the maximum number of iterations, r is the nonlinear proportional coefficient, which is used to adaptively control the number of explorers pNum and the number of followers fNum, b is a constant coefficient, and l is the disturbance deviation factor.

[0168] In the sparrow search algorithm, the explorer guides the flow of the entire population, and its position update formula is:

[0169]

[0170] In the formula, is the position information of the i-th sparrow in the j-dimension when the number of iterations is iter, α∈(0,1] is a random number, R2∈[0,1] and S T ∈[0.5,1] are warning value and safety value respectively, R2<S T It indicates that the foraging environment is safe and the explorer can search in a larger range. Conversely, it indicates that the alerter finds a threat and warns other sparrows. At this time, all sparrows need to move to a safe area. Q is a normally distributed random number, and L is a 1×D matrix. It can be seen that the explorer position update in the iterative process mainly depends on the position of the previous generation of explorers, and the global search capability is limited.

[0171] In contrast, in step S4, the present invention uses the osprey global search strategy to update the explorer position to make up for the above shortcomings. The osprey optimization algorithm seeks optimization by simulating the hunting behavior of the osprey, and the algorithm has a wider global search range and good local stagnation escape ability. Therefore, the global exploration strategy of the osprey optimization algorithm is introduced into the sparrow search algorithm to replace the explorer position update method of the sparrow search algorithm.

[0172] Specifically, considering the explorer as an osprey, the position set of all candidate prey of the i-th osprey is specified by the following formula:

[0173] FP i ={X k |k∈{1,2,…,n}∧F k <F i}∪{Xbest} (23)

[0174] Among them, Xbest is the best Osprey position;

[0175] At this time, the osprey randomly moves to the location of a candidate prey. In this process, the position update of the j-th dimension of the i-th osprey is described by the following formula:

[0176]

[0177] Among them, SF i,j represents the position of the prey selected by the i-th osprey in the j-th dimension; r i,j is a random number in [0,1]; I is a random number in {1,2}; x i,j and are the positions of the i-th osprey before and after the j-th dimension movement. If the objective function value is better in the new position after the movement, the previous position of the osprey is replaced by the following formula:

[0178]

[0179] It can be seen that when ospreys move towards their prey, they make full use of the information of each individual in the population, which enables effective search over a larger area.

[0180] In addition, in step S4, the position of the follower is updated according to the sparrow search mechanism as follows:

[0181]

[0182] in, is the worst position of the sparrow in the j dimension at the iter-th iteration, is the best position of the explorer in the j-dimension at the iter+1th iteration; rand{-1,1} represents a random value in [-1,1], and Q is a random number from a normal distribution; when i>n / 2, it means that the i-th follower with a lower fitness has not obtained food and will fly to other places to continue foraging; when i≤n / 2, the i-th follower will be at the optimal position Searching for food nearby, the corresponding algorithm enters the local search stage.

[0183] In step S4, the position of the sentinel is updated according to the sparrow search mechanism:

[0184]

[0185] Where β∈N(0,1) is the step size control parameter; K is a random number in [-1,1]; F i 、F w 、F g They represent the current sparrow fitness value, the global worst fitness value and the best fitness value respectively; ε is a very small constant to avoid 0 in the denominator.

[0186] In the initial iteration of the sparrow search algorithm, individuals in the population should have a divergent trend to obtain better global development capabilities. As the number of iterations increases, sparrows gradually gather, and the individual local exploration capabilities should be enhanced while improving the convergence speed. Therefore, in step S5, specifically, the number of iterations iter is used as the degree of freedom of the adaptive t distribution. From the morphological characteristics of the t distribution curve, it can be seen that the degree of freedom is small in the initial iteration and the curve is flat. At this time, the individuals in the population enter a wide search mode; otherwise, the curve is close to the normal distribution curve, and the algorithm can obtain a faster convergence speed. The perturbation of the position by the adaptive t distribution is as follows:

[0187]

[0188] Where t(iter) represents the adaptive t distribution function with the current iteration number iter as the degree of freedom parameter; if the positions of all individuals in the population are perturbed indiscriminately, a lot of computing resources will be wasted and the computing time will be prolonged. Therefore, a dynamic selection rule is set to randomly select some individual positions for perturbation. The basis of the rule is: in the early stage of iteration, the probability of perturbation is high to avoid falling into the local optimum too early and affecting the global search; in the later stage of iteration, the probability of perturbation is low to give full play to the local search performance of the algorithm and improve the convergence speed. Based on this, the probability of perturbation p is:

[0189] p=w1-w2×(iter max -iter) / iter max (29)

[0190] Among them, w1 and w2 are the upper limit and variation range of the selection probability respectively, and w1 can be set to 0.5 and w2 to 0.1.

[0191] In step S6, it is determined whether the algorithm has reached the maximum number of iterations iter max If it is reached, the optimal solution of the radar observation error model at this time is output as the estimation result of the radar system error, that is, the improved sparrow search algorithm is used to complete the solution of equation (11), otherwise, return to step S3;

[0192] In step S7, the estimated results of the radar system error are substituted into equations (30) and (31) in turn, the target position measured by the radar is corrected, and the corrected target position (x LRc (k),y LRc (k),z LRc (k)),

[0193]

[0194]

[0195] In a specific embodiment, the radar error correction method based on the improved sparrow search algorithm provided by the present invention is simulated and verified, and the estimation effects of the existing KF (Kalman filtering), GLS (Generalized Least Squares), SSA (Sparrow Search Algorithm) algorithms and the improved sparrow search algorithm (hereinafter referred to as ISSA) provided by the present invention on the system error are analyzed and compared under the same conditions.

[0196] The simulation conditions are shown in Table 1 below. Assume that the radar coordinates are (68.923°, -137.259°, 51.856m), the ranging system error Δr is 1300m, the azimuth system error Δθ is 0.498°, the elevation system error Δη is 0.544°, the observation noise obeys Gaussian distribution, the GNSS system communication delay is 1s, the starting position of the reference source is (69.014°, -136.754°, 10000m), and the end position is (69.535°, -135.219°, 10000m). The reference source motion is modeled using the following formula with the radar local coordinate system as the reference coordinate system.

[0197]

[0198] Table 1 Simulation conditions

[0199]

[0200] Based on the derived radar observation error model, the radar system error is estimated using the GLS, KF, SSA and ISSA algorithms respectively. The convergence results of 200 observation points are taken. Table 2 shows the root mean square error RMSE and average calculation time of 100 Monte Carlo simulations of the four algorithms under the same conditions. Among them, RMSE is calculated by the following formula, M is the number of simulations; the average time is the time used to estimate the radar system error under the software and hardware conditions of the current PC.

[0201]

[0202] Table 2 Performance comparison of different algorithms

[0203]

[0204] As shown in Table 2, ISSA is the most accurate in estimating system errors, followed by SSA, while the estimation results of KF and GLS algorithms are similar and the effect is poor. The ISSA algorithm improves the accuracy of ranging system error estimation results by about 62%, 61% and 48% compared with KF, GLS and SSA; in the azimuth system error estimation results, the improvement of ISSA is 79%, 79% and 65% respectively; in terms of elevation system error, ISSA improves by 79%, 78% and 60% respectively; in GNSS system communication delay estimation, ISSA improves by 49%, 48% and 4% compared with the other three algorithms. It can be seen that ISSA and SSA have higher accuracy in estimating system errors than KF and GLS algorithms. The main reason is that the former does not need to linearize the nonlinear equations and thus avoids the loss of accuracy in the process. However, high computational complexity and long computational time are common problems of group optimization algorithms. The ISSA algorithm solution time is nearly half of the SSA calculation time. This shows that the present invention reduces the computational complexity of SSA by integrating multiple strategies, accelerates algorithm convergence, and improves real-time performance.

[0205] Figure 2a-2d The estimation effects of the four algorithms on radar system errors with different numbers of observation points are shown, and the convergence of the algorithms is demonstrated. Figure 2a The middle vertical axis represents the ranging system error. Figure 2b The middle vertical axis represents the azimuth system error. Figure 2c The middle vertical axis represents the elevation system error. Figure 2d The middle vertical axis represents communication delay.

[0206] It can be seen from the figure that as the number of observation points increases, the accuracy of system error estimation gradually improves. Under the above simulation conditions, the ISSA algorithm can converge the system error estimation value to the true value using about 40 observation points of the reference source target motion, while the other three algorithms require more observations to converge the estimation results, which shows that ISSA has good convergence and solution accuracy. In addition, from Figure 2a It can be seen that the solution results of SSA fluctuate greatly, which is most likely the result of the solution being stuck in a local optimum. In comparison, the fluctuation of ISSA is smaller, indicating that the algorithm has a strong ability to jump out of the local optimum and the solution results are more stable.

[0207] The radar observation result is corrected by using the system error estimation value obtained by the ISSA algorithm provided by the present invention. The target track before and after correction is compared. Figure 3 Obviously, the corrected radar observation track is closer to the real track, but due to the existence of measurement noise, there is still a certain difference between the radar observation track and the real track, which can be reduced through subsequent data processing (filtering, etc.).

[0208] Figure 4a-4c The radar observation errors before and after correction in the XYZ three-axis directions were compared, and the RMSE of 200 observation values ​​before and after radar correction in the three directions were calculated to be 1037.1m (172.2m), 1044.4m (235.2m) and 995.1m (222.5m), respectively. After correction, the radar observation accuracy was improved by 83%, 77% and 78%, respectively. It can be seen that the method provided by the present invention can significantly reduce the influence of system errors on the radar observation target track, verifying the effectiveness of the method provided by the present invention.

[0209] In summary, the present invention transforms the nonlinear model solving problem into a multi-dimensional and multi-peak optimization problem, thereby avoiding the introduction of deviations in the linearization process of the nonlinear system; at the same time, a variety of strategies are used to improve the convergence speed and solution accuracy of the sparrow search algorithm, so that the radar system error estimation takes into account both accuracy and real-time performance, thereby improving the radar calibration effect and improving the target track accuracy.

[0210] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A radar error correction method based on an improved sparrow search algorithm, characterized in that: The steps include: S1. Establish a radar observation error model and input radar observation data, GNSS push data and radar station coordinate information; S2, improve the initialization of the sparrow search algorithm, randomly generate candidate populations, and use chaotic mapping and reverse learning to expand the population range, sort the individuals in the population according to the fitness value, and select multiple individuals with higher fitness values ​​to form a new initial population; S3, adaptively adjust the number of explorers and followers according to the iteration progress; S4, update the explorer position according to the Osprey global search strategy, and update the positions of the followers and sentinels according to the sparrow search mechanism; S5, using the dynamically selected adaptive t-distribution perturbation strategy to accelerate the convergence speed and further find the optimal individual, and calculate the individual position and fitness value after the perturbation; S6, judging whether the algorithm has reached the maximum number of iterations, if so, outputting the optimal solution of the radar observation error model at this time as the estimation result of the radar system error, otherwise returning to step S3; S7, using the estimation result of the radar system error, correcting the target position measured by the radar, and outputting the corrected target position; In step S1, a radar observation error model is first established, and the cooperative target detected by the radar is used as a reference source. The cooperative target is an aircraft equipped with GNSS and capable of pushing its position in real time through a data link, and the reference source position data measured by the GNSS is associated with the radar observation data, time-aligned, and coordinate-transformed; In step S1, when establishing the radar observation error model, the following steps are specifically included: First, consider the position deviation caused by communication delay, and set the GNSS data push cycle of the cooperation target to be T G , the radar measurement period is T R , GNSS data push time is The radar measurement time is The time difference between the two is The following relationship is obtained: Δt2+T G =T R +Δt1 (1) The position of the cooperative target is pushed and reconstructed periodically through smoothing and interpolation algorithms, so that T G =T R ,but That is, the communication delay is a constant value Δt. After estimating this value, the position deviation caused by the communication delay is corrected in combination with the speed of the cooperative target aircraft. Next, suppose that the geographical location received at time k includes the latitude L G (k), longitude λ G (k) and altitude H G (k), converted to the ECEF coordinate system: Where e is the eccentricity of the Earth and C is calculated by: Where E q is the equatorial radius; The data measured by the radar at time k contains the radial distance r of the cooperative target m (k), azimuth angle θ m (k), elevation angle η m (k), transform it into the local Cartesian coordinate system with the radar position as the origin coordinate: Then transform to the ECEF coordinate system with the center of the earth as the origin: Among them, (x s ,y s ,z s ) is the radar geographic coordinate (L s ,λ s ,H s ) in the ECEF coordinate system can be calculated using formula (2), where T is the rotation matrix: The transmission of GNSS position information takes Δt, so the position information received at time k is actually the coordinate information of the cooperative target at time k-Δt. During the Δt time, the cooperative target moves a certain distance. Assuming that the cooperative target moves in a uniform linear motion, its actual position (x EGT (k),y EGT (k),z EGT (k)) and GNSS positioning (x EG (k),y EG (k),z EG (k)) has the following relationship: where v x 、v y 、v z are the velocities of the cooperative target aircraft along the XYZ axes in the radar local coordinate system; Next, let the radar system error be Δr is the ranging system error, Δθ is the azimuth system error, Δη is the elevation system error, and the radar measurement noise is According to formula (4), the actual position of the cooperative target at time k in the radar local coordinate system is: Transformed into the ECEF coordinate system: Both equations (7) and (9) represent the real coordinates of the same reference source in the ECEF coordinate system at a certain moment, so we can get: Substituting formula (8) into the equation, we get: At this point, the communication delay and radar system error are combined to establish an integrated error. The integrated system error vector is recorded as make Then we have: Take N measurements of the reference source and construct the objective function: In the formula, Ω is the definition domain of β. In the subsequent steps, the improved sparrow search algorithm is used to optimize formula (13) to estimate the system error vector β.

2. The radar error correction method based on the improved sparrow search algorithm according to claim 1 is characterized in that: Step S2 specifically includes: Assume that in the D-dimensional search space consisting of n sparrows, the position of each sparrow is expressed as: The corresponding sparrow's fitness is expressed as: The improved sparrow search algorithm is initialized and a candidate initialization population X is randomly generated as shown in formula (14). Then, the chaotic Bernoulli mapping is used to enhance the randomness and diversity of the initial population. The iterative formula of the chaotic Bernoulli mapping is: Among them, the subscript k is the number of chaotic iterations, λ is a constant, and the generated chaotic sequence z i,j Mapped into the sparrow search space: x i,j =x L +(x U -x L )×z i,j (17) Where x U and x L are the upper and lower bounds of the search space respectively; Substitute X in equation (14) into equation (17) to generate the chaotic population Y; On the other hand, the refraction reverse learning mechanism is used to further expand the range of optional solutions. i,j The reverse solution of for: In the formula, a j and b j They represent the minimum and maximum values ​​of the jth dimension of the current population, respectively, and k is the lens zoom factor; Substitute X in equation (14) into equation (18) to generate the reverse learning population Z; Then, sort the individuals in populations X, Y, and Z according to their fitness values, and select the first n individuals to form a new initial population, recorded as:

3. The radar error correction method based on the improved sparrow search algorithm according to claim 2 is characterized in that: In step S3, in the early stage of iteration, in order to expand the search range and increase the proportion of explorers in the population, when switching to a mode based on local precise search, the number of followers is increased to improve the algorithm convergence accuracy and speed; In addition, the adaptive adjustment formula for the number of explorers and followers is constructed as follows: pNum=rn (21) fNum=(1-r)n (22) In the formula, iter is the number of iterations, iter max is the maximum number of iterations, r is the nonlinear proportional coefficient, which is used to adaptively control the number of explorers pNum and the number of followers fNum, b is a constant coefficient, and l is the disturbance deviation factor.

4. The radar error correction method based on the improved sparrow search algorithm according to claim 3 is characterized in that: In step S4, when updating the explorer position according to the osprey global search strategy, the explorer is regarded as an osprey, and the position set of all candidate prey of the i-th osprey is specified by the following formula: FP i ={X k |k∈{1,2,…,n}∧F k <F i }∪{Xbest} (23) Among them, Xbest is the best Osprey position; At this time, the osprey randomly moves to the location of a candidate prey. In this process, the position update of the j-th dimension of the i-th osprey is described by the following formula: Among them, SF i,j represents the position of the prey selected by the i-th osprey in the j-th dimension; r i,j is a random number in [0,1]; I is a random number in {1,2}; x i,j and are the positions of the i-th osprey before and after the j-th dimension movement. If the objective function value is better in the new position after the movement, the previous position of the osprey is replaced by the following formula:

5. The radar error correction method based on the improved sparrow search algorithm according to claim 4 is characterized in that: In step S4, when the position of the follower is updated according to the sparrow search mechanism, its position is updated as: in, is the worst position of the sparrow in the j dimension at the iter-th iteration, is the best position of the explorer in the j-dimension at the iter+1th iteration; rand{-1,1} represents a random value in [-1,1], and Q is a random number from a normal distribution; When i>n / 2, it means that the i-th follower with lower fitness has not obtained food and will fly to other places to continue foraging; When i≤n / 2, the i-th follower will be in the optimal position Searching for food nearby, the corresponding algorithm enters the local search stage.

6. The radar error correction method based on the improved sparrow search algorithm according to claim 5 is characterized in that: In step S4, when the position of the sentinel is updated according to the sparrow search mechanism, its position is updated as: Where β∈N(0,1) is the step size control parameter; K is a random number in [-1,1]; F i 、F w 、F g They represent the current sparrow fitness value, the global worst fitness value and the best fitness value respectively; ε is a very small constant.

7. The radar error correction method based on the improved sparrow search algorithm according to claim 6 is characterized in that: In step S5, specifically, the number of iterations iter is used as the degree of freedom of the adaptive t distribution, and the perturbation of the position by the adaptive t distribution is as follows: Where t(iter) represents the adaptive t distribution function with the current iteration number iter as the degree of freedom parameter; A dynamic selection rule is set to randomly select some individual positions for perturbation. The basis of the rule is: in the early stage of iteration, the probability of perturbation is relatively high to avoid falling into the local optimum too early and affecting the global search; in the later stage of iteration, the probability of perturbation is relatively low to give full play to the local search performance of the algorithm and improve the convergence speed. Based on this, the probability of perturbation p is set as: p=w1-w2×(path max -iter) / iter max (29) Among them, w1 and w2 are the upper limit and variation range of the selection probability, respectively. max For the maximum number of iterations, set w1=0.5, w2=0.

1.

8. The radar error correction method based on the improved sparrow search algorithm according to claim 7 is characterized in that: In step S6, it is determined whether the algorithm has reached the maximum number of iterations iter max If it is reached, the optimal solution of the radar observation error model at this time is output as the estimation result of the radar system error, that is, the improved sparrow search algorithm is used to complete the solution of equation (11), otherwise, return to step S3; In step S7, the estimated results of the radar system error are substituted into equations (30) and (31) in turn, the target position measured by the radar is corrected, and the corrected target position (x LRc (k),y LRc (k),z LRc (k)),

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