An online high-rotation body angular rate estimation method based on improved sparrow search algorithm without gyro

Abstract

The application discloses a high-rotation body angular rate online estimation method based on an improved sparrow search algorithm under a non-gyroscope condition. According to the working principle and output characteristics of a magnetic resistance sensor, the indirect and direct relationship between the magnetic resistance sensor and the high-rotation body angular rate is explored, a multi-objective fitness function with the angular rate as an optimization object is designed, and thus the construction of an angular rate online estimation model is completed. According to the advantages and disadvantages of the SSA, in order to make the sparrow search directional and fast, an adaptive dynamic step strategy and a dynamic compression search strategy are proposed to improve the traditional SSA, so as to improve the optimization ability and the ability to jump out of a local extreme value of the algorithm. The ISSA is used to optimize and solve the angular rate online estimation model, so as to realize the online estimation of the high-rotation body angular rate under the non-gyroscope condition.

Description

Technical Field

[0001] This invention belongs to the field of angular rate acquisition technology under complex, highly dynamic, and strongly interfered environments, and relates to an online estimation method for the angular rate of a high-rotational body based on an improved sparrow search algorithm under gyroscope-free conditions. Background Technology

[0002] The angular rate of a high-speed spiral vehicle is typically sensed directly by an onboard gyroscope. However, its launch environment is harsh, characterized by high transients and strong impacts, and it exhibits high dynamic characteristics during flight, including high overload (≥10000g) and high rotational speed (≥10r / s). This complex environment leads to the following problems with the gyroscope: 1) Gyroscope malfunction, resulting in saturated, cutoff, or constant output signals; 2) Gyroscope performance degradation, where it may still function but with varying degrees of change in parameters, leading to low data accuracy; 3) Complete gyroscope failure, where the output signal fails to reflect the vehicle's angular rate, rendering the data unreliable. However, the angular rate of a high-speed spiral vehicle is crucial for its real-time positioning, autonomous decision-making, and flexible control accuracy. Therefore, ensuring accurate real-time sensing of the angular rate of a high-speed spiral vehicle in the absence of a gyroscope is a pressing problem that needs to be solved.

[0003] Magnetoresistive sensors, due to their advantages of low cost, high overload resistance, all-weather operation, and low power consumption, have been widely used in the field of high-rotational body angular rate sensing and have become a new direction for research on accurate angular rate sensing of high-rotational bodies under gyroscope-less conditions. Currently, research on angular rate sensing using magnetoresistive sensors mainly focuses on the analysis of their output signals. This involves using a magnetoresistive sensor strapped to the high-rotational body to generate a sine / cosine waveform output signal as the carrier rotates at high speed, and then using signal analysis to obtain the angular rate. These methods can effectively and accurately obtain the roll rate, but the pitch and yaw rates cannot be obtained solely by the magnetoresistive sensor and require the assistance of other sensors. Furthermore, they cannot accurately obtain the full angular rate of the high-rotational body when the gyroscope is completely ineffective or there is no external auxiliary signal. Thomas E. Harkins et al. from the U.S. Army Laboratory proposed a method to obtain the roll, pitch, and yaw rates of a high-rotational body using only a magnetoresistive sensor. This method constructs a mathematical model based on the relationship between the magnetoresistive sensor and the angular rate, uses low-pass filtering to obtain the roll rate, and then calculates the pitch and yaw rates. While this method can obtain the full angular velocity of a high-rotational body, its accuracy is limited, especially since the frequency threshold for the low-pass filter is difficult to determine. However, the magnetoresistive sensor and angular velocity mathematical model in the literature provide a new approach for sensing the angular velocity of a high-rotational body without a gyroscope. The problem of solving this mathematical model can be transformed into a multi-objective optimization problem, with angular velocity as the object to be optimized, and an intelligent optimization algorithm used to solve the model. Therefore, finding a high-precision intelligent optimization method to solve the angular velocity sensing problem has become extremely urgent.

[0004] Currently, well-known intelligent optimization algorithms include Genetic Algorithm (GA), Particle Swarm Optimization Algorithm (PSO), and Simulated Annealing Algorithm (SA), as well as several novel intelligent optimization algorithms proposed domestically and internationally in recent years: Butterfly Optimization Algorithm (BOA), Sine-Cosine Optimization Algorithm (SCA), Cuckoo Search Algorithm (CS), and Sparrow Search Algorithm (SSA). Among these, the Sparrow Search Algorithm (SSA), proposed by Xue Jiankai et al. in 2020, is a novel swarm intelligence algorithm. SSA offers advantages such as high solution accuracy, fast convergence speed, and good stability in optimization problems. It has been widely applied in fields such as multi-component fault diagnosis of wheelset bearings, optimal model parameter identification of proton exchange membrane fuel cell stacks, and integrated model optimization for dynamic reconfiguration of active distribution networks. Therefore, SSA can be introduced to address the online estimation and optimization problem of angular rate parameters in the mathematical model of magnetoresistive sensors and angular rate. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide an online estimation method for the angular rate of a high-spiral body based on an improved sparrow search algorithm under gyroscope-free conditions. This method can improve the optimization ability and the ability to escape local extrema of the algorithm, thereby realizing the online estimation of the angular rate of a high-spiral body under gyroscope-free conditions.

[0006] An online method for estimating the angular rate of a high-rotational body includes the following steps:

[0007] Step 1: Set the number of individuals n in the population, the number of discoverers PD in the population, the number of scouts SD in the population, the warning value R2, the safety value ST, the maximum number of iterations M, and the control step size ξ;

[0008] Step 2: Initialize the position information of each sparrow in the population according to the following formula to obtain the initialized population;

[0009]

[0010] Where, ω initial The initial value of the angular velocity is set; r∈[-1,1] is a random number;

[0011] Step 3: Substitute the sparrow's position information as angular velocity into the following formula to calculate the fitness value of each sparrow in the current population:

[0012]

[0013] In the formula, ω=[ω x ω y ω z [] represents the angular velocity of the high-rotational body, f(ω) is the fitness function; α is the weight; H b(k -1) H b(k) This represents the three-axis components of the geomagnetic vector at time k-1 and time k in the carrier coordinate system; For H b(k) The derivative; The attitude transformation matrix of the vehicle coordinate system between time k-1 and time k is:

[0014]

[0015] in, [q0 q1 q2 q3] = q is the attitude change quaternion;

[0016] According to the angle increment sample extraction method, we get:

[0017]

[0018] Where T represents the sampling time;

[0019] The attitude change quaternion can be obtained from the angle increment:

[0020]

[0021] Find the position corresponding to the minimum fitness among all sparrows, which is the optimal position, and the position corresponding to the maximum fitness, which is the worst position;

[0022] Step 4: When t is less than the maximum number of iterations M, calculate the adaptive dynamic step size w according to the following formula:

[0023]

[0024] Where Δx is the range of values ​​for the sigma function; rand represents a random number in the range [0,1] that follows a uniform distribution.

[0025] Step 5: Randomly select PD sparrows from the population as discoverers, and update the positions of the discoverers according to the following formula;

[0026]

[0027] In the formula, j = 1, 2, 3…d, where d is the dimension of the variable in the problem to be optimized; and Let represent the position information of the i-th sparrow in the j-th dimension during the t-th and t+1-th iterations; Q is a random number following a normal distribution; L represents a 1×d matrix where all elements are 1.

[0028] Step 6: Randomly select (n-PD) sparrows from the population as new members, and update their positions according to the following formula:

[0029]

[0030] In the formula, It is the optimal position occupied by the discoverer in the (t+1)th iteration. Let A represent the worst position of all sparrows in the current t-th iteration; let A be a 1×d matrix, where each element is randomly assigned a value of 1 or -1, and A + =A T (AA T ) -1 ;

[0031] Step 7: Randomly select SD sparrows from the population as scouts, and update the scouts' positions according to the following formula:

[0032]

[0033] In the formula, K∈[-1,1] is a random number; f represents the optimal position of all sparrows in the current t-th iteration; i f is the fitness value of the i-th sparrow in the t-th iteration; b and f w These are the minimum and maximum fitness values ​​among all sparrows in the current t-th iteration, respectively; ε is the smallest constant.

[0034] Step 8: Determine If the requirements are met, update the sparrow positions in the population according to the following formula:

[0035]

[0036] Step 9: Let t = t + 1, return to step 4; when t = M, end the iterative calculation at the current time and execute step 10;

[0037] Step 10: Obtain the optimal position among all sparrows, which is the optimal angular velocity ω. best Let ω initial =ω best If k = k + 1, return to step 2 to estimate the angular rate at the next moment, until the task ends.

[0038] The present invention has the following beneficial effects:

[0039] This invention discloses an online estimation method for the angular rate of a high-rotational body based on an improved sparrow search algorithm under gyroscope-free conditions. Based on the working principle and output characteristics of a magnetoresistive sensor, the indirect and direct relationships between the sensor and the angular rate of the high-rotational body are explored. A multi-objective fitness function with angular rate as the optimization object is designed to construct an online angular rate estimation model. Considering the advantages and disadvantages of the Sparrow Search Algorithm (SSA), an adaptive dynamic step size strategy and a dynamic compression search strategy are proposed to improve the traditional SSA in order to enhance the directionality and speed of the sparrow search. This improves the algorithm's optimization ability and its ability to escape local extrema. The ISSA algorithm is then used to optimize and solve the online angular rate estimation model, thereby achieving online estimation of the angular rate of a high-rotational body under gyroscope-free conditions. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention;

[0041] Figure 2(a) shows the Sigma function curve, and Figure 2(b) shows the boundary curve of the adaptive dynamic step size. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] The technical solution adopted in this invention is as follows: This invention constructs an online estimation model for high-rotational body angular rate using only a magnetoresistive sensor, and uses an improved sparrow search algorithm to achieve stable sensing of high-rotational body angular rate under gyroscope-free conditions.

[0044] (1) Indirect relationship between information sensed by magnetoresistive sensor and angular rate

[0045] During high-speed spiral flight, a magnetoresistive sensor strapped to the carrier can measure the three-axis components of the geomagnetic vector in the carrier coordinate system in real time. The three-axis components of the geomagnetic vector in the geographic coordinate system are: Since the range of a high-frequency cyclone is very small relative to the Earth's radius, it is assumed that the magnitude and direction of the geomagnetic vector remain constant in the geographic coordinate system. This can be obtained from the latitude and longitude of the launch site and time using the International Geomagnetic Reference Field (IGRF12) model. Based on the coordinate transformation relationship, we can obtain:

[0046]

[0047] In the formula, Let be the attitude transformation matrix between the vehicle coordinate system and the navigation coordinate system. [θ γ ψ] represent the pitch angle, roll angle, and yaw angle, respectively.

[0048] For both time k and time k-1, equation (1) holds, that is:

[0049]

[0050] In the formula, H b(k-1) H b(k) H represents the three-axis components of the geomagnetic vector at times k-1 and k in the carrier coordinate system; n(k -1) H n(k) H represents the three-axis components of the geomagnetic vector at time k-1 and time k in the geographic coordinate system; n(k) =H n(k-1) ; This represents the attitude transformation matrix between the vehicle coordinate system and the navigation coordinate system at time k-1 and time k;

[0051] Since the high-speed spiral body has a short flight time and a short landing distance, it can be assumed that the navigation coordinate system n does not change. Therefore, the attitude transformation matrix of the navigation coordinate system at the initial time and time k is... for:

[0052]

[0053] In the formula, I 3×3 It is a 3×3 identity matrix.

[0054] Further expansion of equation (2) according to the chain rule yields:

[0055]

[0056] Equation (4) represents the indirect relationship between the information sensed by the magnetoresistive sensor and the angular velocity. Wherein, This represents the attitude transformation matrix of the vehicle coordinate system at time k-1 and time k;

[0057] (2) Direct relationship between information sensed by magnetoresistive sensor and angular rate

[0058] Differentiating both sides of equation (1) simultaneously, we get:

[0059]

[0060] According to equation (3), in equation (5)

[0061] In addition, ω=[ω x ω y ω z [] indicates the angular velocity of a high-rotational body; To obtain an antisymmetric matrix, substituting this equation into equation (5) yields:

[0062]

[0063] Multiply both sides of Equation (6) on the left by We can obtain:

[0064]

[0065] In the formula, Numerical differential operation can be carried out using Legendre polynomials. Equation (7) is the direct relationship between the information sensed by the magnetoresistive sensor and the angular rate.

[0066] Combining Equation (4) and Equation (7) can construct a fitness function:

[0067]

[0068] In the formula, α is the weight, with a value between 0 and 1, and generally 0.5 is selected.

[0069]

[0070] Among them, [q0 q1 q2 q3] = q is the attitude change quaternion. Equation (8) is the online estimation model of the angular rate of a high-spin body under the condition of no gyroscope.

[0071] According to the angular increment single-sample extraction method, we can obtain:

[0072]

[0073] According to the angular increment, the attitude change quaternion can be obtained:

[0074]

[0075] It can be seen from Equations (8) to (10) that Equation (8) can be used as the fitness function, with the angular rate as the optimization target, and an intelligent optimization algorithm is used to achieve the online estimation of the angular rate.

[0076] Although SSA has the advantages of simplicity, flexibility, and few parameters, it still has the disadvantages of low optimization accuracy, slow convergence speed, and being easily trapped in local optima when facing complex problems. Taking Equation (8) as the optimization target, in order to estimate the angular rate accurately and quickly, the traditional SSA needs to be improved.

[0077] (3) Adaptive dynamic step size strategy

[0078] In the SSA algorithm, for the discoverer, when R2 < ST, this means that there is no predator around the foraging environment at this time, and the discoverer can perform extensive search operations, but its search has no specific direction and the search range is too broad, making it easy to fall into the boundary area. Therefore, the improved result for the update of the discoverer is:

[0079]

[0080] In the formula, t is the number of iterations, j = 1, 2, 3...d, and d is the dimension of the variable in the problem to be optimized. and Let Ri represent the position information of the i-th sparrow in the j-th dimension during the t-th and t+1-th iterations. R2∈[0,1] and ST∈[0,1] represent the warning value and the safety value, respectively. In this invention, the safety value is 0.8, and the warning value is a random number following a uniform distribution. Q is a random number following a normal distribution. L represents a 1×d matrix, where each element is 1. w is the adaptive dynamic step size, expressed as:

[0081]

[0082] In the formula, M represents the maximum number of iterations. Δx is the range of values ​​for the sigma function, typically Δx = 5. rand ∈ [0,1] is a uniformly distributed random number. The adaptive dynamic step size is designed inspired by the sigma function, and its variation with the number of iterations is shown in the attached figure. Figure 2(a) and 2(b) As shown.

[0083] For joiner updates, an adaptive dynamic step size is introduced to improve joiner updates, resulting in:

[0084]

[0085] In the formula, It is the optimal position occupied by the discoverer in the (t+1)th iteration. Let A represent the worst position of all sparrows in the current t-th iteration. Let A be a 1×d matrix, where each element is randomly assigned a value of 1 or -1, and A + =A T (AA T ) -1 .

[0086] The improved result of introducing adaptive dynamic step size for scout updates is as follows:

[0087]

[0088] In the formula, K∈[-1,1] is a random number; f represents the optimal position of all sparrows in the current t-th iteration; i f is the fitness value of the i-th sparrow in the t-th iteration; b and f w These are the minimum and maximum fitness values ​​among all sparrows in the current t-th iteration, respectively; ε is a minimum constant to avoid zero in the denominator.

[0089] (4) Dynamic compression search strategy

[0090] The introduction of adaptive dynamic step size aims to guide the Sparrow Search algorithm towards the optimal position in a directional manner. To prevent the SSA algorithm from getting trapped in local optima, a dynamic compression search strategy is designed. After each iteration, if the following conditions are met... but:

[0091]

[0092] In the formula, τ is the set threshold, ξ is a very small constant, ξ represents the control step size, and r∈[-1,1] is a random number.

[0093] As the number of iterations increases, when the fitness value no longer changes, equation (15) is executed, which is equivalent to re-initializing near the optimal position, making it faster and more accurate to approach the optimal position.

[0094] In summary, the steps of the ISSA-based online angular rate estimation method are as follows:

[0095] Step 1: Set the number of individuals n in the population, the number of discoverers PD in the population, the number of scouts SD in the population, the warning value R2, the safety value ST, the maximum number of iterations M, and the control step size ξ;

[0096] Initial value of design angular velocity ω initial ;

[0097] Step 2: Initialize the position information of each sparrow in the population according to the following formula to obtain the initialized population;

[0098]

[0099] Where, ω initial The initial value of the angular velocity is set, and the initial value of the angular velocity is ω. initial It can be set to zero, or set according to experience and actual situation; r∈[-1,1] is a random number;

[0100] Step 3: According to equations (9) and (10), substitute the sparrow's position information as the angle rate into equation (8) to calculate the fitness;

[0101] Step 4: When t is less than the maximum number of iterations M, calculate the adaptive dynamic step size w according to formula (12):

[0102] Step 5: Randomly select PD sparrows from the population as discoverers, and update the positions of the discoverers according to formula (11);

[0103] Step 6: Randomly select (n-PD) sparrows from the population as new members, and update the positions of the new members according to formula (12);

[0104] Step 7: Randomly select SD sparrows from the population as scouts, and update the scouts' positions according to formula (14):

[0105] Step 8: Determine If the requirements are met, update the sparrow positions in the population according to the following formula:

[0106]

[0107] Step 9: Let t = t + 1, return to step 4; when t = M, end the iterative calculation at the current time and execute step 10;

[0108] Step 10: Obtain the optimal position among all sparrows, which is the optimal angular velocity ω. best Let ω initial =ω best If k = k + 1, return to step 2 to estimate the angular rate at the next moment, until the task ends.

[0109] An online estimation model for the angular rate of a high-rotational body is constructed based on the indirect and direct relationships between the output information of the magnetoresistive sensor and the angular rate. An improved SSA (Search-Simulation Algorithm) is developed by combining an adaptive dynamic step-size strategy and a dynamic compression search strategy. Using angular rate as the optimization object, the angular rate estimation model is solved using ISSA (Independent ISSA), thereby achieving real-time online estimation of the angular rate of the high-rotational body.

[0110] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A high body angular rate online estimation method, characterized in that, The method comprises the following steps: Step 1: setting the number of individuals in the population n, the number of discoverers in the population PD, the number of scouts in the population SD, the early warning value R2, the safety value ST, the maximum number of iterations M and the control step length ξ; Step 2: the position information of each sparrow in the population is initialized according to the following formula, and an initialized population is obtained; where ω initial is a set initial angular velocity value; r ∈ [-1, 1] is a random number; Step 3: the position information of the sparrow is substituted into the following formula as the angular velocity to calculate the fitness value of each sparrow in the current population: In the formula, ω=[ω x ω y ω z [] represents the angular velocity of the high-rotational body, f(ω) is the fitness function; α is the weight; H b(k-1) H b(k) This represents the three-axis components of the geomagnetic vector at time k-1 and time k in the carrier coordinate system; For H b(k) The derivative; The attitude transformation matrix of the vehicle coordinate system between time k-1 and time k is: wherein, [q0 q1 q2 q3] = q is the pose change quaternion; According to the angular increment single-subsample extraction method, we have: Wherein, T represents the sampling time; According to the angular increment, the attitude change quaternion can be obtained: The position corresponding to the minimum fitness value of all sparrows is found, that is, the optimal position, and the position corresponding to the maximum fitness value is found, that is, the worst position; Step 4: when t is less than the maximum number of iterations M, the adaptive dynamic step length w is calculated according to the following formula: Wherein, Δx is the value range of the sigma function; rand represents a random number in the range of [0, 1] obeying uniform distribution; Step 5: randomly select PD sparrows in the population as discoverers, and update the positions of the discoverers according to the following formula: In the formula, j = 1, 2, 3...d, d is the dimension of the problem variable to be optimized; and represents the position information of the i-th sparrow in the j-th dimension in the t-th iteration and the t+1-th iteration; Q is a random number subject to normal distribution; L represents a 1xd matrix, wherein each element in the matrix is all 1; Step 6: randomly select (n-PD) sparrows in the population as joiners, and update the positions of the joiners according to the following formula: wherein, is the optimal position occupied by the discoverer in the t+1th iteration, denotes the worst position of all the sparrows in the current tth iteration; A denotes a 1 x d matrix, wherein each element is randomly assigned as 1 or -1, and A + = A T (AA T ) -1 ; Step 7: randomly select SD sparrows in the population as scouts, and update the positions of the scouts according to the following formula: where K ∈ [-1, 1] is a random number; Xtrepresents the optimal position of all sparrows in the current tthiteration;f i is the fitness value of the ith sparrow individual in the current tthiteration;f b andf w are the minimum and maximum fitness values of all sparrows in the current tthiteration, respectively; ε is the minimum constant; Step 8: Judgment If the requirements are met, update the sparrow position in the population according to the following formula: Step 9: let t=t+1, return to step 4; when t=M, end the iteration calculation at the current time, and execute step 10; Step 10: get the optimal position in all sparrows, that is, the optimal angular rate ω best , let ω initial = ω best , k = k + 1, return to step 2, and proceed with the angular rate estimation of the next moment until the task is completed.

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