Gyroscope model parameter identification method based on multi-innovation additional fractional-order gradient

Abstract

The present invention discloses a gyroscope model parameter identification method based on multi-innovation additional fractional-order gradient, comprising: constructing a three-degree-of-freedom gyroscope system model according to unknown parameters of the three-degree-of-freedom gyroscope system; adjusting the three-degree-of-freedom gyroscope system model by integer-order gradients and fractional-order gradients to obtain an additional fractional step descent iterative formula; performing multi-innovation expansion on the additional fractional step descent algorithm iterative formula by multi-innovation theory to obtain a multi-innovation additional fractional-order gradient descent iterative formula; obtaining input data and output data of the three-degree-of-freedom gyroscope, and iteratively solving the multi-innovation additional fractional-order gradient descent iterative formula by a gradient descent method according to the input data and the output data to obtain a parameter identification result; obtaining current input voltage data, and calculating the current input voltage data by bringing into a system model with the parameter identification result to obtain an output of the current attitude angle of the three-degree-of-freedom gyroscope.

Description

Technical Field

[0001] The present invention belongs to the technical field of fractional-order modeling and parameter identification, and in particular to a gyroscope model parameter identification method based on multiple new information and additional fractional-order gradients. Background Art

[0002] The gyroscope is a torque amplification device used for attitude control. It was first introduced in the early 20th century. With its excellent measurement and positioning performance, it has become an important component of the inertial navigation system. It has been widely used in defense construction fields such as launch vehicles, space stations, aircraft carriers, radars, etc. In daily life, gyroscopes are also widely used in common items such as camera pans, mobile terminals, drones, VR equipment, etc. The gyroscope is a high-speed rotating gyro rotor fixed on the suspension, and then a sliding constraint device that surrounds each other is added to its outer side, so that the gyro main axis has one or more directions of free rotation in the spatial structure. With the continuous development of science and technology, scholars can use the gyroscope's fixed axis and precession to build a benchmark, and use this benchmark to provide parameters such as attitude angle and deflection direction for the carrier. When the direction of the angular momentum of the flywheel is changed, a large output torque is generated on the gyro effect to ensure the stable operation of the carrier.

[0003] At present, the research on gyroscope modeling methods mainly focuses on two aspects: mechanism modeling and model parameter identification. The mechanism modeling method is to construct the state space model of the gyroscope based on the dynamic equation of the gyroscope. This method cannot accurately obtain the physical parameters of the system, and there will be many uncertainties and nonlinear disturbances in the operation of the gyroscope, resulting in low modeling accuracy. The model parameter identification technology uses the input and output observation data of the actual gyroscope system to identify the model parameters through numerical calculation methods. This method can effectively overcome the influence of internal uncertainty and external interference on the model, so it has higher modeling accuracy.

[0004] The existing system identification methods mainly include least squares method, stochastic gradient descent method, frequency domain subspace method, filter approximation method, neural network, wavelet integral operation matrix, modulation function, etc. Some swarm intelligence optimization algorithms are also widely used in system identification, such as particle swarm algorithm, whale algorithm, fruit fly algorithm, cuckoo algorithm, ant colony algorithm, lion colony algorithm, etc. Among the above methods, the stochastic gradient descent algorithm has attracted widespread attention from researchers due to its wide adaptability and easy engineering implementation. However, the traditional stochastic gradient descent algorithm has slow convergence speed and low convergence accuracy, and the model parameter identification speed and identification accuracy need to be further improved.

[0005] With the continuous development of fractional calculus, scholars have found that fractional calculus has strong flexibility, and expanded the integer-order gradient to the fractional-order gradient. The model parameters are identified using the fractional-order gradient. Although it can speed up the identification accuracy of the parameters to a certain extent, the identification results depend on the choice of fractional order. If the order is not chosen properly, the algorithm will not converge or the convergence accuracy will be reduced.

[0006] In summary, the existing integer-order gradient descent algorithm for parameter identification of the three-degree-of-freedom gyroscope model has the problems of slow parameter identification speed and low accuracy. Simply relying on fractional orders can easily lead to algorithm non-convergence or reduced convergence accuracy, resulting in the three-degree-of-freedom gyroscope system model not accurately representing the dynamic change process of the gyroscope attitude angle, and cannot be effectively applied to subsequent three-degree-of-freedom gyroscope control or applications. Summary of the invention

[0007] In order to solve the above technical problems, the present invention proposes a gyroscope model parameter identification method based on multi-innovation additional fractional-order gradient. On the basis of the traditional integer-order gradient, this method adds a fractional-order gradient and uses two gradients to synchronously identify model parameters. In addition, combined with the multi-innovation principle, the two gradients are expanded into a multi-innovation matrix, and the observation data is fully utilized to identify the system parameters, speed up the system identification speed and identification accuracy, and establish a more accurate gyroscope model to solve the problems existing in the above-mentioned prior art.

[0008] To achieve the above object, the present invention provides a gyroscope model parameter identification method based on multiple innovations and additional fractional-order gradients, comprising:

[0009] According to the unknown parameters of the three-degree-of-freedom gyroscope system, a three-degree-of-freedom gyroscope system model is constructed;

[0010] The three-degree-of-freedom gyroscope system model is adjusted by integer-order gradients and fractional-order gradients to obtain an additional fractional-step descent iterative formula;

[0011] Through the multi-innovation theory, the iterative formula of the additional fractional step descent algorithm is expanded with multiple innovations to obtain the multi-innovation additional fractional order gradient descent iterative formula;

[0012] Obtain observation data of the three-degree-of-freedom gyroscope, and iteratively solve the multi-information additional fractional-order gradient descent iterative formula through the gradient descent method according to the observation data to obtain parameter identification results; wherein the observation data includes the input voltage data of the three-degree-of-freedom gyroscope system and the corresponding output attitude angle;

[0013] The relationship between the input data and output data of the three-degree-of-freedom gyroscope system is reflected through a three-degree-of-freedom gyroscope system model with parameter identification results.

[0014] Optionally, the three-degree-of-freedom gyroscope system model is:

[0015] y(t)=a1y(t-1)+a2y(t-2)+bu(t-1)

[0016] Where y(t) represents the output of the gyroscope at time t, that is, the attitude angle, u(t) represents the input voltage of the gyroscope at time t, t represents the data time series, a1, a2, b represent the unknown parameters of the gyroscope system, and the unknown parameters are rewritten as the coefficient matrix θ = [a1, a2, b].

[0017] Optionally, the additional fractional step-down iteration formula is:

[0018]

[0019] in, is the estimated value of the coefficient matrix θ of the unknown parameters at time t, and the output input matrix of the gyroscope Where n represents the maximum sampling value, T is the transpose of the matrix, and e(t) is the output error. and r(t) are the expansions of integer-order gradient and fractional-order gradient step factors, Γ is the gamma function, α is the fractional-order differential, is the diagonal matrix of the unknown parameters of the three-degree-of-freedom gyroscope, and t represents the data time series.

[0020] Optionally, the output error is:

[0021]

[0022] Where y(t) represents the output of the gyroscope at time t.

[0023] Optionally, the multi-innovation additional fractional gradient descent iteration formula is:

[0024]

[0025] Where p is the multi-innovation length, E(p,t) is the multi-innovation matrix of the output error e(t), and Φ(p,t) is The multi-innovation matrix, and r(t) are the expansions of integer-order gradient and fractional-order gradient step factors, Γ is the gamma function, α is the fractional-order differential, is the estimated value of the coefficient matrix θ at time t, where t represents the data time series.

[0026] Optionally, in the multi-innovation additional fractional-order gradient descent iterative formula, the expansion of the integer-order gradient step factor is for

[0027]

[0028] Optionally, in the multi-innovation additional fractional-order gradient descent iterative formula, the expansion formula r(t) of the fractional-order gradient step factor is:

[0029]

[0030] Optionally, after obtaining the parameter identification result, the following steps are also included:

[0031] The parameter identification results are quantitatively evaluated according to the evaluation index δ, where:

[0032]

[0033] Optionally, after obtaining the parameter identification result, the following steps are also included:

[0034] The parameter identification results are substituted into the three-degree-of-freedom gyroscope system model and the current motor voltage data is obtained. The current motor voltage data is calculated by the three-degree-of-freedom gyroscope system model with the parameter identification results to obtain the current attitude angle of the three-degree-of-freedom gyroscope.

[0035] Compared with the prior art, the present invention has the following advantages and technical effects:

[0036] 1. The present invention can accurately identify the system parameters of a three-degree-of-freedom gyroscope, and the constructed model can accurately describe the dynamic change process of the gyroscope attitude angle.

[0037] 2. The present invention utilizes two gradients, integer order and fractional order, to synchronously identify system parameters, with fast parameter identification speed and high accuracy.

[0038] 3. The present invention adds an additional fractional-order gradient on the basis of the integer-order gradient, thereby avoiding the problem of inaccurate parameter identification caused by improper selection of fractional orders.

[0039] 4. The three-degree-of-freedom gyroscope system model constructed by the present invention can be widely used in the controller design of optoelectronic stabilization platforms, unmanned aerial vehicles, balance vehicles and other systems, laying the foundation for the simulation and application of advanced control technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0041] Figure 1 is a schematic diagram of the collected gyroscope input and output data according to an embodiment of the present invention;

[0042] Figure 2It is a fitting effect diagram of the three-degree-of-freedom gyroscope model constructed in an embodiment of the present invention and experimental data;

[0043] Figure 3 is a comparison diagram of gyroscope system parameter identification errors when different orders of additional fractional gradients are applied in an embodiment of the present invention;

[0044] Figure 4 4 is a comparison diagram of gyroscope system parameter identification errors under different innovation lengths according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0046] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0047] The present invention relates to a gyroscope model parameter identification method based on multi-information additional fractional-order gradient, comprising the following steps: first, collecting the input and output data of a three-degree-of-freedom gyroscope to construct a gyroscope system model. Then, constructing an additional fractional-order gradient, and using integer-order gradients and fractional-order gradients to jointly identify unknown parameters of the gyroscope system. Finally, based on the multi-information theory, an additional multi-information fractional-order gradient descent iterative formula is established, and the observation data at the past moment and the current moment are used to jointly identify the unknown parameters. The present invention can accurately identify the system parameters of a three-degree-of-freedom gyroscope, and the constructed model can accurately describe the dynamic change process of the gyroscope attitude angle. The problem of inaccurate parameter identification caused by improper selection of fractional orders is avoided.

[0048] The technical solution of the present invention includes the following contents:

[0049] Step 1: Collect the input and output data of the three-degree-of-freedom gyroscope and build the system model of the gyroscope. The system model of the three-degree-of-freedom gyroscope can be expressed as

[0050] y(t)=a1y(t-1)+a2y(t-2)+bu(t-1) (1)

[0051] Where y(t) represents the output of the gyroscope at time t, i.e., the attitude angle. u(t) represents the input voltage of the gyroscope at time t. t represents the data time series, a1, a2, b represent the unknown parameters of the gyroscope system model, and the unknown parameters can be rewritten as the coefficient matrix θ = [a1, a2, b].

[0052] Step 2: According to the iterative law of the gradient descent algorithm, use the integer order gradient and the fractional order gradient to jointly identify the unknown parameters. That is, adjust the system model according to the integer order gradient and the fractional order gradient to obtain the additional fractional order gradient descent iterative formula, which is:

[0053]

[0054] in, is the estimated value of the coefficient matrix θ of the unknown parameters at time t, and the gyroscope system output input matrix Where n represents the maximum value of the total sampling, T is the transpose of the matrix, and e(t) is the output error. and r(t) are the expansions of integer-order gradient and fractional-order gradient step factors, Γ is the gamma function, α is the fractional-order differential, is the diagonal matrix of the unknown parameters of the three-degree-of-freedom gyroscope.

[0055] Step 3: According to the multi-innovation theory, the current data of the three-degree-of-freedom gyroscope used for parameter identification is expanded into the form of a multi-innovation matrix, and the unknown parameters are jointly identified using the data of the past and current moments. The additional fractional step descent algorithm iterative formula is expanded with multi-innovation, and a multi-innovation additional fractional order gradient descent iterative formula is constructed, which is:

[0056]

[0057] Where p is the multi-innovation length. E(p,t) is the multi-innovation matrix of the output error e(t), and Φ(p,t) is The multi-innovation matrix.

[0058] Step 4: Set the initial values ​​of the unknown parameters of the three-degree-of-freedom gyroscope system, use the additional multi-information fractional-order gradient descent iterative formula proposed in the present invention as a basis, and iteratively solve the unknown parameters of the system by combining the gradient descent algorithm with the observed data to obtain the parameter identification results. Use the evaluation index δ to quantitatively evaluate the parameter identification results. And compare the effects of different fractional differential orders on the gyroscope model fitting effect.

[0059] The parameter identification results are substituted into the system model and the current motor voltage data is obtained. The current motor voltage data is calculated by bringing into the system model with the parameter identification results to obtain the current attitude angle of the three-degree-of-freedom gyroscope.

[0060] Step 5: Change the multi-innovation length and compare and analyze the impact of different multi-innovation lengths on the gyroscope model fitting effect.

[0061] The above technical solution of the present invention is described in detail:

[0062] Step 1: The three-degree-of-freedom gyroscope is mainly composed of a gyroscope, a servo motor, a data acquisition card, a power amplifier, and a host computer. The host computer relies on the Quarc semi-physical simulation platform and collects the input and output data of the system, i.e., the observation data, based on the Simulink software. The data collection mainly uses the Quarc database module, which can transmit and collect data in real time, and has fast data collection speed and high accuracy. In the present invention, the data collection interval is set to 0.025s, the collection time is 50s, and the collected input and output data are as follows: Figure 1 As shown in the figure. The voltage of the motor is input to the host computer, the input signal is transmitted to the data acquisition card through the Quarc semi-physical simulation platform, the signal is amplified by the power amplifier, and applied to the servo motor. By continuously adjusting the motor voltage, the gyroscope attitude angle can be precisely controlled.

[0063] The three-DOF gyroscope system can be expressed as

[0064] y(t)=a1y(t-1)+a2y(t-2)+bu(t-1) (1)

[0065] Where y(t) represents the output of the gyroscope at time t, i.e., the attitude angle. u(t) represents the input voltage of the gyroscope at time t. t represents the data time series, a1, a2, b represent the unknown parameters of the gyroscope system, and the unknown parameters can be rewritten as the coefficient matrix θ = [a1, a2, b].

[0066] Step 2: The gradient descent algorithm is a kind of iterative method. In the process of parameter identification, the unknown parameters of the system can be identified when the minimum value of the loss function is obtained by iterating step by step along the direction of gradient descent. The integer-order gradient direction is the partial differential of the function, while the fractional-order gradient direction is the fractional differential of the function.

[0067] Define the criterion function for additional fractional gradients

[0068]

[0069] Where y(t) represents the output of the gyroscope at time t, that is, the attitude angle, and the gyroscope system output input matrix Where n represents the maximum sampling value of the system and T is the transpose of the matrix.

[0070] The additional fractional gradient descent algorithm adds fractional gradients on the basis of integer gradients and uses dual gradients to identify θ synchronously. Therefore, the additional fractional gradient descent algorithm can be expressed as

[0071]

[0072] in, is the estimated value of the coefficient matrix θ of the unknown parameters at time t, is the estimated value of the parameter vector θ. γ and μ are the step size factors of integer and fractional gradients, respectively. represents the gradient, and α is the fractional differential.

[0073] Substituting formula (4) into formula (5), we can get

[0074]

[0075] in, is the additional fractional gradient, is the diagonal matrix of the unknown parameters of the three-degree-of-freedom gyroscope, with the offset term ε = 0.01. γ and μ can be expanded into the following form

[0076]

[0077] Define the output error in formula (6)

[0078]

[0079] Combining formulas (6), (7), (8), and (9), we can get the iterative formula of the additional fractional gradient descent algorithm as follows:

[0080]

[0081] Step 3: The additional fractional gradient descent method uses the flexibility of fractional calculus to simultaneously identify the unknown parameters in the three-degree-of-freedom gyroscope through integer gradients and fractional gradients. The use of two gradients for synchronous identification can improve the identification accuracy and speed, and can effectively overcome the problem that the single integer gradient converges slowly and the descent speed of the fractional gradient depends on the selection of the fractional differential order. However, both gradients only use the data at the current moment, resulting in insufficient utilization of available information, thereby limiting the ability to improve the accuracy of parameter identification in each iteration. Therefore, in order to further improve the speed and accuracy of parameter identification, the multi-innovation principle is introduced, and a high-precision identification method for three-degree-of-freedom gyroscope parameters based on multi-innovation additional fractional gradient descent is established.

[0082] The multi-innovation theory combines current and past data to construct a multi-innovation matrix, and then uses this matrix to estimate the current parameters. In this case, y(t), e(t) is called single innovation, and we expand them into multi-innovation matrices Y(p,t), Φ(p,t), and E(p,t) respectively.

[0083] Y(p,t)=[y(t),y(t-1),…,y(t-p+1)] T (10)

[0084]

[0085] E(p,t)=[e(t),e(t-1),…,e(t-p+1)] T (12)

[0086] The criterion function of the multi-innovation additional gradient descent algorithm can be expressed as

[0087]

[0088] Using formulas (10), (11) and (12), the single innovation in formula (2) is expanded into a multi-innovation matrix, and the iterative formula of the multi-innovation additional fractional gradient descent algorithm can be obtained:

[0089]

[0090] Compared with formula (2), formula (3) uses more observation data in the parameter identification process, and the data utilization rate is higher. Formula (2) only uses the data at the current time, that is, time t; while formula (3) uses the data from time t-p+1 to time t, where p = 1, 2, 3, ... is the multi-information length. Therefore, formula (3) uses more data in the parameter identification process, and the data utilization rate is higher.

[0091] Step 4: Set the initial values ​​of the unknown parameters of the three-DOF gyroscope system. From formula (1), it can be seen that the gyroscope system has three unknown parameters a1, a2, and b, and we set their initial values ​​to 0. The order of the additional fractional gradient is set to 1.2, and the multi-information length is set to p=3. Then, the additional multi-information fractional gradient descent algorithm proposed in the present invention is used to identify the unknown parameters of the system. In order to verify the accuracy of parameter identification and three-DOF gyroscope model construction, the evaluation index δ is used for quantitative evaluation.

[0092]

[0093] The parameter identification is performed using the additional multi-innovation fractional-order gradient descent method proposed in the present invention, and the identification results obtained are as follows:

[0094] y(t)=0.4950y(t-1)+0.5048y(t-2)-0.0006u(t-1) (17)

[0095] By collecting the input voltage data u(t) of the three-degree-of-freedom gyroscope and inputting the voltage data into the three-degree-of-freedom gyroscope model shown in formula (17), the attitude angle of the three-degree-of-freedom gyroscope can be output. According to the attitude angle, the horizontal position of the optoelectronic stabilization platform can be accurately obtained, and then the stability accuracy of the platform's visual axis can be obtained. Through the attitude feedback control method, the stability of the visual axis of the optoelectronic stabilization platform can be achieved. In addition, the attitude angle can be used as the detection feedback data of the control system of the balance car and the unmanned aerial vehicle. By comparing with the set attitude angle, their position offset error can be obtained. According to the real-time attitude angle output by formula (17), an advanced control system is designed, and feedback control is adopted to keep the unmanned aerial vehicle or the balance car stable and balanced in real time. This is also the key to the benefits generated by this patent, that is, an accurate model of the three-degree-of-freedom gyroscope is established, which lays the foundation for the control system design of the optoelectronic stabilization platform, the unmanned aerial vehicle, and the balance car.

[0096] from Figure 2 It can be seen that the proposed method can accurately identify the parameters of the three-degree-of-freedom gyroscope system. The identification system can accurately describe the dynamic characteristics of the gyroscope. The constructed model accurately characterizes the dynamic change process of the attitude angle.

[0097] In the additional fractional gradient descent method, different fractional orders will affect the model parameter identification results. In order to verify the modeling accuracy of the gyroscope under different fractional orders, the fractional orders are set to 0.5, 0.8, 1.2, and 1.5 respectively. The multi-innovation length remains unchanged, that is, p = 3. And the model parameter identification corresponding to different fractional orders is as follows Figure 3 shown.

[0098] from Figure 3 It can be seen that with the continuous increase of fractional differential order, the identification speed of the three-DOF gyroscope parameters is faster and the identification accuracy is higher. This is because the method proposed in this patent has two gradients, fractional order and integer order, and the dual gradients are jointly identified, which can effectively improve the convergence speed and convergence accuracy. Even when α=0.5, the convergence speed of the evaluation index is still very high, thus verifying the effectiveness of the method proposed in this patent.

[0099] Step 5: In the additional multi-innovation fractional gradient descent method, in addition to the adjustable fractional order, there is another adjustable parameter, namely the multi-innovation length. The longer the multi-innovation length, the larger the matrix dimension and the more information used. Therefore, the multi-innovation length will also affect the modeling accuracy of the three-degree-of-freedom gyroscope. In order to analyze the impact of the multi-innovation length on the modeling accuracy, p is set to 1, 3, 5, 7 respectively, and the fractional order remains unchanged (α = 1.2). The identification results are as follows: Figure 4 shown.

[0100] from Figure 4It can be seen that when the multi-new information length p = 1, only the new information at the current moment is used to estimate the three-degree-of-freedom gyroscope parameters, and the evaluation index converges slowly. With the continuous increase of the new information length, when p = 3, the identification speed and accuracy of the model parameters are greatly increased. This is because the multi-new information matrix uses past moment data and current moment data to synchronously identify the model parameters, so the identification result is more accurate. When p = 7, the amount of data used is larger, the evaluation index converges faster, and the three-degree-of-freedom gyroscope modeling accuracy is higher. In summary, the effectiveness of the method proposed in this patent in gyroscope modeling applications is verified.

[0101] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A gyroscope model parameter identification method based on multiple innovations and fractional-order gradients, characterized in that: include: According to the unknown parameters of the three-degree-of-freedom gyroscope system, a three-degree-of-freedom gyroscope system model is constructed; According to the three-degree-of-freedom gyroscope system model, an additional fractional step-descent iteration formula is obtained; Through the multi-innovation theory, the iterative formula of the additional fractional step descent algorithm is expanded with multiple innovations to obtain the multi-innovation additional fractional order gradient descent iterative formula; Obtain the observation data of the three-degree-of-freedom gyroscope, and iteratively solve the multi-information additional fractional-order gradient descent iterative formula based on the observation data to obtain the parameter identification result; The observation data include the input voltage data of the three-degree-of-freedom gyroscope system and the corresponding output attitude angle; The relationship between the input data and output data of the three-degree-of-freedom gyroscope system is reflected through a three-degree-of-freedom gyroscope system model with parameter identification results; The three-degree-of-freedom gyroscope system model is: y(t)=a1y(t-1)+a2y(t-2)+bu(t-1) Where y(t) represents the output of the gyroscope at time t, that is, the attitude angle, u(t) represents the input voltage of the gyroscope at time t, t represents the data time series, a1, a2, b represent the unknown parameters of the gyroscope system model, and the unknown parameters are rewritten as the coefficient matrix θ = [a1, a2, b]; The process of obtaining the additional fractional step-down iteration formula includes: Constructing a criterion function with additional fractional gradients Where y(t) represents the output of the gyroscope at time t, that is, the attitude angle, and the gyroscope system output input matrix Where n represents the maximum value of system sampling, and T is the transpose of the matrix; The additional fractional gradient descent algorithm is expressed as: in, is the estimated value of the coefficient matrix θ of the unknown parameters at time t, is the estimated value of the parameter vector θ; γ and μ are the step size factors of integer and fractional gradients, respectively. represents the gradient, α is the fractional differential; Bringing the criterion function of the additional fractional gradient into the additional fractional gradient descent algorithm, we get: in, is the additional fractional gradient, is the diagonal matrix of the unknown parameters of the three-degree-of-freedom gyroscope, ε represents the offset term; γ and μ are expanded into the following form: μ=1 / r(t), The output error is: The iterative formula of the additional fractional gradient descent algorithm is obtained as follows: in, is the estimated value of the coefficient matrix θ of the unknown parameters at time t, and the output input matrix of the gyroscope Where n represents the maximum sampling value, T is the transpose of the matrix, and e(t) is the output error. and r(t) are the expansions of integer-order gradient and fractional-order gradient step factors, Γ is the gamma function, α is the fractional-order differential, is the diagonal matrix of the unknown parameters of the three-degree-of-freedom gyroscope, and t represents the data time series.

2. The method according to claim 1, characterized in that The output error is: Where y(t) represents the output of the gyroscope at time t.

3. The method according to claim 1, characterized in that The multi-innovation additional fractional-order gradient descent iteration formula is: Where p is the multi-innovation length, E(p,t) is the multi-innovation matrix of the output error e(t), and Φ(p,t) is The multi-innovation matrix, and r(t) are the expansions of integer-order gradient and fractional-order gradient step factors, Γ is the gamma function, α is the fractional-order differential, is the estimated value of the coefficient matrix θ at time t, where t represents the data time series.

4. The method according to claim 3, characterized in that In the multi-innovation additional fractional-order gradient descent iterative formula, the expansion of the integer-order gradient step factor is for:

5. The method according to claim 3, characterized in that: In the multi-innovation additional fractional-order gradient descent iterative formula, the expansion formula r(t) of the fractional-order gradient step factor is:

6. The method according to claim 3, characterized in that After obtaining the parameter identification results, it also includes: The parameter identification results are quantitatively evaluated according to the evaluation index δ, where:

7. The method according to claim 1, characterized in that After obtaining the parameter identification results, the following steps are also included: The parameter identification results are substituted into the three-degree-of-freedom gyroscope system model and the current motor voltage data is obtained. The current motor voltage data is calculated by the three-degree-of-freedom gyroscope system model with the parameter identification results to obtain the current attitude angle of the three-degree-of-freedom gyroscope.

Images