86 results about "Perturbation theory" patented technology

The invention discloses a method and a device for full-wave-shape inversion based on a time domain-step velocity-stress elastic wave equation, wherein the method includes: adopting an adjoint method based on the perturbation theory, and confirming the adjoint equation of the time domain-step velocity-stress elastic wave equation and a corresponding gradient expression, in regard to model parameters, of an objective functional; conforming a forward-propagating wave field according to the time domain-step velocity-stress elastic wave equation, and conforming an inverse time extrapolation adjoint wave field according to the adjoint equation; confirming the gradient, in regard to the model parameters, of the objective functional according to the forward-propagating wave field, the inverse time extrapolation adjoint wave field and the gradient expression; and using a gradient iterative algorithm to carry out multi-scale full-wave-shape inversion. According to the method for the full-wave-shape inversion, before transmitted in an inverse-time mode, a wave field residual error does not need pretreatment, the conversion problems of particle velocity and particle displacement do not need to be considered, and inversion calculation efficiency can be improved.

The invention provides a system and a method for testing microwave complex permittivity of a dielectric material. The system comprises a coaxial-open-type resonant cavity and a coupling quantity adjuster. The method includes the steps: a, recording resonant frequency f0 of the system without any sample loaded in a testing range and a quality factor Q0 of a corresponding frequency point; b, testing thickness d of a to-be-tested sample, and testing to acquire resonant frequency f1 of the system after the sample is loaded in the testing range and a Q1 of a corresponding loaded quality factor; c, utilizing a perturbation theory of the resonant cavity to extract complex permittivity of a to-be-tested material. By the system and the method, high-accuracy testing of the complex permittivity of the microwave dielectric material is realized, and troublesome precise calibration does not need to be performed on a network analyzer, so that testing time is reduced, and requirements, on sample manufacturing, of testing are lowered.

Metasurfaces comprise a two-dimensional periodic array of single-resonator unit cells. Single or multiple dielectric gaps can be introduced into the resonator geometry in a manner suggested by perturbation theory, thereby enabling overlap of the electric and magnetic dipole resonances and directional scattering by satisfying the first Kerker condition. The geometries suggested by perturbation theory can achieve purely dipole resonances for metamaterial applications such as wave-front manipulation with Huygens' metasurfaces.

The invention relates to a parameter acquisition method for a primary loop system of a pressurized water reactor. The model parameter acquisition method comprises the steps of combining the characteristic that the pressurized water reactor is complicated in model structure, provided with nonlinear links, long in stable transition time, great in number of model parameters and variables, mutual coupling and the like, recognizing model parameters by adopting submodules, and checking the parameters by adopting an overall model; selecting input and output variables of each module to perform testing; reducing influences imposed on a recognition effect by noise signals through preprocessing; initializing the variables based on a differential equation of each module and a program setting method, and enabling the model to be stable in initialization; recognizing parameters of each module based on a parameter perturbation theory and an intelligent optimization method; checking the parameters and the model under various conditions by combining the submodules and the overall module; and acquiring nuclear power unit system mathematic model parameters applicable to electric power system analysis. The modules are fine and clear in structure, the model parameters are definite in meaning, the variables required by recognition are easy to acquire, the parameter acquisition method is quick, efficient and accurate, and the practicability is high.

The invention discloses an unmanned aerial vehicle formation keeping control method based on self-adaptive control. The formation keeping control method can be designed for unmanned aerial vehicles according to unmanned aerial vehicle formation and unmanned aerial vehicle queues interfered by unknown outside. Each unmanned aerial vehicle comprises a flight control system and a self-adaptive formation keeping controller. The flight control systems linearize nonlinear models of unmanned aerial vehicles based on a small perturbation theory, and a reference model of a self-adaptive control systemis established according to the relative degree of required control amount. Self-adaptive control law online-updating controller parameters are designed so that the unmanned aerial vehicles can more accurately trace given instructions. The self-adaptive formation keeping controllers converge errors to zero according to formation flight separation distances between a leading plane and wing planes,and leading plane growth speed, heading and height instructions are designed for the self-adaptive formation keeping controllers so that the wing planes can be more accurately trace a flight path of the leading plane. The good tracing property and stability of the whole closed-loop system are ensured, so that the system has certain robust performance.

The invention discloses a distributed fiber disturbance sensor based on a Sagnac interferometer. A Sagnac interferometer is used for coupling an arm, synchronously a delayed fiber ring is added, namely a delayed fiber ring is superposed in a single Sagnac interferometer to form two Sagnac interferometers with different length; the time division multiplexing of the two Sagnac interferometers with different length is realized by the propagation of optical pulses in the interferometer; and the positions of disturbing points are calculated to realize the distributed sensing of the disturbance according to the amplitude of output signals of two Sagnac interferometers. The sensor has the advantages of low cost, simple structure and good stability.

The invention discloses a method for calculating equivalent electromagnetic parameters of a wave absorbing honeycomb structure. The method specifically comprises the following steps: 1. deriving a strong perturbation theory framework; 2. substituting the electromagnetic parameters and structural parameters of the wave absorbing honeycomb structure into the strong perturbation theory framework in step 1 to obtain a substantially closed-form expression of effective permittivity tensor (shown in the description) and equivalent permeability tensor ( shown in the description) of the wave absorbing honeycomb structure, wherein the expression consists of an initial value part and a dispersion characteristic function; 3. expanding the initial value part obtained in step 2 , and simplifying a dispersion characteristic function expression to obtain a final closed-form expression for calculating the equivalent electromagnetic parameters of the wave absorbing honeycomb structure. Compared with the traditional calculation method, the method provided by the invention can reflect the dispersion characteristic of the equivalent electromagnetic parameters, and can be used for calculating the equivalent electromagnetic parameters of the wave absorbing honeycomb structure more accurately within a relatively wide frequency band.

The invention provides a system and method of testing complex dielectric constant of a material based on a gradient coaxial resonator. The system comprises the gradient coaxial resonator and a coupling device. The method comprises the steps: 1) testing and recording resonant frequency f0 and quality factor Q0 in a corresponding cavity working mode when no sample is loaded; 2) measuring diameter DSand thickness dS of a sample under test, placing the sample in a sample area, and testing and recording resonant frequency fS and quality factor QS in the corresponding cavity working mode when the sample is loaded; 3) using resonator perturbation theory to calculate complex dielectric constant of the material under test. The system and method have the advantages that high-precision testing of complex dielectric constant at normal temperature is achieved for a microwave dielectric material, required cavity size and sample size for low frequency testing can be reduced, a sealed-bottom tube clamp can also be used to test the complex dielectric constant of liquid and powdery materials.

The invention discloses a dielectric filter convenient for adjusting frequency and coupling bandwidth, and the problems of the prior art such as inability of facilitating actual operation, complicated debugging technology, and low efficiency are solved. The dielectric filter comprises a filter body, which is provided with a radio frequency connector. The filter body comprises a plurality of dielectric single cavities, which all made of hard ceramic dielectric materials, and a plurality of coupling windows, and the adjacent dielectric single cavities are connected together by the coupling window, and in addition, the dielectric single cavities and the coupling windows are provided with blind holes. According to a resonant cavity perturbation theory, by changing the sizes of the blind holes of the dielectric single cavities, the frequencies of the dielectric single cavities are adjusted; and by changing the sizes of the blind holes of the coupling windows, coupling quantities among the dielectric single cavities are adjusted. The dielectric filter has advantages of high stability, low loss, light weight, low costs, small size, simple assembly, and ability of facilitating tuning of the same plane.

The invention relates to a multi-group section perturbation method for uncertainty analysis of reactor physics calculation. The multi-group section perturbation method comprises the following steps: (1), on the basis of ENDF / B, making a multi-group section database and a point-by-point section database at different temperatures by using a nuclear database section processing program NJOY, and making the point-by-point section database in a resonant reaction channel at a resonant energy section into an ultra-fine-group database according to the equal rib width; (2), perturbing the point-by-point section database in the energy section corresponding to a certain energy group in a certain reaction channel so as to obtain a perturbed point-by-point section database; (3), strictly transferring perturbation of the point-by-point section database into the multi-group section database by using a linear and nonlinear perturbation transferring method; and (4), reconstructing by adopting a reaction channel section self-consistency principle to obtain a perturbed multi-group section database. According to the invention, the section of a basic reaction channel can be finely sampled; approximate treatment in the multi-group section perturbation process can also be reduced; and thus, a precise multi-group section sample can be obtained.

The invention relates to a flexible mechanical arm sliding-mode control designing method based on a singular perturbation theory. The method includes four steps that (1) dynamics modeling of a flexible mechanical arm is performed; (2) partial differential equation (PDE) model decomposition is performed; (3) a control law is designed; (4) designing is finished. According to the flexible mechanical arm sliding-mode control designing method based on the singular perturbation theory, firstly, a Hamilton principle is utilized, and a PDE model of a whole system is determined; the original PDE model is decomposed into a concentrating slow subsystem which represents whole rigidity movement and a quick subsystem which describes system vibration by means of the singular perturbation theory; then a sliding-mode control law is designed by respectively aiming at the quick and slow subsystems, the designed control law is subjected to convergence analysis by the aid of a lyapunov function, and reasonability and stability of the control law are verified. Finally, a compound control law is obtained according to the singular perturbation theory.

The invention relates to the technical field of solution parameter measurement and relates to a system for measuring a solution concentration by using a perturbation method. The system comprises a microwave resonant cavity sensor, a wave detector, a voltage-controlled oscillator, a frequency tracking module, a frequency measuring module and a main control processing module, wherein frequency modulated signals generated by the voltage-controlled oscillator under the control of the main control processing module are divided into two ways; one way is mixed with local oscillator signals so as to generate difference frequency signals; the other way is led into a waveguide and is transmitted and coupled by the waveguide to be coupled into a resonant cavity; reflecting signal inside the resonant cavity enters the wave detector through a circulator; modulating signals output from the wave detector are transmitted into the frequency tracking module; the frequency tracking module comprises an amplitude discriminating module and a phase discriminating module; the main control processing module is used for controlling the carrier frequency of the voltage-controlled oscillator; the output of the frequency measuring module is accessed to the main control processing module; and the main control processing module obtains the corresponding relationship between a frequency offset and a solution concentration. The system can realize accurate and real-time measurement to the solution concentration.

The invention discloses an optical fiber distributed disturbance sensor, and a method, by which the disturbance sensor can achieve disturbance positioning. The method is characterized in that light path output signals from an interferometer are divided into three equal paths of light, pass through analyzers with polarization angle differences of 0 DEG, 60 DEG and minus 60 DEG respectively, enter a photo detector and are converted to electrical signals therein, are subjected to the square summing calculation after being conditioned by filtered signals and amplified signals, get rid of the DC amount by filtration, and are taken as the final interference output signals for related computation so that disturbance positioning can be carried out. The method can ensure the final interference signals always remain in a certain amplitude range and available, and the possibility of the signals being zero is zero. The invention solves the problem in the prior dual interferometer type distributed disturbance sensor that the sensor doesn't work when the amplitude of the light path output signals of the interferometer changes to zero because of the random variation of the polarization state of light wave.

The method optimizes the development of a heterogeneous porous medium within the context of enhanced recovery of a fluid in place, by fast determination of the position of the front separating a sweeping fluid and the fluid in places having application for development of oil reservoirs or gas. The velocity field in the neighbourhood of the front is determined only once by means of a flow simulator. Then a relation describing the position of the front in the heterogeneous medium is defined by freedom from the viscous coupling by means of the perturbation theory, and by accounting for the velocity fluctuations in the front advance direction and the velocity fluctuations in the direction perpendicular to the front advance direction. Finally, for each time interval, the position of the front is reconstructed by means of a fast Fourier transform and injection of the sweeping fluid is optimized according to the position of said front.

The invention discloses a broadband low profile microstrip antenna suitable for dual mode operation in a microwave millimeter wave frequency band. The antenna is a rectangular patch loaded with a specific transverse slit and a longitudinal slit. The antenna is coupled and excited by a substrate integrated waveguide feeding slot. The antenna has advantages of simple structure, low profile, easy processing, wide bandwidth, low cross-polarization in a design frequency band and stable radiation pattern. Influence of an adhesion layer between an antenna dielectric layer and a feeding network can beconsidered in design by using a cavity model and a perturbation theory, to improve accuracy of calculating theoretical size of the antenna.

The method obtains a correlation linear matrix which is convenient for experimental measurement by utilizing perturbation theory and approximate method to establish simple matrix algorithm in depending upon relation of FRA gain spectrum variation amount and multiwavelength pumping light power regulation amount based on FRA actual operation state in engineering system of wavelength division multiplexing. To calculate out the corresponding regulation value of pumping light power according to the differential value of gain spectrum at monitored apparent gain spectrum off-flag, the on-line dynamic feedback regulation and control can be achieved for FRA power and gain spectrum in large scale of dynamic scope.

The invention relates to a prediction method of a multistage axial-flow compressor stall margin. The prediction method comprises the following steps: according to a situation of the rotating stall inception of an axial-flow compressor, adopting a small perturbation theory to establish a three-dimensional compressible Euler equation which describes a flow field; applying harmonic decomposition and a dispersion relation to establish a boundary condition on the hub and the leaf opex of each drainage basin; adopting a three-dimensional semi-actuator model to carry out modelling on a stator and a rotor, and adopting a mode matching technology, the conservation law and the representation condition of compressor loss characteristics on an interface to obtain a characteristic value problem which solves a linearized flow field; and solving the characteristic value problem to obtain the characteristic disturbance frequency of a compression system, and judging system stability through the characteristic disturbance frequency, wherein a judgement standard is that the disturbance frequency [Omega] is a complex number, [Omega] is [Omega]R+i[Omega]I, disturbance is attenuated along with time evolution when the imaginary part [Omega]I of the frequency is greater than 0, the system is stable, otherwise, [Omega]I is less than 0, the disturbance is amplified along with time, and the system loses stability. The prediction method can be used for predicting the rotating stall inception of the multistage axial-flow compressor.

The invention discloses a power system vibration mode matching method based on a matrix perturbation theory. The method comprises the following steps: first, calculating to obtain a characteristic value and a characteristic vector corresponding to an initial system mode before parameter change by applying characteristic value analysis, and then calculating approximate values corresponding to the system mode of the characteristic value and the characteristic vector after the parameters change by utilizing the matrix perturbation theory; then, determining the corresponding relationship between the approximate values of the characteristic value and the characteristic vector before and after the parameters change; later on, finding a mode which is closest to the approximate values from exact values of the system mode after the parameters change, establishing the corresponding relationship between the exact values and the approximate values of the system mode after the parameters change; finally, establishing the matching and corresponding relationship between the system modes before and after the parameters change according to a contact link between the system modes after and before the approximate values of the system modes serving as parameters change. The method has the beneficial effects that the principle is simple and clear, the discrimination is fine and the criteria are complete.

The invention relates to a glide trajectory error propagation analysis method based on the perturbation theory. The method comprises the following steps: establishing a pole-changing coordinate system by adopting a glide trajectory reentry longitudinal plane as a pole-changing equatorial plane; establishing an aircraft kinetic model in the pole-changing coordinate system and a motion perturbation equation; solving a state-transition matrix to obtain the analytic solution of the perturbation equation; and establishing an error propagation module in a common coordinate system based on the coordinate change. The glide trajectory error propagation analysis method provided by the method strives for filling up the blank of a glide trajectory perturbation factor influence mechanism analysis method of a hypersonic velocity glide aircraft, and lays a foundation and a method support for deepening the error propagation mechanism acquaintance and establishing a trajectory rapid correction method.

The invention discloses a reliability analysis method for a heat transfer system containing fuzzy parameters. The method comprises the following steps that: carrying out the finite element modeling of a heat transfer system; utilizing a fuzzy variable to represent uncertain input parameters, and establishing the fuzzy finite element equation of the heat transfer system; selecting a cut set level, and converting the fuzzy variable into an interval variable so as to obtain one group of interval finite element equations; utilizing a perturbation theory to solve the interval finite element equations to obtain the upper and lower bounds of interval temperature response; according to the temperature response, establishing an ultimate state function which represents system reliability, and calculating the upper and lower bounds of the ultimate state function; utilizing an interval sorting method to process the ultimate state function to obtain an interval reliability index under each cut set level; and carrying out integral computation on the interval reliability index under the cut set level, and finally, obtaining the fuzzy reliability index of the heat transfer system. On a premise that calculation efficiency is guaranteed, by use of the method, the fuzzy reliability calculation accuracy of the heat transfer system can be effectively improved, which can not be realized by general commercial software.

The invention relates to an analytical guidance method for a standard control miss distance of a terminal guidance section. The analytical guidance method comprises the following steps: firstly, modeling the terminal guidance section; secondly, dividing a standard control trajectory at the terminal guidance section into a zero-order standard control trajectory and a first-order standard control trajectory according to a canonical perturbation theory; thirdly, performing analytic solution on a zero order item of the standard control trajectory at the terminal guidance section; fourthly, performing analytic solution on a first order item of the standard control trajectory at the terminal guidance section; and fifthly, acquiring a complete analytical solution of the standard control trajectory, and calculating a guidance command. The analytical guidance method disclosed by the invention has the advantages that firstly, an idea of taking a zero attack angle as standard control over the terminal guidance section of a homing missile is put forward, and a motion equation of the standard control trajectory is simplified; in addition, an attack angle required by guided correction is enabled to be located near zero, and speed loss brought by the guided correction is reduced; secondly, analytic solution is performed on a longitudinal trajectory at the terminal guidance section by adopting a canonical perturbation method, and high-precision analytical solutions of firing range, height, speed and trajectory inclination angle are obtained; and thirdly, a guidance method based on a generalized standard control miss distance is provided, and normal acceleration of the missile is greatly reduced; and meanwhile, the terminal attack angle is enabled to be converged to be zero.

The invention discloses a robust self-adaptive sliding-mode control method for a flexible-hinge space station manipulator. The robust self-adaptive sliding-mode control method comprises the followingsteps: first, through the utilization of Lagrangian methods of the second kind and through the combination with the system momentum and momentum moment conservation relation, analyzing and establishing a system dynamics model of a flexible-hinge space station manipulator system, wherein the carrier position and attitude are both uncontrollable; next, for the actual situation that the flexibility of each joint hinge is relatively high in the actual application of the space station manipulator, exporting a singular perturbation mathematical model applicable to the control system design through the introduction of a joint flexibility compensation controller and through the combination with double time scale decomposition of singular perturbation theory; and then, through the utilization of the singular perturbation mathematical model, decomposing the flexible-hinge space station manipulator system into a fast subsystem and a slow subsystem which are independent of each other, designing the robust self-adaptive sliding-mode control for the slow subsystem, and designing a moment differential feedback controller for the fast subsystem. Consequently, the control purposes of not only eliminating the negative impact of the flexibility of a flexible hinge on the positioning precision and the stability of the space station manipulator but also effectively overcoming the buffeting defect in the conventional sliding-mode control can be fulfilled.

The invention provides a finite element model correction method based on the perturbation method for a complex model under uncertainty, comprising: deducing an iteration form for average and covariance matrixes for under-correction parameters of the complex model; determining complex model correction target average and covariance matrixes; determining initial estimated values of the under-correction parameters of the complex model; calculating a sensitivity matrix and modal frequencies for the under-correction parameters of the complex model through finite element analysis; reading finite element calculation results of the complex model, and calculating an intermediate variable conversion matrix and the covariance matrix; correcting an average and covariance of the under-correction parameters of the complex model to obtain updated parameters; performing cyclic iteration to carry out parameter correction. File reading-writing and data transmission channels are established based on the commercial mathematical software MATLAB and the finite element simulation software NASTRAN; the method is suitable for solving model correction problems where both system parameters of a complex modeland test data present uncertainty, and corrected parameters have high average precision.

The invention discloses a free surface shape reconstruction method for a nonzero-digit TWI system. The method puts forward a hysterisis error reverse elimination algorithm based on analysis of a testing optical path of the nonzero-digit TWI system through the perturbation theory and Hamilton characteristic functions. Meanwhile, the virtual wave calculation and generation technology is applied to the nonzero-digit TWI system, so that the problem that how to inverse the surface shape of a part to be tested through a collected array interferogram in a high-precision mode is solved. Besides, an iterative algorithm is put forward and used for the final solution of the surface shape in the solution process of the actual surface shape of the part to be tested.

The present invention provides a non-equal phase front correction method of a material complex permittivity quasi-optical cavity method wideband test. The sample wideband complex permittivity accuracy test can be realized. Gaussian beam electromagnetic field phase distribution in a quasi-optical cavity is analyzed, and an actual phase distribution function at the upper surface of a sample is obtained according to the upper surface of a sample to be tested, namely the matching relation of the air and a waist radius at a medium area interface. The perturbation theory is employed to solve the stored energy at the gap of the surface plane and the wavefront spherical surface so as to obtain frequency shift caused by phase mismatching of the sample surface and the wavefront. The non-equal phase surface at the upper surface of the sample is corrected through combination of a preset format; the influence of non-equal phase surface errors caused by thickness of the sample in the quasi-optical cavity method wideband test is corrected, the wideband test of the material complex permittivity through adoption of the quasi-optical cavity method can be effectively performed, and the precision of the multimode wideband test of the quasi-optical cavity method can be improved.

The invention discloses a phase optical time-domain reflectometer and optical fiber double-pulse difference based perturbation detector, and belongs to the field of distributed optical fiber sensing.The perturbation detector comprises an ECL laser, couplers, polarization controllers, acousto-optic modulators, a signal generator, circulators, symmetrical surface core to-be-detected optical fiber,balance detectors, a differential circuit, a low-pass filter, a high-frequency data acquisition card and a computer. Certain pulse width difference is introduced under the pumping of two beams of pulses by using a symmetrical double-core optical fiber, and a problem of the contradiction between the detection sensitivity and the space resolution of the system can be solved to a certain extent through differential processing. Meanwhile, a problem of frequency instability or frequency drift of a light source can also be solved by using a differential detection method so as to acquire a miniaturized optical time-domain reflectometer which is high in detection sensitivity, high in space resolution and good in stability; and the problem of the contradiction between the detection sensitivity andthe space resolution of the original phase sensitive optical time-domain reflectometer is solved, and the space resolution can be improved while high measurement sensitivity is ensured.

The invention discloses a quick fuzzy sound pressure solving method based on a high-order perturbation theory. The method comprises the following steps that finite element modeling on a structural vibration sound radiation problem is performed; a fuzzy finite element equation of the sound radiation problem is built by considering fuzzy uncertain variables of the model; a cut set level is selected, and the fuzzy variables are converted into interval variables through cut set calculation; the interval variables with the uncertainty exceeding 5% are decomposed into multiple subintervals through a subinterval decomposing technique, and then a set of subinterval finite element equations are obtained; all the subinterval finite element equations are solved on the basis of the high-order perturbation theory, and an interval change range of the sound pressure is obtained; all the sound pressure intervals at the cut set level are recombined to obtain a subordinating degree function of the fuzzy sound pressure. According to the method, the structural vibration sound radiation problem containing the fuzzy uncertain variables can be systematically solved, the calculating precision of a perturbation method is further improved while the calculating efficiency is guaranteed, and the advantages cannot be achieved by common commercial software.

The invention discloses an aircraft uncertain aerodynamic load upper and lower boundary assessment method based on the high-order interval perturbation theory. The method includes the steps that in consideration of uncertainty in the manufacturing and flying processes of an aircraft, uncertain parameters are quantitatively represented with interval vectors first, a subsonic velocity steady aerodynamic force model including the interval uncertain parameters is established through the vortex-lattice method for a two-dimensional rigid wing, a calculation expression of the lift coefficient can be obtained through calculation based on the Taylor series expansion and high-order perturbation theory, the mid-value and radius of a lift coefficient response interval can be obtained based on the Neumann series expansion and high-order perturbation theory, and the upper boundary and lower boundary of the lift coefficient can be obtained based on the interval computation rule. By means of the method, the boundaries of an uncertain aerodynamic load response can be obtained, and objective and effective data is provided for structural aerodynamic configuration design and flying state control of the aircraft.

The invention discloses a distributed fiber disturbance sensor of a Sagnac interferometer and a disturbance positioning method thereof, comprising the following steps, using a Sagnac interferometer to couple an arm, synchronously adding a delayed fiber ring, namely superposing a delayed fiber ring in a single Sagnac interferometer to form two Sagnac interferometers with different length; realizing the time division multiplexing of the two Sagnac interferometers with different length by the propagation of optical pulses in the interferometer; and calculating the positions of disturbing points to realize the distributed sensing of the disturbance according to the amplitude of output signals of two Sagnac interferometers. The sensor has the advantages of low cost, simple structure and good stability.

The invention provides a missile free section ballistic deviation analysis and prediction method considering J2 influence, comprising the steps of carrying out decomposition of J2 gravitation vectorsand derivation of a free section ballistic deviation analysis and prediction model, and obtaining expressions of perturbation forces in different coordinate axis directions through decomposition of the J2 gravitation vectors; and according to a state space perturbation theory, substituting the decomposed J2 gravitational vector expressions into an integral solution expression of the trajectory deviation of the free flight section of the missile, and performing integration to obtain a complete analytical expression of each deviation. Compared with other methods in the prior art, the method provided by the invention has the advantages that the calculation time consumption of the method is 10-5s, the calculation error of the position under any shot direction is smaller than 50 meters, the calculation result is represented in an inertial system, and the method can directly participate in missile-borne guidance calculation without extra coordinate conversion.