47 results about "Linearization error" patented technology

The invention relates to an ephemeris broadcast and time synchronization method for Beidou pseudolite deformation monitoring, and belongs to the technical field of satellite positioning. The method comprises the following steps: constructing a linearization error equation based on a pseudo-range observation value, and solving a clock error correction amount in combination with a robust iterative algorithm to improve the time synchronization precision; analyzing ephemeris parameters of the Beidou GEO satellite, calculating earth-fixed coordinates of the Beidou GEO satellite, and rotating and adapting the earth-fixed coordinates; establishing an affine transformation relationship between the pseudo-satellite coordinates and GEO ephemeris, and generating optimized pseudo-satellite ephemeris data; and a time synchronization protocol is designed, and clock skew is compensated through bidirectional timestamp interaction of the main base station and the pseudo satellite. According to the method, nanosecond synchronization of the pseudo-satellite and the real satellite is realized, the ephemeris parameter redundancy problem of the static pseudo-satellite is optimized, multi-system cooperative work is supported, and the deformation monitoring reliability and precision under the complex terrain are remarkably improved.

The present invention discloses a visual inertial odometry method and system based on transformation error state, and relates to the technical field of visual inertial odometry optimization. The technical points of the present invention include: estimating posture information using a transformation extended Kalman filter, including: establishing a system continuous-time motion model and measurement equation based on real-time acquired visual and IMU data; establishing a linearized error state system based on the system continuous-time motion model and measurement equation; designing a linear time-varying transformation, and using the linear time-varying transformation to transform the linearized error state system into an error state system in which the system state is independent of the system's unobservable subspace; performing state estimation based on the transformed linearized error state system to obtain estimated posture information. The present invention proposes a transformation-based method to solve the inconsistency problem in VINS, alleviates the observability mismatch problem, and ensures that the visual inertial odometry using the transformation extended Kalman filter has consistent estimation results.

The invention relates to the technical field of wireless and terminals, and particularly provides a positioning method and device, electronic equipment and a computer program product. The method comprises the following steps: acquiring a first ranging signal of a first positioning source and a second ranging signal of a second positioning source corresponding to a to-be-positioned target; the observation noise is determined based on the first ranging signal, the second ranging signal and a preset random model, and the preset random model is determined at least based on a first signal characteristic of the first observation noise and a second signal characteristic of the second observation noise; determining a positioning combination result based on speed constraint and observation noise; and performing nonlinear processing on the positioning combination result, and determining a final positioning result of the to-be-positioned target. According to the invention, the random model is refined according to the characteristics of different positioning sources, the continuous smooth positioning of the transition scene is achieved, and the linearization error is weakened, so that the availability, smoothness and accuracy of the positioning result are improved.

The invention discloses an extended Kalman filtering method based on dynamic self-adaption residual error enhancement, and relates to the field of optimization algorithm error accumulation methods, and the extended Kalman filtering method based on dynamic self-adaption residual error enhancement significantly improves the sensing precision and reliability of a system through cooperative processing of multi-source heterogeneous sensing information, and improves the accuracy and reliability of the system. A sliding window covariance estimator is introduced, time-varying statistical characteristics of IMU angular velocity noise and GPR echo noise are identified in real time, a dual-threshold residual monitoring mechanism is designed, Jacobian matrix update frequency is dynamically adjusted to balance linearization errors and calculation loads, a robust correction term based on a Mahalanobis distance is established, and the robustness of the algorithm is improved. And abnormal observation interference caused by intermittent failure of the sensor is effectively inhibited.

The invention relates to the technical field of computers, and discloses an industrial object-oriented Gaussian approximation filtering method for a nonlinear system. Mathematical modeling is carried out on a physical system to be subjected to state estimation, and a nonlinear state space model corresponding to the physical system is obtained; matching the first Gaussian distribution of the system state at the time t to a given distribution through a moment matching operation based on the non-linear state-space model to determine a predictive estimate and a predictive estimate error of the system state at the time t; acquiring a system observation value at the moment t; iteratively updating the optimal estimation and the optimal estimation error of the system state at the moment t based on a natural gradient descent method and a Fisher information matrix associated with the second Gaussian distribution of the system state at the moment t, and obtaining the optimal estimation and the optimal estimation error at the moment t until an iteration stop condition is met; linearization errors can be avoided, and more accurate system state estimation of a nonlinear system is provided.

The invention relates to the technical field of digital filters, and discloses a quantization sensing wide linear minimum error mode adaptive filter, which performs non-uniform low-bit quantization on an input signal and an expected signal by using a quantization parameter to obtain a corresponding quantization value; constructing a linear factor based on the quantization parameter; based on the non-roundness of the input signal, constructing a normalized correlation matrix of the input signal and the linearized error signal, and constructing a compensation matrix in combination with a linear factor; obtaining input signal quantized values at a current moment and a historical moment, constructing an augmented input signal vector, calculating a product of the augmented input signal vector and the compensation matrix, and constructing a corrected input vector; performing wide linear filtering on the corrected input vector to obtain an output signal, and calculating an error signal in combination with an expected signal quantized value; and updating the weight vector at the next moment by using the corrected input vector and the error signal. According to the invention, by introducing a non-uniform low-bit quantization and deviation compensation mechanism, the cost and energy consumption of the analog-to-digital converter are remarkably reduced, and a relatively low steady-state error is kept.

The invention belongs to an intelligent driving control technology of coal mining equipment, and provides a flux-weakening control strategy of a mining permanent magnet driving motor based on dynamic parameter identification in order to solve the problem that internal flux linkage parameters cannot be accurately observed after the motor enters a flux-weakening area in the operation process of the motor. The unscented Kalman filter is introduced to construct the permanent magnet flux linkage observer when the driving motor works in the weak magnetic area, the random distribution of a nonlinear system is accurately estimated, the linearization error of a traditional Kalman filter is avoided, more accurate state estimation is obtained, meanwhile, the self-adaptive technology is utilized, and the reliability of the system is improved. The observation noise of the permanent magnet flux linkage observer is identified and corrected, and the influence of interference on system operation is effectively suppressed.

The invention relates to an optical satellite remote sensing image autonomous accurate positioning method and device, and the method comprises the steps: obtaining two pieces of image data of a target region and imaging data corresponding to the two pieces of image data at different observation angles through a target ground load of a target satellite, respectively constructing an imaging equation corresponding to each piece of image data according to the imaging data; constructing an error equation based on the imaging equation, the mounting angle of the target ground load and the latitude and longitude information of the homonymy point between the two image data; and linearizing the error equation to generate a linearized error equation, solving the linearized error equation to obtain a target homonymy point latitude and longitude and a target load mounting angle corresponding to the target satellite, and performing autonomous positioning of the target satellite according to the target homonymy point latitude and longitude and the target load mounting angle. Therefore, the problems that a traditional calibration technology based on ground reference data highly depends on the precision and timeliness of an external reference image, the geometric calibration precision is greatly influenced and the like are solved.

The invention discloses a system inertia and primary frequency modulation coefficient estimation method and device, equipment and a medium. A Sigma point set is generated according to posterior state estimation including inertia, primary frequency modulation coefficient and frequency deviation at the last moment and covariance of the posterior state estimation; a prediction state and statistics thereof are obtained through nonlinear state transfer function transformation; obtaining a predicted measurement value and a statistic thereof through measurement function transformation, and calculating a cross covariance of a state and measurement; the prediction state is updated by using the actual frequency deviation and the Kalman gain calculated based on the measurement covariance and the cross covariance, and the current optimal state estimation is obtained; and finally, inertia and a primary frequency modulation coefficient are extracted from state estimation. According to the method, real-time, joint and online accurate identification of the inertia and the primary frequency modulation coefficient is realized, the problems of linearization error and parameter coupling neglect of a traditional method are effectively solved, the robustness and accuracy of estimation are remarkably improved, and reliable state sensing support is provided for stable analysis of the frequency of a power system.

The invention discloses a recursive augmented least square-based dynamic linearization error-assisted model-free adaptive control method and system, and a storage medium, relates to the field of control methods, and aims to solve the problem that the dynamic response performance of a controlled system cannot be effectively improved by an existing model-free adaptive control method. And dynamic linearization errors in a model-free adaptive control process cannot be effectively utilized to suppress disturbance. According to the method, an expansion full-format dynamic linearization data model of a controlled system is established by considering a dynamic linearization error in a control process, a controlled object is compensated based on the expansion full-format dynamic linearization data model, and an expansion pseudo gradient of the controlled system is estimated based on a recursive augmented least square method; and obtaining a model-free adaptive controller based on the expanded full-format dynamic linearization data model at the moment k based on the improved criterion function, inputting the compensated control input signal of the controlled object into the controlled object, calculating the dynamic linearization error difference of the system, and carrying out model-free adaptive control.

The invention relates to the field of signal processing, and discloses a virtual phase line boundary folding processing method and system for a multi-baseline phase interferometer, and the method comprises the following steps: carrying out the division of sub-interferometers, and generating an initial candidate modulus pair set based on the physical constraint of the system; performing boundary folding detection on the measurement phase pair, and judging whether the measurement phase pair falls into a boundary dangerous area; if a folding risk is detected, generating a corresponding virtual modulus pair, and expanding the initial candidate modulus pair set by using the virtual modulus pair to form an expanded candidate set; based on a minimum linearization error criterion, selecting an optimal modulus pair which is most matched with the measurement phase pair from the extended candidate set; and calculating a global fuzzy number vector step by step, and finally estimating a signal arrival angle. According to the method, the boundary folding effect is actively identified and compensated, so that the robustness and accuracy of angle measurement under the condition of low signal-to-noise ratio are remarkably improved.

The invention discloses a shape error correction method for free-form surface machining, which comprises the following steps of: analyzing the path characteristics of an original cutter through a linearization error theory, establishing a slow cutter servo turning cutter path simulation model, and describing the cutting path of the cutter by adopting an Archimedes spiral. And on the basis, cutter radius compensation is carried out, cutter contact data after compensation are obtained, and the accuracy of a cutting track is ensured. Then, obtaining point clouds of the free-form surface to be processed, and obtaining source point clouds and target point clouds respectively; in order to realize reliable matching between the source point cloud and the target point cloud, point cloud coarse registration is used for coarse registration, and then point cloud fine registration is used for fine registration. And finally, calculating a shape error through a least square method, and applying the shape error to correction so as to obtain a processed free-form surface type.

The application relates to the field of signal processing and discloses a multi-baseline phase interferometer virtual phase line boundary folding processing method and system. The method comprises the following steps: performing sub-interferometer division, and generating an initial candidate modulus pair set based on system physical constraints; performing boundary folding detection on a measured phase pair, and judging whether the measured phase pair falls into a boundary dangerous area; if folding risk is detected, corresponding virtual modulus pairs are generated, the initial candidate modulus pair set is expanded by using the virtual modulus pairs, and an expanded candidate set is formed; based on a minimum linearization error criterion, an optimal modulus pair most matched with the measured phase pair is selected from the expanded candidate set; a global ambiguity vector is solved step by step, and finally, a signal angle of arrival is estimated. Through active identification and compensation of boundary folding effects, the robustness and accuracy of angle measurement under low signal-to-noise ratio conditions are significantly improved.

The present invention discloses a single-segment linearization modeling method for energy flow of an electric-gas interconnected system, which relates to the technical field of power system optimization, and includes the following steps: constructing a single-segment linearization energy flow model based on the state space transformation theory according to the correlation between the linearization error of the energy flow model and the variable state space; constructing a single-segment linearization model of pipeline flow and pipeline storage of a natural gas system with the gas pressure amplitude power function as the state space variable; constructing a state space variable optimization selection model with the goal of minimizing the global maximum error, and proposing a split solution strategy for the state space variable optimization selection model; establishing a system optimal energy flow model for the electric-gas interconnected system; and simulating and verifying the system optimal energy flow model. The present invention provides a basic model with high accuracy and low representation complexity for the optimization decision of the electric-gas interconnected system through transformation state space selection and single-segment linear processing of nonlinear natural gas model, thereby improving the calculation efficiency of optimization decision.

The invention belongs to a battery parameter estimation method, and provides a lithium battery SOC estimation method and a related device for solving the technical problems that when a model-based method is adopted to estimate the SOC of a lithium battery, in an environment with high nonlinear intensity, the linearization error is easy to increase, and the estimation precision is obviously reduced or even diverged. And performing equivalent circuit modeling on the to-be-estimated lithium battery to obtain an equivalent circuit model. And establishing a voltage state equation and a transfer function based on the electrical characteristic parameters of the elements in the equivalent circuit model. And carrying out HPPC test on the lithium battery to be estimated, carrying out parameter identification by adopting a recursive least square method with a forgetting factor, and determining electrical characteristic parameter values of elements in the equivalent circuit model. And in combination with electrical characteristic parameter values of elements in the equivalent circuit model, estimating the SOC of the lithium battery by adopting an EKPF algorithm.

This invention discloses a multi-sensor fusion positioning method for complex port environments, comprising: S1, establishing a multi-sensor coordinate system; S2, extracting constraints in environments with GPS signals and rich structure; S3, extracting constraints in environments without GPS signals but with rich structure; S4, extracting constraints in environments without GPS signals and with degraded structure; and S5, establishing a nonlinear fusion positioning framework for different sensors, fusing all nonlinear constraints obtained from different sensors in different environments. This method achieves seamless vehicle positioning under changing scene features and environments, effectively reduces linearization errors, and solves the positioning problem in degraded structure environments.

This invention discloses a collaborative localization and obstacle avoidance control system and method for unmanned aerial vehicle (UAV) swarms. This method uses a first comprehensive cost function to issue swarm change commands only when the accuracy improvement from configuration changes significantly outweighs the cost of flight maneuvers, effectively filtering out the ping-pong effect caused by frequent swarm changes. Through coarse-to-fine hierarchical localization processing, the method utilizes FM coarse localization solutions to resolve the TDOA observation equations in the far-field high-altitude region. GDOP The technical challenge of regional divergence is addressed by using a "hot start" mechanism to map the initial value of GN to EKF in real time, thus avoiding the accuracy collapse caused by the accumulation of linearization errors in the cold start phase of traditional filtering algorithms. This invention overcomes the limitation of decoupling the logic of "obstacle avoidance" and "positioning accuracy maintenance." Within the rolling optimization framework of model predictive control, it explicitly embeds rigid geometric constraints based on the Laplace matrix, enabling the cluster to replace disordered drift with elastic compression when performing obstacle avoidance actions.

The invention discloses a multi-robot cooperative positioning method and system based on UWB relative distance measurement, relates to the technical field of multi-robot cooperative positioning, and aims to solve the problem of cluster cooperative autonomous navigation of a multi-robot system in an environment that external navigation equipment is unavailable or weak communication exists. According to the technical key points, a state model of a multi-robot cooperative positioning problem and a UWB relative measurement model are established, and a linearization error state system is deduced; the reason of inconsistency of standard extended Kalman filtering in cooperative positioning is analyzed, and the essence of the standard extended Kalman filtering is revealed to be from considerable asynchronization between an original nonlinear system and a linearization error state system of an estimator. The invention designs a method based on linear time-varying transformation, constructs a KD-EKF algorithm with a time-invariant and unobservable subspace, and performs Monte Carlo contrast simulation to verify that the KD-EKF has higher positioning precision and better consistency compared with a standard EKF method and an FEJ-EKF method. A multi-robot system experimental platform based on the Tucker ground robot is developed, and experimental verification is carried out on the designed KD-CL algorithm. Experimental results verify the superiority and effectiveness of the proposed algorithm.

The invention provides a method and system for calculating a Cole-Cole model by using a rational fraction approximation method, a medium and a product, and relates to the field of electric digital data processing. An error expression between a Cole-Cole target model and a rational fraction approximation function before solving is multiplied by a denominator polynomial of the approximation function, and a denominator coefficient to be solved is moved to a linear expression from a denominator position, so that a linearized error function is obtained. Then, on the basis of the linearization error, discrete sampling points are selected in the full frequency band, and a target function with the purpose of minimizing the sum of errors is established. A nonlinear problem which needs to be solved through complex iteration originally is converted into an optimization problem which can be solved in a one-time and deterministic mode through a standard linear solving algorithm. The high efficiency of the solving process and the stability of the result are ensured, the effect and the accuracy of the induced polarization effect are improved, and meanwhile the cost is reduced.

The invention relates to the technical field of mobile robots, and discloses an efficient laser radar inertial positioning method, which comprises the following steps: establishing a kinetic model based on detection data of an inertial sensing unit, and realizing forward evolution of pose estimation; motion compensation is carried out on the radar point cloud obtained through laser radar scanning through reverse evolution, and compensated radar point cloud coordinates are obtained; using the compensated radar point cloud coordinates to construct a detection residual error; performing single-step iterative updating of pose estimation by using the constructed detection residual error to obtain real-time estimation of the pose; according to the method, from the angle of the rear end of the positioning system, the complete estimation of the pose is calculated through single-step iterative updating, so that the positioning efficiency is effectively improved; the invariant extended Kalman filter is used for fusing sensor information to realize positioning, and introduction of linearization errors in the whole pose estimation process is avoided, so that the efficiency is improved, and the positioning precision is ensured.

The application provides a multi-agent reinforcement learning active power distribution network collaborative optimization method and system, belongs to the field of active power distribution network operation optimization and intelligent control, and constructs a global linearized voltage sensitivity model; each distributed resource is regarded as an agent, a local observation vector of each agent is input into a policy network to obtain an original action, and a real node voltage is calculated; whether the real node voltage satisfies a voltage safety constraint is checked, if yes, the original action is taken as an execution instruction, and if not, step 4 is entered; in step 4, online correction is performed, active injection adjustment, reactive injection adjustment and node voltage relaxation variable are solved jointly, and a candidate safety action is obtained; in step 5, power flow checking is performed, and a linearization error compensation term is updated; if the real node voltage does not satisfy the voltage safety constraint, the updated linearization error compensation term is substituted into step 4, an action correction amount is solved, and steps 4 and 5 are iteratively executed; and the safety projection layer prediction accuracy and the action correction reliability are improved.

The invention belongs to the technical field of wind power prediction, and particularly relates to a method for predicting ultra-short-term wind power based on an improved UKF algorithm. According to the method, a square root UKF, normalized innovation square gating and self-adaption, multi-information joint updating and multi-model interaction technologies are fused on the basis of the UKF. The method comprises the following steps: establishing a nonlinear state space model, generating a propagation sigma point by SR-UKF to complete time updating, acquiring, measuring and executing NIS gating, fusing and innovating a multi-information strategy and self-adapting to a noise covariance, constraining a projection to ensure that a physical boundary and the covariance are positive definite, fusing multiple working condition probabilities by IMM, and outputting a prediction result and uncertainty information. According to the method, linearization errors are avoided, and prediction robustness is improved; the problems of phase lag, unstable numerical value and the like are solved through multiple technologies respectively, second-to-minute level accurate prediction is achieved, and meanwhile deliverable capacity information capable of being directly used for control and performance is output.

The present invention relates to the field of control methods and is directed to solving the problem that existing model-free adaptive control methods cannot effectively improve the dynamic response performance of a controlled system and cannot effectively utilize the dynamic linearization error in the model-free adaptive control process to suppress disturbances. The method of the present invention considers the dynamic linearization error in the control process to establish an extended full-format dynamic linearization data model of the controlled system, compensates the controlled object based on this, estimates the extended pseudo-gradient of the controlled system based on the recursive augmented least squares method, obtains a model-free adaptive controller based on the extended full-format dynamic linearization data model at time k based on an improved criterion function, inputs the compensated controlled object control input signal into the controlled object, calculates the system dynamic linearization error difference, and performs model-free adaptive control.

A method for estimating a constrained zonotope enclosing a motion state of at least one mobile target, the method comprising: a) linearizing a nonlinear transition model at an element of a first zonotope (Zx(tk-1)), b) computing transition linearization errors at different elements of the first zonotope (Zx(tk-1)), c) computing a second zonotope that contains all linearization errors, d) propagating (102) the first zonotope so as to obtain an a priori zonotope ({circumflex over (Z)}x(tk)) enclosing the motion state at a second moment (tk) after the first moment (tk-1), wherein the a priori zonotope ({circumflex over (Z)}x(tk)) is a linear projection of a hypercube, the hypercube being subject to at least one linear constraint, e) updating (104) the a priori zonotope ({circumflex over (Z)}x(tk)) so as to obtain an a posteriori constrained zonotope (Z′x(tk)) enclosing the motion state at the second moment (tk).

The invention discloses a multi-robot consistency cooperative positioning method and system based on transformation, and relates to the technical field of robot positioning. According to the technical key points, the method comprises the following steps: acquiring motion information of a plurality of robots and relative measurement information among the robots; a linearization error state system is established based on self motion information and relative measurement information, and an unobservable subspace of the linearization error state system keeps time unchanged and is independent of a linearization point; a transformation extended Kalman filter with considerable consistency is designed based on a linearization error state system, and multi-robot cooperative positioning is carried out by using the transformation extended Kalman filter. According to the method, the relation between the original system and the unobservable subspace of the transformed linearization error state system is established, the method based on transformation is provided to establish the linearization error state system, and the problem of inconsistency caused by mismatching of observability is solved. Experiments show that the method is superior to an existing method in the aspects of accuracy and consistency.

The application relates to an optical satellite remote sensing image autonomous accurate positioning method and device, wherein the method comprises the following steps: acquiring two image data of a target area and imaging data corresponding to the two image data by a target satellite target ground load at different observation angles, and constructing an imaging equation corresponding to each image data according to the imaging data; constructing an error equation based on the imaging equation, the installation angle of the target ground load and the longitude and latitude information of homonymic points between the two image data; linearizing the error equation to generate a linearized error equation, and solving the linearized error equation to obtain the longitude and latitude of target homonymic points corresponding to the target satellite and the installation angle of the target load, and performing autonomous positioning of the target satellite according to the longitude and latitude of the target homonymic points and the installation angle of the target load. Therefore, the problem that the traditional calibration technology based on ground reference data highly depends on the accuracy and timeliness of external reference images and greatly influences the accuracy of geometric calibration is solved.

The present invention discloses a method and system for multi-robot consistent collaborative positioning based on transformation, which relates to the field of robot positioning technology. The technical points of the present invention include: obtaining the self-motion information of multiple robots and the relative measurement information between the robots; establishing a linearized error state system based on the self-motion information and the relative measurement information, wherein the unobservable subspace of the linearized error state system remains time-invariant and independent of the linearization point; designing a transformed extended Kalman filter with observable consistency based on the linearized error state system, and utilizing it to perform multi-robot collaborative positioning. Among them, by establishing a relationship between the unobservable subspaces of the original system and the transformed linearized error state system, a transformation-based method is proposed to establish a linearized error state system, which solves the inconsistency problem caused by observability mismatch. Experiments show that the present invention is superior to existing methods in terms of accuracy and consistency.

The application discloses a kind of flexible connection constraint under multi-node distributed filtering estimation method, belong to deep space exploration technical field.The implementation method of the application is as follows: by selecting the node with maximum observability in adjacent node, the state estimation thereof is utilized to establish flexible connection constraint, and the constraint least square problem of distributed filtering estimation is formed;The condition that inequality constraint is converted into equality constraint needs to be satisfied is analyzed using KKT condition, the flexible connection constraint is converted from inequality constraint to equality constraint, to avoid optimization process under the influence of inequality constraint to fall into local optimum, by constraint local linearization, the analytical expression of node state estimation mean value and estimation error covariance is obtained, the efficient estimation of flexible lander node state is realized, and the state estimation result conforming to the physical characteristics of flexible connection is generated;In addition, the nonlinear constraint linearization error is reduced by iterative estimation, and the node state estimation accuracy of flexible lander is further improved.

The application provides a distributed off-road vehicle state observation method based on visual fusion and nonlinear MHE. First, the front road surface texture features are extracted through the vehicle-mounted visual system and the adhesion coefficient distribution is predicted. Then, the MHE framework is used to explicitly process the physical constraints. The problems that the results of traditional filtering algorithms such as EKF are prone to divergence under strong nonlinear working conditions due to linearization errors, and the state values that violate the physical laws are calculated under extreme working conditions due to the lack of explicit physical constraints are solved. The optimal state is solved under the premise of meeting the physical constraints, and the physical consistency of state estimation is ensured, and the robustness under off-road working conditions is improved.

The invention discloses a mapping pseudo-spectral model prediction convex optimization method for Mars entry trajectory planning, and the method comprises the steps: converting a non-uniform Chebyshev-Gauss-Labatto collocation point into an approximately uniform Mapped Chebyshev-Gauss-Labatto collocation point through employing Kosloff-Tal-Eaer mapping, improving the ill-conditioned property of a differential matrix, and reducing the numerical oscillation; a gravity center interpolation format is constructed on the basis of Mapped Chebyshev-Gauss-Labatto collocation points, the state increment and the control correction are accurately approached, and zigzag fluctuation of a constant value control profile is inhibited; according to a mixed trajectory updating strategy, a reference trajectory is updated in combination with Lagrange interpolation and numerical integration, linearization error accumulation is reduced, and the high-precision task requirement is met. According to the method, the smoothness, efficiency and reliability of mars entering trajectory optimization are remarkably improved.