A method for quickly determining inertial navigation errors based on spatial target angle distance assistance

Abstract

The application discloses a kind of based on space target angle distance auxiliary inertial navigation error fast determination method, by at least two pointing of star camera optical axis is carried out high frequency multiple observation to obtain sufficient effective asynchronous measurement information, to ensure the observability of navigation error parameter;By establishing the optimization model with navigation position error as the estimated parameter, the first round optimization is carried out using nonlinear least square algorithm, and the position error is iteratively estimated;By establishing the optimization model with navigation position error and velocity error as joint estimated parameter, the first round optimization result is used as position error parameter initial value, the carrier position of inertial navigation solution is corrected using the position error estimated by the first round, and the second round optimization is carried out using nonlinear least square algorithm again, the change trend of carrier position in state propagation process can be effectively extracted, so as to effectively estimate the velocity error, and the estimation accuracy of position error is further improved based on the first round optimization.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of astronomical / inertial integrated navigation method, and relates to an inertial navigation error rapid determination method based on space target angular distance asynchronous observation assistance. BACKGROUND

[0002] Inertial navigation, as a navigation technology with complete navigation information, high data update rate, strong autonomy, strong anti-interference ability, all-weather and all-day working, has been widely applied in the fields of aviation, aerospace, navigation and the like, but the navigation error thereof increases with time accumulation. With the improvement of imaging technology and data processing capability, a star camera with photographic observation capability can simultaneously observe stars and space targets with certain brightness and orbit prior information, and obtain instantaneous measurement information such as starlight vector and target line-of-sight direction vector, which can be used as a space reference information source for navigation and positioning of a space carrier. As an important astronomical navigation sensor, the star camera has the characteristics of high measurement accuracy, non-time accumulation of error, strong autonomy and high reliability, but has the disadvantages of being easily affected by the visibility and observation conditions of astronomical observation objects, discontinuous output of measurement information and low data update rate. Therefore, the fusion of the measurement information of the two can complement each other and meet the application requirements of long-time and high-precision autonomous navigation.

[0003] Since the number of observable stars and space targets by the optical camera is closely related to the field of view angle, sensitivity and other performance indicators of the optical camera, and the imaging exposure, star map and target recognition processing also require a certain time, the data update rate of the star camera is low, and the star camera provides measurement information indirectly related to the position of the carrier, the observability of the carrier velocity is low, and the velocity error is difficult to be effectively estimated. How to effectively utilize the limited measurement information in quantity and accuracy to realize rapid and accurate estimation of the navigation error parameters is a problem to be solved at present, which will be described from the following aspects of the installation mode of the star camera, the observability improvement method, the measurement information utilization method and the error estimation method.

[0004] Since the number of target satellites is limited, and the observation field of view of the star camera is limited by the field of view angle, only one target satellite can be observed in most cases, and even if two or more target satellites are observed in the field of view of the star camera, the angular distance between the observed target satellites is small, which seriously limits the geometric constraint degree of the measurement information provided by the target satellites on the state estimation. At this time, if all the observable target satellites in the field of view are identified and processed, not only a long processing time is consumed, but also the accuracy of the state estimation is not improved. Therefore, usually one target satellite with good observability in the field of view of the star camera is selected for identification and processing, and the corresponding target direction vector measurement information is output.

[0005] Furthermore, the limitation of the optical axis rotation angle of the astronomical camera also restricts the degree of constraint on the carrier state estimation. To improve the observability of the carrier state as much as possible, for objects with relatively stable flight and few attitude maneuvers, a astronomical camera mounting method based on a rotating base can be adopted. During flight, the rotation of the mounting base can make a significant adjustment to the optical axis of the astronomical camera to observe a larger area of ​​the sky, alleviating the limitation of the optical axis rotation angle. For objects with many attitude maneuvers during flight, such as small high-speed rotating missiles and hypersonic gliders, the astronomical camera can be mounted using a strapdown method, that is, the astronomical camera and inertial devices are fixed to the airframe. During flight, the astronomical camera can change the direction of its optical axis with the carrier's attitude maneuvers, thereby observing space targets in different areas of the sky and improving the observability of the carrier state. Although both mounting methods can improve the accuracy of state estimation, the mounting method based on a rotating base requires a larger optical observation window. This not only places higher demands on the external structural strength and streamlined design of the spacecraft, but also further enhances the aero-optical effects with the increase of window size, seriously affecting the accuracy of astronomical observations. Star cameras based on strapdown mounting change their optical axis orientation as the carrier's attitude changes, eliminating the need for larger optical windows and offering advantages in overall structural design, cost, and observation accuracy.

[0006] Besides improving state observability as much as possible, constructing a more accurate measurement model to effectively utilize measurement information is another way to improve the accuracy of state estimation. There are two ways to utilize target direction vector measurement information: one is to establish the relationship between the target direction vector and the carrier position, and directly construct a measurement model based on the target direction vector. This method uses relatively raw measurement information, has a high information utilization rate, and the constructed model has a low degree of nonlinearity. However, the installation error and axis perturbation error of the star camera seriously affect the measurement accuracy of the target direction vector. When the installation error and axis perturbation error of the star camera are large, it is impossible to establish an accurate measurement model based on the target direction vector. The other method is to calculate the angular distance between the target direction vector and the starlight vectors of several background stars, and then construct a measurement model based on the angular distance. Since the effects of axis perturbation error on the target direction vector and starlight vector cancel each other out when calculating the angular distance, and the accuracy of the angular distance is independent of the magnitude of the coordinate system transformation error, the angular distance-based processing method avoids the influence of star camera axis perturbation error and installation error.

[0007] Commonly used navigation error estimation methods fall into two categories: state-based methods and parameter-based methods. State-based methods, including Kalman filtering, particle filtering, and unscented filtering, establish system state and measurement models, treating the navigation error to be estimated as part of the system state vector. They then recursively estimate navigation error parameters online. However, the estimated error parameters require a certain amount of time to converge stably. Furthermore, when the initial error parameters are large, the convergence time is long and may even cause filter divergence, making it difficult to meet the requirement of rapid error parameter determination. Additionally, the estimation accuracy obtained by state-based methods is affected by the accuracy of the system model and noise parameters.

[0008] Typical parameter estimation methods include linear least squares and nonlinear least squares. Linear least squares only requires establishing a measurement model between the estimated error parameter and the system measurement information, and uses the least squares criterion to obtain the estimated value of the error parameter. The estimation accuracy is not limited by the accuracy of the measurement noise, and it is simple to implement and has good speed. Nonlinear least squares establishes an optimization model related to the parameter to be estimated and uses nonlinear optimization methods such as Gauss-Newton method and Levenberg-Marquardt method for iterative solution, which ensures the accuracy of parameter estimation. Summary of the Invention

[0009] To address the problem that the state estimation method based on Kalman filtering has a long convergence time or even fails to converge when the initial navigation error is large and the astronomical measurement information is limited, this invention combines the nonlinear least squares parameter iterative optimization method with the information fusion idea based on asynchronous measurement and synchronous processing, and designs a fast inertial navigation error determination method based on asynchronous observation of space target angular distance.

[0010] This invention relates to a method for rapidly determining inertial navigation errors based on spatial target angular range assistance. The specific steps are as follows:

[0011] Step 1: Initialize the inertial navigation system's relevant state parameters.

[0012] Step 2: Solve the measurement information of the inertial device to obtain the carrier position, velocity and attitude calculated by the inertial navigation system.

[0013] Step 3: Construct the state equations of the astronomical / inertial integrated navigation system.

[0014] Step 4: Time update of the astronomical / inertial integrated navigation system.

[0015] Step 5: Perform asynchronous measurement information acquisition using the satellite camera.

[0016] Step 6: Based on the angular distance measurement, establish an optimization model with the navigation position error as the parameter to be estimated, and use a nonlinear optimization method to perform the first round of optimization to obtain a preliminary estimate of the navigation position error.

[0017] Step 7: Based on the angular distance measurement, establish an optimization model with navigation position error and navigation speed error as the parameters to be estimated. Use the result of the first round of optimization as the initial value of the position error, and then use the nonlinear optimization method to perform a second round of iterative optimization to obtain the final estimated values ​​of the navigation position error and speed error parameters.

[0018] The advantages of this invention are:

[0019] 1. The present invention provides a method for rapidly determining inertial navigation errors based on asynchronous observation of the angular distance of space targets, which has good speed.

[0020] 2. The present invention provides a method for rapid determination of inertial navigation error based on asynchronous observation of spatial target angular distance. It employs an iterative solution method to ensure the estimation accuracy of inertial navigation error parameters.

[0021] 3. The present invention is a method for rapid determination of inertial navigation error based on asynchronous observation of space target angular distance. Under the condition that the field of view of the star camera and the rotation angle of the optical axis are limited, the asynchronous measurement and acquisition method designed can effectively ensure the observability of the parameters to be estimated.

[0022] 4. The present invention provides a method for rapid determination of inertial navigation error based on asynchronous observation of spatial target angular distance. By constructing an optimization model related to navigation position error and velocity error, it can effectively utilize the changing trend of the carrier position during state propagation and effectively estimate the velocity error when the initial velocity error is large.

[0023] 5. The present invention is based on a method for rapid determination of inertial navigation error assisted by asynchronous observation of spatial target angular distance. It designs a two-round optimization process. The second round uses the optimization model that has been corrected by the position error estimated in the first round. Based on the optimization in the first round, the effective estimation of velocity error in the second round further improves the estimation accuracy of position error.

[0024] 6. The present invention provides a method for rapid determination of inertial navigation error based on asynchronous observation of spatial target angular distance. It is simple to implement and is applicable not only to astronomical / inertial integrated navigation systems based on star camera observation, but also to other fields. Attached Figure Description

[0025] Figure 1 This is an overall flowchart of the method for rapid determination of inertial navigation error based on asynchronous observation of spatial target angular distance in this invention;

[0026] Figure 2This is a flowchart of the asynchronous measurement information acquisition of spatial target angular distance in the method of the present invention;

[0027] Figure 3 This is a flowchart illustrating the optimization solution of navigation error parameters based on the Gauss-Newton method in the method of this invention.

[0028] Figure 4 The convergence curve of the objective function for the first round of optimization using the method of this invention;

[0029] Figure 5 The convergence curve of the objective function for the second round of optimization using the method of this invention;

[0030] Figure 6 The variation trend of position error under different axis disturbance errors;

[0031] Figure 7 The trend of velocity error variation under different shaft disturbance errors;

[0032] Figure 8 The trend of position error under different installation errors;

[0033] Figure 9 The trend of speed error variation under different installation errors. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings.

[0035] This invention relates to a method for rapid determination of inertial navigation errors based on asynchronous observation of the angular distance of space targets, such as... Figure 1 As shown, the specific steps are as follows:

[0036] Step 1: Initialize the relevant state parameters of the inertial navigation system solution.

[0037] Step 2: Solve the measurement information of the inertial device to obtain the carrier position, velocity and attitude calculated by the inertial navigation system.

[0038] Using the launch point inertial coordinate system (referred to as the launch inertial system) as the navigation coordinate system, the differential equations for the strapdown inertial navigation system in the launch inertial system are:

[0039]

[0040] In the formula, the superscript li represents the inertial system; V li P represents the velocity of the carrier in the inertial frame; li Indicates the position of the carrier in the inertial frame; f b Indicates the specific force under the load system; g li q represents the gravitational acceleration vector in the inertial frame; q is the attitude quaternion of the carrier. The angular velocity of the carrier; This is the transformation matrix from the carrier system to the launch inertial system.

[0041] The measurement information of the inertial device is solved by equation (1) to obtain the carrier position, velocity and attitude calculated by the inertial navigation system.

[0042] Step 3: The state vector of the astronomical / inertial integrated navigation system is constructed by using the navigation state error and the main error components of the inertial device, and then the state equation of the astronomical / inertial integrated navigation system is constructed.

[0043] The state vector of the navigation system, composed of navigation state error and the main error components of inertial devices, is as follows:

[0044]

[0045] Where φ is the platform error angle vector; This is the velocity error vector; ε is the position error vector; ε is the constant drift error vector of the three-axis gyroscope. This is the constant bias error vector of the triaxial accelerometer; the superscript T indicates transpose.

[0046] The state equation for the astronomical / inertial integrated navigation system is as follows:

[0047]

[0048] Where t is time; F(t) is the system state transition matrix; G(t) is the noise factor matrix; and W(t) is the system noise.

[0049] Step 4: If the astronomical / inertial navigation system has reached its time update time, perform the time update and then proceed to Step 5; if the time update time has not yet arrived, return to Step 2 to continue the inertial navigation calculation.

[0050] Discretizing the state equations of the astronomical / inertial integrated navigation system constructed in step three yields:

[0051] X k =X(t) k )=Φ k|k-1 X k-1 +w k,k-1 (4)

[0052] The above formula is written in a simplified form; where the subscript k represents discrete time, corresponding to time t. k , t k = kΔt, where Δt represents the discrete period, which is the time update period. Φ k|k-1 For from t k1 to t k The state transition matrix, Φ k|k-1 =Φ(t)k ,t k-1 );w k,k-1 The discretized result is from t k1 to t k Process noise.

[0053]

[0054] In the formula, I is the identity matrix; F = F(t) k-1 ) is the state transition matrix at time k-1.

[0055] Using the state transition matrix Φ k|k-1 The state estimate at time k-1 The state estimate at time k is obtained by recursion.

[0056]

[0057] In this context, the superscript "^" indicates an estimated value.

[0058] Step 5: If astronomical navigation has not yet been started, or if astronomical navigation has been started but there is no astronomical measurement information at the current moment, return to step 2 to continue inertial navigation calculation; if astronomical navigation has been started and outputs astronomical measurement information at the current moment, then perform asynchronous measurement information acquisition by the star camera.

[0059] From the perspective of ensuring the speed of error parameter determination and the effectiveness of parameter estimation, such as Figure 2 As shown, the present invention sets the following asynchronous measurement information acquisition method for satellite cameras:

[0060] 1) Set the high-frequency observation frequency and the number of observations under the same direction. Considering that the more times the direction is set, the longer the error propagation time will be and the lower the effectiveness of asynchronous measurement information, the optical axis direction is set to 2 times here.

[0061] 2) Under the first direction of the star camera's optical axis (pointing to the sky area with better observability as much as possible), the target satellite and star within the field of view are continuously observed multiple times at a preset observation frequency. The starlight vector of the star and the line-of-sight vector of the target satellite are obtained through imaging exposure and star map recognition, and then the angular distance measurement information between the star and the target satellite is obtained. The changes of the state transition array during the time update process at each observation moment are recorded.

[0062] 3) The optical axis pointing angle can be changed by relying on the attitude maneuver of the carrier or by rotating the star camera mounting platform, so that the optical axis pointing of the star camera changes from the first pointing direction to the second pointing direction. If the optical axis pointing direction is changed by relying on the attitude maneuver of the carrier, the size of the optical axis pointing angle depends on the size of the attitude maneuver of the carrier. If the optical axis pointing direction is changed by rotating the star camera mounting platform, the optical axis pointing angle can be set in the range of 40° to 80°, so that the observation information can form a better geometric constraint on the state as much as possible.

[0063] 4) Under the second direction of the star camera's optical axis, the target satellite and star within the field of view are continuously observed multiple times at a preset observation frequency. The starlight vector of the star and the line-of-sight vector of the target satellite are obtained through imaging exposure and star map recognition processes. In turn, the angular distance measurement information between the star and the target satellite is obtained, and the changes of the state transition array during the time update process at each observation moment are recorded.

[0064] By utilizing the recorded state transition array and the prior orbit information of the target satellite identified in the star camera's field of view, the relationship between the navigation error parameters at the current moment and asynchronous measurements can be established in subsequent steps.

[0065] 5) During the second downward observation process, determine whether the total number of observations under the two directions has reached the total number of observations m×n (m is the number of directions, and n is the number of observations under each direction). If it has not reached the total number of observations, return to step two; if it has reached the total number of observations, proceed to steps six and seven in sequence.

[0066] Step 6: Construct an optimization model with navigation position error as the parameter to be estimated, and use the Gauss-Newton method to perform the first round of optimization to obtain a preliminary estimate of the navigation position error.

[0067] A. Establish an optimization model based on angular distance measurement, with navigation position error as the parameter to be estimated.

[0068] Establish an objective function with navigation position error as the parameter to be estimated:

[0069]

[0070] Where, m i For t k-i The number of angular distances between the stellar vectors measured at time and the direction vectors of the spatial target (consistent with the number of observable stars); t k-i For the alignment times of all asynchronous measurements, i = 0, 1, 2, ..., k; α g (t k-i ) for star cameras in t k-i The angular distance between the g-th observed star and the target satellite, measured at time g, is:

[0071] αg (t k-i )=arccos{[S g (t k-i )]TL(t k-i ) / |S g (t k-i )| / |L(t k-i )|}+ε α (8)

[0072] In the formula, t k Indicates the current time, t j For the j-th asynchronous measurement time, j = 1, 2, ..., m × n - 1; S g (t k-i ) for t k-i The starlight vector measurement of the g-th observed star at time t; L(t) k-i ) for t k-i The direction vector measurement of the target satellite at that moment; ε α This represents the angular distance measurement error. Indicates the inertial system based on t j Inertial navigation error vector X(t) at time t j The state transition yields t. k-i Position error at time use For t k-i Inertial navigation solution position at time 1 The error is corrected, and then the carrier position and the space target position are determined by the error-corrected position. Determine t k-i The angular distance between the vector of the g-th observed star and the vector of the space target at time g, i.e., the calculation of the angular distance in the inertial frame, satisfies:

[0073]

[0074] The calculation of angular distance in the Earth's inertial frame satisfies:

[0075]

[0076] In this context, the superscript 'i' indicates the ground inertial system and the superscript 'li' indicates the launch inertial system. Represented as t k-i The projection of the starlight vector measurement of the g-th observed star in the Earth's inertial frame at time g; This is the transformation matrix from the ground inertial frame to the Earth inertial frame. The transformation matrix from Earth inertial frame to ground inertial frame is calculated from the initial longitude λ0 and the initial latitude L0; Let be the state transition error matrix from the originating inertial frame to the originating inertial frame, caused by the initial longitude error δλ0 and the initial latitude error δL0, respectively, satisfying the following relationships:

[0077]

[0078] From equation (4), we can obtain

[0079]

[0080] Since the subscripts in the subsequent formulas correspond to different state components, the abbreviation method is not used in the subsequent formulas to make the expression clearer.

[0081] By using the transformation method from equation (4) to equation (12), t can be derived. ki and t j The state vector at time t satisfies the following relationship:

[0082] X(t k-i )=Φ(t k-i ,t j )[X(t j )-w(t j ,t k-i )]=[Φ(t j ,t k-i )] -1 [X(t j )-w(t j ,t k-i )](13)

[0083] Here, Φ(t) k-i ,t j )=[Φ(t j ,t k-i )] -1 Let Φ P (t k-i ,t j ) is Φ(t) k-i ,t j Rows 7-9 of the diagram can be written in the form of a block matrix based on the corresponding state components:

[0084]

[0085] Where, Φ pφ (t k-i ,t j ), Φ pv (t k-i ,t j ), Φ pp (t k-i ,t j ), Φ pε (t k-i ,t j ), Φ P(t k-i ,t j The state transition matrix components corresponding to the platform error angle, velocity error, position error, gyroscope drift, and accelerometer bias are shown in the figure.

[0086] From this, we can derive t ki Position error components at time With t j Inertial navigation error state X(t) at time t j The following relationship exists between them:

[0087]

[0088] φ(t j ) for t j The platform error angle at any given time.

[0089] Considering that a large initial position error can severely affect model linearization and observation synchronization, and to avoid a decrease in position estimation accuracy due to inaccurate velocity error estimation, the first round of optimization only considers the initial position error caused by t. j Position error at time Construct the vector of parameters to be estimated θ j Equation (15) is simplified to:

[0090]

[0091] Establish based on equations (9) and (16) and Relationship:

[0092]

[0093] Then, establish optimization goals:

[0094]

[0095] B. Iterative estimation of navigation position error parameters based on Gauss-Newton method.

[0096] The objective function established in step A is a nonlinear least squares problem, which requires solving using nonlinear optimization methods such as the Gauss-Newton method and the Levenberg-Marquardt algorithm. Considering the issue of fast convergence, the Gauss-Newton method is used here. Figure 3 As shown, the specific steps are as follows:

[0097] (1) Set the initial value θ for the iteration of navigation error parameters. j,0 Incremental change threshold Δθ j,min Minimum threshold F of objective function min and the maximum number of iterations k′ max ;

[0098] (2) If the current iteration step k′ has reached the maximum iteration step k′ max If the iteration stops, proceed to step (3);

[0099] (3) Let the parameter estimate in the k′-th iteration be denoted as . Since the first round of optimization only used the position error as the parameter to be estimated, that is t represents the value obtained in the k′-th iteration. j The estimated position error at time t can be obtained from equation (16):

[0100]

[0101] In the formula, for The state transition obtained in the k′-th iteration is t k-i The estimated position error at time t is used to estimate the position error at time t. k-i Inertial navigation solution position at time 1 Correct the error:

[0102]

[0103] In the formula, This represents the inertial navigation solution position corrected in the k′-th iteration, which is then combined with the error-corrected carrier position and the space target position. Determine t k-i The angular distance between the vector of the g-th observed star and the vector of the space target at time g:

[0104]

[0105] Then calculate the objective function value in the k′-th iteration:

[0106]

[0107] (4) If the objective function value If the value is less than the threshold, stop the iteration; otherwise, proceed to step (5).

[0108] (5) In the k′-th iteration, calculate the objective function with respect to the current parameters to be estimated. Jacques

[0109] ratio matrix

[0110]

[0111] Constructing normal incremental equations based on the least squares criterion:

[0112]

[0113] In the formula, The increment is the parameter increment for the k′-th iteration. If the increment is less than the increment change threshold, the iteration stops; otherwise, a new error parameter estimate is obtained based on the increment.

[0114]

[0115] Will As the parameter estimate for the k′+1th iteration, return to step (3) to continue the next iteration.

[0116] Step 7: Construct an optimization model with navigation position error and velocity error as joint parameters to be estimated, and use the position error estimated in the first round to correct the carrier position calculated by the inertial navigation system. Then, use the Gauss-Newton method to perform a second round of optimization to obtain the final estimated values ​​of navigation position error and velocity error parameters.

[0117] A. Establish an optimization model based on angular distance measurement, with navigation position error and velocity error as the parameters to be estimated.

[0118] To further improve the estimation accuracy of navigation position error and effectively utilize the changing trend of the carrier position during state propagation to effectively estimate navigation velocity error, an optimization model based on angular distance measurement is established, using the estimation result obtained in the first round of optimization as the initial value of position error, with navigation position error and navigation velocity error as the parameters to be estimated.

[0119] Adding the navigation speed error to the parameters to be estimated in the optimization model simplifies equation (15) to:

[0120]

[0121] That is, from t j Position error at time and speed error Construct the vector of parameters to be estimated

[0122] Establish based on equations (27) and (16) and Relationship:

[0123]

[0124] Then, the optimization model of equation (28) is established, and the position of the carrier calculated by the inertial navigation is corrected by the position error estimated in the first round.

[0125] The specific form of the second-round optimization model is as follows:

[0126]

[0127] B. Iterative estimation of navigation position and velocity error parameters based on the Gauss-Newton method to complete the second round of optimization. The specific steps are the same as step B of the first round of optimization.

[0128] Example

[0129] Simulations were conducted using a high-speed transport vehicle equipped with a satellite camera. An astronomical / inertial combined navigation system was employed. Astronomical navigation initiated after the vehicle's boost phase. The satellite camera observed the target satellite and observable stars, measuring the direction vector of the target satellite and the starlight vector of the stars. The satellite camera's astronomical observation frequency was 0.5 Hz, with an astronomical measurement accuracy of 3”. The satellite camera's installation error was 3”, the optical lens's half-angle of view was 9°, the angle between the satellite camera's optical axis and the normal axis of the mounting base was 20°, and the optical axis perturbation error was 3”. It was assumed that one target satellite and five background stars could be identified at each observation moment, with an observation frequency of 10 Hz under the same optical axis direction, and 10 consecutive observations. The gyroscope accuracy was 0.02° / h, the accelerometer accuracy was 10 μg, the position accuracy of the space target with certain prior orbital information was 10 m, the initial position error of the transport vehicle was 1000 m, and the initial velocity error was 100 m / s.

[0130] Fifty Monte Carlo simulations were performed under the above simulation conditions. The effectiveness of the proposed method was evaluated using the root mean square statistics of the residual position error and residual velocity error after iteration. The residual error was defined as the difference between the navigation error propagated to the last measurement moment and the navigation error parameter estimated after iterative optimization.

[0131] The maximum number of iterations is set to 10. The convergence curve of the objective function value (i.e., the curve showing the change of the sum of squares of the residual vector) during the first round of optimization is as follows: Figure 4 As shown, the convergence curve of the objective function value in the second round of optimization is as follows: Figure 5 As shown.

[0132] Depend on Figure 4 It can be seen that in the iterative optimization process using navigation position error as the parameter to be estimated, the objective function value tends to converge after 5 iterations. From Figure 5 It can be seen that in the iterative optimization process using navigation position error and navigation speed error as the parameters to be estimated, the objective function converges to the minimum value after two iterations. This is because the Gauss-Newton method has the advantage of fast convergence, and using the result obtained in the first round of optimization as the initial value of navigation position error for the second round of optimization further accelerates the convergence speed of the second round of optimization. The navigation error statistics at different stages are shown in Table 1.

[0133] Table 1. Navigation Error Statistics at Different Stages

[0134]

[0135] Simulation results show that the navigation position error at the last measurement moment is 11247.5m, the remaining navigation position error after the first round of optimization is 312.2m, and the remaining navigation position error after the second round of optimization is 255.1m; the navigation velocity error at the last measurement moment is 173.40m / s, and the remaining navigation velocity error after the second round of optimization is 58.52m / s. The estimation accuracy of the navigation position error after the first round of optimization is 97.22%, the estimation accuracy of the velocity error after the second round of optimization is 66.25%, and the estimation accuracy of the position error is 97.73%, meaning that the effective estimation of the velocity error further improves the accuracy of the position error estimation.

[0136] The initial position error of the carrier was set to 3000m, and the initial velocity error to 100m / s. Other simulation conditions remained unchanged. The axis disturbance error and installation error of the star camera were varied, and 50 Monte Carlo simulations were performed. The corresponding trends of position and velocity errors were plotted as follows: Figure 6 to Figure 9 As shown.

[0137] Depend on Figure 6 and Figure 7 It can be seen that after two rounds of optimization, the position and velocity errors hardly change with the change in axis perturbation error. This is because when calculating the angular distance using the target satellite's direction vector and the starlight vector, the effects of the axis perturbation error on the two vectors cancel each other out. Figure 8 and Figure 9 It can be seen that as the installation error increases, the position error and velocity error after the two rounds of optimization fluctuate within a certain range and are almost unaffected by the installation error. This is because the angular distance measurement accuracy has the advantage of not being affected by coordinate system transformation error.

[0138] In summary, under the condition of large initial position and velocity errors, after two rounds of optimization and iteration, the proposed method can accurately and quickly determine the navigation position and velocity errors in the initial stage of astronomical navigation and avoid the impact of large star camera installation errors and axis disturbance errors on the accuracy of error determination.

Claims

1. A method for rapidly determining inertial navigation errors based on spatial target angular distance assistance, characterized in that: The specific steps are as follows: Step 1: Initialize the inertial navigation system's relevant state parameters; Step 2: Solve the measurement information of the inertial device to obtain the carrier position, velocity and attitude calculated by the inertial navigation system; Step 3: Construct the state equations of the astronomical / inertial integrated navigation system; Step 4: Time update for the astronomical / inertial integrated navigation system; Step 5: Acquire asynchronous measurement information from the satellite camera; Step 6: Based on the angular distance measurement, establish an optimization model with the navigation position error as the parameter to be estimated, and use a nonlinear optimization method to perform the first round of optimization to obtain a preliminary estimate of the navigation position error; Step 7: Based on the angular distance measurement, establish an optimization model with navigation position error and navigation speed error as the parameters to be estimated. Use the result of the first round of optimization as the initial value of the position error, and then use the nonlinear optimization method to perform a second round of iterative optimization to obtain the final estimated values ​​of the navigation position error and speed error parameters.

2. The method for rapid determination of inertial navigation error based on spatial target angular distance assistance as described in claim 1, characterized in that: The asynchronous measurement information acquisition method for the satellite camera in step 5 is as follows: A. Set the high-frequency observation frequency and number of observations under the same direction; preset two different optical axis directions; B. Under the first direction of the star camera's optical axis, continuously observe the target satellite and star within the field of view multiple times at a preset observation frequency. Obtain the starlight vector of the star and the line-of-sight vector of the target satellite through imaging exposure and star map recognition processes, thereby obtaining the angular distance measurement information between the star and the target satellite, and recording the changes in the state transition array during the time update process at each observation moment. C. Change the optical axis pointing angle so that the optical axis of the star camera changes from the first pointing direction to the second pointing direction; D. Under the second direction of the star camera's optical axis, the target satellite and star within the field of view are continuously observed multiple times at a preset observation frequency. The starlight vector of the star and the line-of-sight vector of the target satellite are obtained through imaging exposure and star map recognition processes. Then, the angular distance measurement information between the star and the target satellite is obtained, and the changes of the state transition array during the time update process at each observation moment are recorded.

3. The method for rapid determination of inertial navigation error based on spatial target angular distance assistance as described in claim 1, characterized in that: In step 6, the optimization model based on angular distance measurement, with navigation position error as the parameter to be estimated, is as follows: In the formula: Depend on Position error at time Construct the vector of parameters to be estimated; for The number of angular distances between the stellar vector and the direction vector of the space target measured at any given moment; For the alignment time of all asynchronous measurements; For star cameras in The angular distance between the g-th observed star and the target satellite in space, measured at time 1; Indicates the current moment; For the first Each asynchronous measurement moment; The transformation matrix from Earth inertial frame to ground inertial frame is given by the initial longitude. and initial latitude Calculated; for The starlight vector measurement of the g-th observed star at time g; Indicates the inertial system based on Inertial navigation error vector at time 1 The result obtained after state transition Position error at time ,use right Inertial navigation solution position at time 1 The error is corrected, and then the carrier position and the space target position are determined by the error-corrected position. Sure The angular distance between the vector of the observed star and the vector of the space target at time g; From arrive The state transition matrix components corresponding to the positional errors in the state transition matrix; The superscript "^" indicates an estimated value.

4. The method for rapid determination of inertial navigation error based on spatial target angular distance assistance as described in claim 1, characterized in that: The optimization model, with navigation position error and velocity error as the parameters to be estimated, is as follows: In the formula: For the reason Position error at time and speed error Construct the vector of parameters to be estimated; for The number of angular distances between the stellar vector and the direction vector of the space target measured at any given moment; For the alignment time of all asynchronous measurements; For star cameras in The angular distance between the g-th observed star and the target satellite in space, measured at time 1; Indicates the current moment; For the first Each asynchronous measurement moment; Indicates the inertial system based on Inertial navigation error vector at time 1 The result obtained after state transition Position error at time ,use right Inertial navigation solution position at time 1 The error is corrected, and then the carrier position and the space target position are determined by the error-corrected position. Sure The angular distance between the vector of the observed star and the vector of the space target at time g; The transformation matrix from Earth inertial frame to ground inertial frame is given by the initial longitude. and initial latitude Calculated; for The starlight vector measurement of the g-th observed star at time g; and From arrive The state transition matrix components corresponding to velocity error and position error; The superscript "^" indicates an estimated value.

5. The method for rapid determination of inertial navigation error based on spatial target angular distance assistance as described in claim 1, characterized in that: Both the first and second rounds of optimization were performed using the Gauss-Newton method, as follows: (1) Set the initial values ​​for the navigation error parameters during iteration. Incremental change threshold Minimum threshold of objective function and maximum number of iterations ; (2) If the current iteration step number Maximum number of iterations reached Then stop the iteration; otherwise, proceed to step (3). (3) Calculate the first Objective function value in step iteration ; (4) If the objective function value If the value is less than the threshold, stop the iteration; otherwise, proceed to step (5). (5) in the In each iteration, the objective function is calculated with respect to the current parameters to be estimated. Jacobian matrix : Constructing normal incremental equations based on the least squares criterion: In the formula, For the first The parameter increment is incremented step by step. If the increment is less than the increment change threshold, the iteration stops; otherwise, a new error parameter estimate is obtained based on the increment. : Will As the first The parameter estimates are obtained, and the process returns to step (3) to continue the next iteration.

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