A method for predicting the moving track of an extraterrestrial celestial body probe
By employing a state vector processing method based on unscented transformation and adaptive adjustment, the problems of prediction accuracy and stability during high-speed travel of extraterrestrial surface probes were solved, achieving higher-precision trajectory prediction.
Patent Information
- Application Number
- CN202411682356.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-22
- Publication Date
- 2026-01-13
- Estimated Expiration
- 2044-11-22
AI Technical Summary
Existing technologies suffer from fragmented, false, and asynchronous state data acquired by telemetry when extraterrestrial surface probes travel at high speeds and move irregularly, leading to a decrease in prediction accuracy and stability.
By employing steps such as unscented transformation, nonlinear system processing, weighted summation, singular value decomposition, and adaptive adjustment, the state vector and covariance processing are optimized to improve prediction accuracy and stability.
It significantly improves the accuracy and stability of extraterrestrial surface probe trajectory prediction, reduces lateral distance and forward angle errors, and is superior to eight other prediction methods.
Smart Images
Figure CN119623040B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of deep space exploration technology, and more specifically to a method for predicting the trajectory of an extraterrestrial surface probe. Background Technology
[0002] Previous methods for predicting the trajectories of extraterrestrial probes have primarily focused on improving the prediction matrix and adding control constraints. This approach is effective for probes with defined orbits, providing good estimates of velocity, angle, and position. However, for probes moving at high speeds and irregularly on extraterrestrial surfaces, telemetry data suffers from fragmentation, falsehoods, and asynchronous movements, thus reducing prediction accuracy.
[0003] Therefore, how to provide a method for predicting the trajectory of extraterrestrial surface probes that can improve prediction accuracy and stability is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0004] In view of this, the purpose of this invention is to provide a method for predicting the movement trajectory of an extraterrestrial surface probe.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A method for predicting the trajectory of an extraterrestrial surface probe includes the following steps:
[0007] S1: Obtain the actual state vector x of the extraterrestrial surface probe. k ; where x k Let k be an n*m dimensional state vector, where k represents time.
[0008] S2: For the actual state vector x k Perform an unscented transformation to obtain the state vector set σ k ;
[0009] S3: Transfer the state vector group σ k Input a nonlinear system and obtain the predicted state vector set σ k+1 ;
[0010] S4: For the predicted state vector group σ k+1 The elements in the matrix are weighted and summed to obtain the predicted state vector.
[0011] S5: Based on the predicted state vector group σ k+1 and the predicted state vector Obtain the predicted state covariance
[0012] S6: Update the predicted state vector Obtain the updated predicted state vector
[0013] Update the predicted state covariance Obtain the updated predicted state covariance
[0014] S7: The updated predicted state covariance... Perform singular value decomposition to obtain the predicted feature diagonal matrix.
[0015] S8: Based on the predicted feature diagonal matrix Calculate the prediction condition number
[0016] S9: For the set of prediction condition numbers Normalization is performed to obtain the set of normalized prediction condition numbers.
[0017] S10: Based on the normalized prediction condition number set For the set of predicted state covariances Processing is performed to obtain the set of region-normalized predicted state covariances.
[0018] S11: Utilizing the state prediction error set Normalized prediction state covariance set for the region Perform adaptive adjustment to obtain the adjusted set of predicted state covariance.
[0019] S12: Repeat S1-S11 continuously to obtain the predicted trajectory; wherein, the predicted state vector updated at each time step in S6 constitutes the predicted trajectory.
[0020] Preferably, the predicted state vector Obtained based on the following formula:
[0021]
[0022] σ k+1 ={σ i,k+1}, i = 0, 1, ..., 2n;
[0023] Where, σ i,k+1 σ k+1 The i-th element in; σ represents time k+1 i,k+1 The weight.
[0024] Preferably, the predicted state covariance Obtained based on the following formula:
[0025]
[0026] in, σ represents time k+1 i,k+1 The covariance weights; Q represents the process noise covariance matrix; T represents the transpose.
[0027] Preferably, the updated predicted state vector Obtained based on the following formula:
[0028]
[0029]
[0030] Among them, K k+1 Z represents the Kalman gain at time k+1; k+1 Let f represent the observation vector at time k+1; f represents the nonlinear function. This represents the set of state prediction errors at time k-1; Represents the set of region-normalized predicted state covariances at time k-2; This represents the set of region-normalized predicted state covariances at time k-1; P represents the state prediction error at times k-γ, k-γ+1, ..., k-2, k-1, respectively; zz,k+1 H represents the nonlinear transformation of the predicted state covariance; H represents the observation matrix; and R represents the observation noise covariance.
[0031] Preferably, the updated state covariance Obtained based on the following formula:
[0032]
[0033]
[0034] in, This represents the set of predicted state covariances adjusted at time k-1;
[0035] Let them represent the adjusted predicted state covariance at times k-γ, k-γ+1, ..., k-2, k-1, respectively.
[0036] Preferably, the prediction condition number Obtained based on the following formula:
[0037]
[0038] in, express The maximum singular value in; express The smaller singular values in the range are: u1, u2 ∈ [3, 6].
[0039] Preferably, the set of normalized prediction condition numbers Obtained based on the following formula:
[0040]
[0041]
[0042]
[0043]
[0044]
[0045]
[0046] in, Let k-γ+1, k-γ+2, ..., k-1, k represent the prediction condition numbers at time points k-γ+1, k-γ+2, ..., k-1, k respectively. Let represent the normalized prediction condition number at times k-γ+1, k-γ+2, ..., k-1, k respectively; min represents finding the minimum value; max represents finding the maximum value.
[0047] Preferably, the set of normalized predicted state covariances for the region Obtained based on the following formula:
[0048]
[0049]
[0050]
[0051]
[0052]
[0053]
[0054] in, Let them represent the predicted state covariances updated at time k-γ+1, k-γ+2, ..., k-1, k respectively;
[0055] Let them represent the region-normalized predicted state covariance at times k-γ+1, k-γ+2, ..., k-1, k respectively.
[0056] Preferably, the adjusted predicted state covariance set Obtained based on the following formula:
[0057]
[0058]
[0059] in, Represents the set of state prediction errors at time k; α and β represent forgetting factors; Let represent the set of regional normalized predicted state covariances at time k-1.
[0060] Preferred, and The calculation formula is:
[0061]
[0062]
[0063] Where λ represents the scaling factor;
[0064] Preferably, the state vector group σ k Obtained based on the following formula:
[0065]
[0066] σ k ={σ i,k}, i = 0, 1, ..., 2n;
[0067] Among them, P xk This represents the true state covariance matrix at time k; express The i-th column; σ i,k σ k The i-th element in.
[0068] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for predicting the trajectory of an extraterrestrial surface probe, which can improve the prediction accuracy and prediction stability. Attached Figure Description
[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0070] Figure 1The flowchart illustrates a method for predicting the trajectory of an extraterrestrial surface probe provided by this invention. Detailed Implementation
[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0072] like Figure 1 As shown in the figure, this invention discloses a method for predicting the trajectory of an extraterrestrial surface probe, comprising the following steps:
[0073] S1: Obtain the actual state vector x of the extraterrestrial surface probe. k ; where x k Let k be an n*m dimensional state vector, where k represents time.
[0074] S2: For the actual state vector x k Perform an unscented transformation to obtain the state vector set σ k ;
[0075] In one embodiment, the state vector group σ k Obtained based on the following formula:
[0076]
[0077] σ k ={σ i,k}, i = 0, 1, ..., 2n;
[0078] Among them, P xk This represents the true state covariance matrix at time k; express The i-th column; σ i,k σ k The i-th element in the equation; λ represents the scaling factor.
[0079] S3: Transfer the state vector group σ k Input a nonlinear system and obtain the predicted state vector set σ k+1 ;
[0080] Specifically: σ k+1 =f(σ k ,u k ,w k ); where u k Indicates control input; w kLet f represent the process noise assumed to be Gaussian distributed, and let f represent the nonlinear function.
[0081] S4: For the predicted state vector group σ k+1 The elements in the matrix are weighted and summed to obtain the predicted state vector.
[0082] In one embodiment, the predicted state vector Obtained based on the following formula:
[0083]
[0084] σ k+1 ={σ i,k+1}, i = 0, 1, ..., 2n;
[0085]
[0086] Where, σ i,k+1 σ k+1 The i-th element in; σ represents time k+1 i,k+1 The weight.
[0087] S5: Based on the predicted state vector group σ k+1 and the predicted state vector Obtain the predicted state covariance
[0088] In one embodiment, the predicted state covariance Obtained based on the following formula:
[0089]
[0090]
[0091] in, σ represents time k+1 i,k+1 The covariance weights; Q represents the process noise covariance matrix; T represents the transpose.
[0092] S6: Update the predicted state vector Obtain the updated predicted state vector
[0093] In one embodiment, the updated predicted state vector Obtained based on the following formula:
[0094]
[0095]
[0096]
[0097]
[0098] Among them, K k+1 Z represents the Kalman gain at time k+1; k+1 Let f represent the observation vector at time k+1; f represents the nonlinear function. This represents the set of state prediction errors at time k-1; Represents the set of region-normalized predicted state covariances at time k-2; This represents the set of region-normalized predicted state covariances at time k-1; P represents the state prediction error at times k-γ, k-γ+1, ..., k-2, k-1, respectively; zz,k+1 H represents the nonlinear transformation of the predicted state covariance; H represents the observation matrix; and R represents the observation noise covariance.
[0099] Update the predicted state covariance Obtain the updated predicted state covariance
[0100] In one embodiment, the updated state covariance Obtained based on the following formula:
[0101]
[0102]
[0103] in, This represents the set of predicted state covariances adjusted at time k-1;
[0104] Let them represent the adjusted predicted state covariance at times k-γ, k-γ+1, ..., k-2, k-1, respectively.
[0105] S7: The updated predicted state covariance... Perform singular value decomposition to obtain the predicted feature diagonal matrix.
[0106] S8: Based on the predicted feature diagonal matrix Calculate the prediction condition number
[0107] In one embodiment, the prediction condition number C xk,k+1 Obtained based on the following formula:
[0108]
[0109] in, express The maximum singular value in; express The smaller singular values in the range are: u1, u2 ∈ [3, 6].
[0110] S9: For the set of prediction condition numbers Normalization is performed to obtain the set of normalized prediction condition numbers.
[0111] In one embodiment, the normalized prediction condition number set Obtained based on the following formula:
[0112]
[0113]
[0114]
[0115]
[0116]
[0117]
[0118] in, Let k-γ+1, k-γ+2, ..., k-1, k represent the prediction condition numbers at time points k-γ+1, k-γ+2, ..., k-1, k respectively. Let represent the normalized prediction condition number at times k-γ+1, k-γ+2, ..., k-1, k respectively; min represents finding the minimum value; max represents finding the maximum value.
[0119] S10: Based on the normalized prediction condition number set For the set of predicted state covariances Processing is performed to obtain the set of region-normalized predicted state covariances.
[0120] In one embodiment, the region-normalized predicted state covariance set Obtained based on the following formula:
[0121]
[0122]
[0123]
[0124]
[0125]
[0126]
[0127] in, Let them represent the predicted state covariances updated at time k-γ+1, k-γ+2, ..., k-1, k respectively;
[0128] Let them represent the region-normalized predicted state covariance at times k-γ+1, k-γ+2, ..., k-1, k respectively.
[0129] S11: Utilizing the state prediction error set Normalized prediction state covariance set for the region Perform adaptive adjustment to obtain the adjusted set of predicted state covariance.
[0130] In one embodiment, the adjusted predicted state covariance set Obtained based on the following formula:
[0131]
[0132]
[0133] in, Represents the set of state prediction errors at time k; α and β represent forgetting factors; Let represent the set of regional normalized predicted state covariances at time k-1.
[0134] S12: Repeat S1-S11 continuously to obtain the predicted trajectory; wherein, the predicted state vector updated at each time step in S6 constitutes the predicted trajectory.
[0135] Finally, the prediction method of this invention was compared with eight other prediction methods (EKF, CKF, AUKF, ES-EKF48, LSTM-EKF, LPV-KF, SSGP-UKF, and MKF).
[0136] The final results show that the prediction method of this invention reduces the average lateral distance error to 3.72 meters, which is 13.29% lower than the other 8 prediction methods.
[0137] The prediction method of this invention reduces the average forward angle error to 22.8 degrees, which is 19.43% lower than the average forward angle error of the other 8 prediction methods.
[0138] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0139] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for predicting the trajectory of an extraterrestrial surface probe, characterized in that, Includes the following steps: S1: Obtain the actual state vector x of the extraterrestrial surface probe. k ; where x k Let k be an n*m dimensional state vector, where k represents time. S2: For the actual state vector x k Perform a traceless transformation to obtain the state vector set σ k ; S3: Transfer the state vector group σ k Input a nonlinear system and obtain the predicted state vector set σ k+1 ; S4: For the predicted state vector group σ k+1 The elements in the matrix are weighted and summed to obtain the predicted state vector. S5: Based on the predicted state vector group σ k+1 and the predicted state vector Obtain the predicted state covariance S6: Update the predicted state vector Obtain the updated predicted state vector Update the predicted state covariance Obtain the updated predicted state covariance S7: The updated predicted state covariance... Perform singular value decomposition to obtain the predicted feature diagonal matrix. S8: Based on the predicted feature diagonal matrix Calculate the prediction condition number S9: For the set of prediction condition numbers Normalization is performed to obtain the set of normalized prediction condition numbers. S10: Based on the normalized prediction condition number set For the set of predicted state covariances Processing is performed to obtain the set of region-normalized predicted state covariances. S11: Utilizing the state prediction error set Normalized prediction state covariance set for the region Perform adaptive adjustment to obtain the adjusted set of predicted state covariance. S12: Repeat S1-S11 continuously to obtain the predicted trajectory; wherein, the predicted state vector updated at each time step in S6 constitutes the predicted trajectory.
2. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 1, characterized in that, The predicted state vector Obtained based on the following formula: s k+1 ={σ i,k+1 },i=0,1...2n; Where, σ i,k+1 σ k+1 The i-th element in; σ represents time k+1 i,k+1 The weight.
3. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 2, characterized in that, The predicted state covariance Obtained based on the following formula: in, σ represents time k+1 i,k+1 The covariance weights; Q represents the process noise covariance matrix; T represents the transpose.
4. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 3, characterized in that, The updated predicted state vector Obtained based on the following formula: K k+1 =P zz,k+1 H T (HP zz,k+1 H T +R) -1 ; Among them, K k+1 Z represents the Kalman gain at time k+1; k+1 Let f represent the observation vector at time k+1; f represents the nonlinear function. This represents the set of state prediction errors at time k-1; Represents the set of region-normalized predicted state covariances at time k-2; This represents the set of region-normalized predicted state covariances at time k-1; P represents the state prediction error at times k-γ, k-γ+1, ..., k-2, k-1, respectively; zz,k+1 H represents the nonlinear transformation of the predicted state covariance; H represents the observation matrix; and R represents the observation noise covariance.
5. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 4, characterized in that, The updated state covariance Obtained based on the following formula: in, This represents the set of predicted state covariances adjusted at time k-1; Let them represent the adjusted predicted state covariance at times k-γ, k-γ+1, ..., k-2, k-1, respectively.
6. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 5, characterized in that, The prediction condition number Obtained based on the following formula: in, express The maximum singular value in; express The smaller singular values in the range are: u1, u2 ∈ [3, 6].
7. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 6, characterized in that, The set of normalized prediction condition numbers Obtained based on the following formula: in, Let k-γ+1, k-γ+2, ..., k-1, k represent the prediction condition numbers at time points k-γ+1, k-γ+2, ..., k-1, k respectively. Let represent the normalized prediction condition number at times k-γ+1, k-γ+2, ..., k-1, k respectively; min represents finding the minimum value; max represents finding the maximum value.
8. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 7, characterized in that, The region-normalized predicted state covariance set Obtained based on the following formula: in, Let them represent the predicted state covariances updated at time k-γ+1, k-γ+2, ..., k-1, k respectively; Let them represent the region-normalized predicted state covariance at times k-γ+1, k-γ+2, ..., k-1, k respectively.
9. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 8, characterized in that, The adjusted prediction state covariance set Obtained based on the following formula: in, Represents the set of state prediction errors at time k; α and β represent forgetting factors; Let represent the set of regional normalized predicted state covariances at time k-1.
10. The method for predicting the trajectory of an extraterrestrial surface probe according to claim 9, characterized in that: and The calculation formula is: Where λ represents the scaling factor; State vector group σ k Obtained based on the following formula: s k ={σ i,k },i=0,1...2n; in, This represents the true state covariance matrix at time k; express The i-th column; σ i,k σ k The i-th element in.
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