Extraterrestrial star catalogue detector movement track prediction method

Abstract

The invention discloses an extraterrestrial star catalogue detector movement track prediction method. The method comprises the following steps: carrying out unscented transformation on an actual state vector xk to obtain a state vector group sigma k; inputting the sigma k into a nonlinear system to obtain a prediction state vector set sigma k + 1; performing weighted summation on elements in the sigma < k + 1 > to obtain a prediction state vector # imgabs0 # based on the sigma < k + 1 > and # imgabs1 #, obtaining a prediction state covariance # imgabs2 # based on the sigma < k + 1 > and # imgabs1 #, updating # imgabs3 # to obtain an updated prediction state vector # imgabs4 #, updating # imgabs5 # to obtain an updated prediction state covariance # imgabs6 #, and performing singular value decomposition on # imgabs7 #; calculating a prediction condition number according to # imgabs9 # by # imgabs8 #, normalizing a prediction condition number set # imgabs11 # by # imgabs10 #, obtaining a normalized prediction condition number set # imgabs12 #, processing a prediction state covariance set # imgabs14 # on the basis of # imgabs13 #, obtaining a regional normalized prediction state covariance set # imgabs15 #, and performing adaptive adjustment on # imgabs17 # by using a state prediction error set # imgabs16 #; and obtaining an adjusted prediction state covariance set # imgabs18 #, and continuously repeating the steps to obtain a movement prediction trajectory. The prediction precision and the prediction stability can be improved.

Description

Technical Field

[0001] The present invention relates to the field of deep space exploration technology, and more specifically to a method for predicting the movement trajectory of an extraterrestrial planetary probe. Background Art

[0002] In the past, the prediction methods for the movement trajectory of extraterrestrial probes mainly improved the prediction method by improving the prediction matrix and adding control constraints. This is more effective for probes with determined orbits and can better estimate the speed, angle and position. However, for high-speed and irregularly moving probes on extraterrestrial surfaces, the telemetry acquired states have problems such as broken, false and asynchronous data, which reduces the prediction accuracy.

[0003] Therefore, how to provide a method for predicting the movement trajectory of an extraterrestrial probe that can improve prediction accuracy and prediction stability is an urgent problem that technical personnel in this field need to solve. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a method for predicting the movement trajectory of an extraterrestrial probe.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for predicting the movement trajectory of an extraterrestrial probe comprises the following steps:

[0007] S1: Get the actual state vector x of the extraterrestrial star detector k ; where x k is a state vector of n*m dimensions, k represents the time;

[0008] S2: the actual state vector x k Perform unscented transformation to obtain the state vector group σ k ;

[0009] S3: The state vector group σ k Input the nonlinear system and obtain the predicted state vector group σ k+1 ;

[0010] S4: the predicted state vector group σ k+1 The elements in are weighted summed to obtain the predicted state vector

[0011] S5: Based on the predicted state vector group σ k+1 and the predicted state vector Get the predicted state covariance

[0012] S6: Update the predicted state vector Get the updated predicted state vector

[0013] Update the predicted state covariance Get the updated predicted state covariance

[0014] S7: Update the predicted state covariance Perform singular value decomposition to obtain the predicted feature diagonal matrix

[0015] S8: According to the predicted feature diagonal matrix Calculate the forecast condition number

[0016] S9: Set of predicted condition numbers Normalize and obtain the normalized prediction condition number set

[0017] S10: Based on the normalized prediction condition number set Forecast state covariance set Processing is performed to obtain the regional normalized prediction state covariance set

[0018] S11: Using the state prediction error set Normalize the predicted state covariance set for the region Perform adaptive adjustment to obtain the adjusted predicted state covariance set

[0019] S12: Continuously repeat S1-S11 to obtain a movement prediction trajectory; wherein the prediction state vector updated at each moment in S6 constitutes the movement prediction trajectory.

[0020] Preferably, the predicted state vector Based on the following formula:

[0021]

[0022] σ k+1 ={σ i,k+1}, i = 0, 1...2n;

[0023] Among them, σ i,k+1 Represents σ k+1 The i-th element in ; represents k+1 time σ i,k+1 The weight of .

[0024] Preferably, the predicted state covariance Based on the following formula:

[0025]

[0026] in, represents k+1 time σ i,k+1 The covariance weight of ; Q represents the process noise covariance matrix; T represents the transpose.

[0027] Preferably, the updated predicted state vector Based on the following formula:

[0028]

[0029]

[0030] Among them, K k+1 represents the Kalman gain at time k+1; z k+1 represents the observation vector at time k+1; f represents a nonlinear function; represents the state prediction error set at time k-1; Represents the regional normalized forecast state covariance set at time k-2; represents the regional normalized prediction state covariance set at time k-1; represents the state prediction error at time k-γ, k-γ+1, ..., k-2, k-1 respectively; P zz,k+1 represents the nonlinear transformation of the predicted state covariance; H represents the observation matrix; R represents the observation noise covariance.

[0031] Preferably, the updated state covariance Based on the following formula:

[0032]

[0033]

[0034] in, represents the set of predicted state covariances adjusted at time k-1;

[0035] They represent the adjusted predicted state covariance at time k-γ, k-γ+1, ..., k-2, and k-1 respectively.

[0036] Preferably, the prediction condition number Based on the following formula:

[0037]

[0038] in, express The maximum singular value in ; express The singular values ​​in are small values; u1,u2∈[3,6].

[0039] Preferably, the normalized prediction condition number set Based on the following formula:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] in, represents the prediction condition number at time k-γ+1, k-γ+2, ..., k-1, k respectively; They represent the normalized prediction condition numbers at time points k-γ+1, k-γ+2, ..., k-1, and k respectively; min means finding the minimum value; and max means finding the maximum value.

[0047] Preferably, the regional normalized predicted state covariance set Based on the following formula:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] in, denote the predicted state covariance after being updated at time k-γ+1, k-γ+2, ..., k-1, k respectively;

[0055] They represent the regional normalized predicted state covariance at time k-γ+1, k-γ+2, ..., k-1, k respectively.

[0056] Preferably, the adjusted predicted state covariance set Based on the following formula:

[0057]

[0058]

[0059] in, represents the state prediction error set at time k; α and β represent the forgetting factors; Represents the regional normalized forecast state covariance set at time k-1.

[0060] Preferably, and The calculation formula is:

[0061]

[0062]

[0063] Among them, λ represents the scale factor;

[0064] Preferably, the state vector set σ k Based on the following formula:

[0065]

[0066] σ k ={σ i,k}, i = 0, 1...2n;

[0067] Among them, P xk Represents the true state covariance matrix at time k; express The i-th column of i,k Represents σ k The i-th element in .

[0068] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for predicting the movement trajectory of an extraterrestrial probe, which can improve prediction accuracy and prediction stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0070] Figure 1A flow chart of a method for predicting the movement trajectory of an extraterrestrial planet probe provided by the present invention. DETAILED DESCRIPTION

[0071] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0072] like Figure 1 As shown, an embodiment of the present invention discloses a method for predicting the movement trajectory of an extraterrestrial probe, comprising the following steps:

[0073] S1: Get the actual state vector x of the extraterrestrial star detector k ; where x k is a state vector of n*m dimensions, k represents the time;

[0074] S2: the actual state vector x k Perform unscented transformation to obtain the state vector group σ k ;

[0075] In one embodiment, the state vector set σ k Based on the following formula:

[0076]

[0077] σ k ={σ i,k}, i = 0, 1...2n;

[0078] Among them, P xk Represents the true state covariance matrix at time k; express The i-th column of i,k Represents σ k The i-th element in ; λ represents the scaling factor.

[0079] S3: The state vector group σ k Input the nonlinear system and obtain the predicted state vector group σ k+1 ;

[0080] Specific: k+1 =f(σ k ,u k ,w k ), where u k represents the control input; w krepresents the process noise assumed to be Gaussian distributed, and f represents the nonlinear function.

[0081] S4: the predicted state vector group σ k+1 The elements in are weighted summed to obtain the predicted state vector

[0082] In one embodiment, the predicted state vector Based on the following formula:

[0083]

[0084] σ k+1 ={σ i,k+1}, i = 0, 1...2n;

[0085]

[0086] Among them, σ i,k+1 Represents σ k+1 The i-th element in ; represents k+1 time σ i,k+1 The weight of .

[0087] S5: Based on the predicted state vector group σ k+1 and the predicted state vector Get the predicted state covariance

[0088] In one embodiment, the predicted state covariance Based on the following formula:

[0089]

[0090]

[0091] in, represents k+1 time σ i,k+1 The covariance weight of ; Q represents the process noise covariance matrix; T represents the transpose.

[0092] S6: Update the predicted state vector Get the updated predicted state vector

[0093] In one embodiment, the updated predicted state vector Based on the following formula:

[0094]

[0095]

[0096]

[0097]

[0098] Among them, K k+1 represents the Kalman gain at time k+1; z k+1 represents the observation vector at time k+1; f represents a nonlinear function; represents the state prediction error set at time k-1; Represents the regional normalized forecast state covariance set at time k-2; represents the regional normalized prediction state covariance set at time k-1; represents the state prediction error at time k-γ, k-γ+1, ..., k-2, k-1 respectively; P zz,k+1 represents the nonlinear transformation of the predicted state covariance; H represents the observation matrix; R represents the observation noise covariance.

[0099] Update the predicted state covariance Get the updated predicted state covariance

[0100] In one embodiment, the updated state covariance Based on the following formula:

[0101]

[0102]

[0103] in, represents the set of predicted state covariances adjusted at time k-1;

[0104] They represent the adjusted predicted state covariance at time k-γ, k-γ+1, ..., k-2, and k-1 respectively.

[0105] S7: Update the predicted state covariance Perform singular value decomposition to obtain the predicted feature diagonal matrix

[0106] S8: According to the predicted feature diagonal matrix Calculate the forecast condition number

[0107] In one embodiment, the prediction condition number C xk,k+1 Based on the following formula:

[0108]

[0109] in, express The maximum singular value in ; express The singular values ​​in are small values; u1,u2∈[3,6].

[0110] S9: Set of predicted condition numbers Normalize and obtain the normalized prediction condition number set

[0111] In one embodiment, the normalized prediction condition number set Based on the following formula:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] in, represents the prediction condition number at time k-γ+1, k-γ+2, ..., k-1, k respectively; They represent the normalized prediction condition numbers at time points k-γ+1, k-γ+2, ..., k-1, and k respectively; min means finding the minimum value; and max means finding the maximum value.

[0119] S10: Based on the normalized prediction condition number set Forecast state covariance set Processing is performed to obtain the regional normalized prediction state covariance set

[0120] In one embodiment, the regional normalized predicted state covariance set Based on the following formula:

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] in, denote the predicted state covariance after being updated at time k-γ+1, k-γ+2, ..., k-1, k respectively;

[0128] They represent the regional normalized predicted state covariance at time k-γ+1, k-γ+2, ..., k-1, k respectively.

[0129] S11: Using the state prediction error set Normalize the predicted state covariance set for the region Perform adaptive adjustment to obtain the adjusted predicted state covariance set

[0130] In one embodiment, the adjusted predicted state covariance set Based on the following formula:

[0131]

[0132]

[0133] in, represents the state prediction error set at time k; α and β represent the forgetting factors; Represents the regional normalized forecast state covariance set at time k-1.

[0134] S12: Continuously repeat S1-S11 to obtain a movement prediction trajectory; wherein the prediction state vector updated at each moment in S6 constitutes the movement prediction trajectory.

[0135] Finally, the prediction method of the present invention was compared with other eight 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 the present invention reduces the average lateral distance error to 3.72 meters, which is 13.29% lower than that of the other eight prediction methods.

[0137] The prediction method of the present invention reduces the average forward angle error to 22.8 degrees, which is 19.43% lower than that of the other eight prediction methods.

[0138] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0139] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one 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 present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the movement trajectory of an extraterrestrial probe, characterized in that: The following steps are involved: S1: Get the actual state vector x of the extraterrestrial star detector k ; where x k is a state vector of n*m dimensions, k represents the time; S2: the actual state vector x k Perform unscented transformation to obtain the state vector group σ k ; S3: The state vector group σ k Input the nonlinear system and obtain the predicted state vector group σ k+1 ; S4: the predicted state vector group σ k+1 The elements in are weighted summed to obtain the predicted state vector S5: Based on the predicted state vector group σ k+1 and the predicted state vector Get the predicted state covariance S6: Update the predicted state vector Get the updated predicted state vector Update the predicted state covariance Get the updated predicted state covariance S7: Update the predicted state covariance Perform singular value decomposition to obtain the predicted feature diagonal matrix S8: According to the predicted feature diagonal matrix Calculate the forecast condition number S9: Set of predicted condition numbers Normalize and obtain the normalized prediction condition number set S10: Based on the normalized prediction condition number set Forecast state covariance set Processing is performed to obtain the regional normalized prediction state covariance set S11: Using the state prediction error set Normalize the predicted state covariance set for the region Perform adaptive adjustment to obtain the adjusted predicted state covariance set S12: Continuously repeat S1-S11 to obtain a movement prediction trajectory; wherein the prediction state vector updated at each moment in S6 constitutes the movement prediction trajectory.

2. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 1, characterized in that: The predicted state vector Based on the following formula: s k+1 ={σ i,k+1 },i=0,1...2n; Among them, σ i,k+1 Represents σ k+1 The i-th element in ; represents k+1 time σ i,k+1 The weight of .

3. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 2, characterized in that: The predicted state covariance Based on the following formula: in, represents k+1 time σ i,k+1 The covariance weight of ; Q represents the process noise covariance matrix; T represents the transpose.

4. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 3, characterized in that: The updated prediction state vector 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 represents the Kalman gain at time k+1; z k+1 represents the observation vector at time k+1; f represents a nonlinear function; represents the state prediction error set at time k-1; Represents the regional normalized forecast state covariance set at time k-2; Represents the regional normalized prediction state covariance set at time k-1; represents the state prediction error at time k-γ, k-γ+1, ..., k-2, k-1 respectively; P zz,k+1 represents the nonlinear transformation of the predicted state covariance; H represents the observation matrix; R represents the observation noise covariance.

5. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 4, characterized in that: The updated state covariance Based on the following formula: in, represents the set of predicted state covariances adjusted at time k-1; They represent the adjusted predicted state covariance at time k-γ, k-γ+1, ..., k-2, and k-1 respectively.

6. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 5, characterized in that: The prediction condition number Based on the following formula: in, express The maximum singular value in ; express The singular values ​​in are small values; u1,u2∈[3,6].

7. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 6, characterized in that: The normalized prediction condition number set Based on the following formula: in, represents the prediction condition number at time k-γ+1, k-γ+2, ..., k-1, k respectively; They represent the normalized prediction condition numbers at time points k-γ+1, k-γ+2, ..., k-1, and k respectively; min means finding the minimum value; and max means finding the maximum value.

8. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 7, characterized in that: The regional normalized prediction state covariance set Based on the following formula: in, denote the predicted state covariance after being updated at time k-γ+1, k-γ+2, ..., k-1, k respectively; They represent the regional normalized predicted state covariance at time k-γ+1, k-γ+2, ..., k-1, k respectively.

9. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 8, characterized in that: The adjusted predicted state covariance set Based on the following formula: in, represents the state prediction error set at time k; α and β represent the forgetting factors; Represents the regional normalized forecast state covariance set at time k-1.

10. The method for predicting the movement trajectory of an extraterrestrial probe according to claim 9, characterized in that: and The calculation formula is: Among them, λ represents the scale factor; The state vector group σ k Based on the following formula: s k ={σ i,k },i=0,1...2n; in, Represents the true state covariance matrix at time k; express The i-th column of i,k Represents σ k The i-th element in .

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