Robust filtering method for spacecraft attitude estimation under model uncertainty

Abstract

This invention discloses a robust filtering method for spacecraft attitude estimation under model uncertainty, comprising the following steps: Step 1, collecting output data from star sensors and gyroscopes during spacecraft operation and using them as quantities; Step 2, establishing a spacecraft attitude estimation system model with multiplication noise, unknown measurement interference, and correlation noise; Step 3, assuming that the state estimate at time k is an error variance upper bound of Ω. k|k‑1 The predicted gain J is calculated. k According to J k We obtain the one-step prediction estimate and the upper bound Ω of the prediction error variance. k+1|k Step 4: Based on the upper bound Ω of the prediction error variance k+1|k The filter gain K is calculated. k+1 According to K k+1 We obtain the state estimate and the upper bound of the error variance Ω. k+1|k+1 Step 5: Determine if the set system running time N has been reached. If k = N, then attitude estimation is complete, and the estimation result is output.

Description

Technical Field

[0001] This invention belongs to the technical field of spacecraft attitude estimation using robust filtering technology, and relates to a robust filtering method for spacecraft attitude estimation under model uncertainty. Background Technology

[0002] With the development of aerospace technology, we have increased our requirements for the accuracy of spacecraft attitude estimation, making spacecraft attitude estimation technology one of the key technologies in aerospace engineering. Researching how to improve the robustness of spacecraft attitude estimation systems in complex environments is crucial. The Extended Kalman Filter (EKF) has been successfully applied in the field of attitude estimation, and it is suitable for situations where the system model is known and the noise is additive. However, in practical applications, due to the complexity of the environment, multiplicative noise, unknown measurement interference, and correlated noise may be encountered. In such cases, the filtering performance of traditional EKF will decrease, or it may even fail to output correct attitude information.

[0003] Traditional Kalman filter design typically assumes that model noise is additive; however, multiplicative noise arises in practical applications. Unlike additive noise, multiplicative noise is state-coupled and can be viewed as a model uncertainty caused by unknown state variables. Traditional Kalman filters usually assume that model noise is uncorrelated Gaussian white noise. Due to the influence of complex environments, process noise and measurement noise may be correlated noise, and improper handling of correlated noise can reduce the accuracy of estimation. In addition to the above problems, phenomena such as jitter during spacecraft operation may lead to unknown measurement interference, which can also be regarded as a type of model uncertainty. The occurrence of these model uncertainties can seriously affect the accuracy of spacecraft attitude estimation, or even prevent the correct output of attitude information. These problems must be addressed to obtain ideal attitude estimation accuracy. Currently, robust filter designs for handling the above problems mainly focus on one or two model uncertainties. In practical applications, multiple model uncertainties often occur. Therefore, research on robust filters for multiplicative noise, unknown measurement interference, and correlated noise is of great significance. Summary of the Invention

[0004] In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a robust filtering method for spacecraft attitude estimation under model uncertainty, so as to improve the accuracy of spacecraft attitude estimation under multiplicative noise, unknown measurement interference and correlated noise environment.

[0005] To address the aforementioned technical problems, this invention provides a robust filtering method for spacecraft attitude estimation under model uncertainty, comprising:

[0006] Step 1: Collect the output data of the star sensor and gyroscope during spacecraft operation and use it as a measurement.

[0007] Step 2: Establish a spacecraft attitude estimation system model with multiplication noise, unknown measurement interference, and correlation noise;

[0008] Step 3: Assume the state estimate at k-1 is The upper bound of the error variance is Ω k|k-1 The predicted gain J is calculated. k According to J k Obtain one-step prediction estimate and the upper bound of the variance of the prediction error Ω k+1|k ;

[0009] Step 4: Based on the upper bound Ω of the prediction error variance k+1|k The filter gain K is calculated. k+1 According to K k+1 Obtain state estimate upper bound of error variance Ω k+1|k+1 ;

[0010] Step 5: Determine if the set system running time N has been reached. If k = N, then attitude estimation is complete, and the estimation result is output. If k < N, then return to step 3.

[0011] Furthermore, the spacecraft attitude estimation system model described in step 2 includes state equations and measurement equations, specifically:

[0012] Choose the attitude quaternion q k and gyroscope drift ρ k State vector The discrete-time state equation is:

[0013]

[0014] Where q = [q1, q2, q3, q4] T =[ρ, q4] T ; ζ represents the gyroscope's output angular rate; Δt represents the gyroscope's sampling time; v The noise of the gyroscope is measured, with a variance of Δtσ. v I 3×3 ;ζ v The noise is gyroscope drift, with variance Δtσ. u I 3×3 ; ω = [ω1, ω2, ω3] is the gyroscope's triangular rate output vector. w k Zero-mean Gaussian white noise, s = 3; ξik B is Gaussian white noise with zero mean and variance of 1; ik For a matrix of appropriate dimension,

[0015] The measurement equations for the three reference vectors are as follows:

[0016]

[0017] Where i = 1, 2, 3; Output vector for star sensor; The star sensor vector; Zero-mean Gaussian white noise, And w k and v k For related noise, E[g(x k )g T (x k )]≤Γ k ;φ i =[φ ix φ iy φ iz ] is the unknown measurement interference vector. ζ i =diag(ζ ix ζ ix ζ iy ζ iy ζ iz ζ iz ), Parameter τ ij For positive,

[0018] Furthermore, the prediction gain J is calculated in step 3. k According to J k Obtain one-step prediction estimate and the upper bound of the variance of the prediction error Ω k+1|k Specifically:

[0019]

[0020]

[0021] Where λ1 and θ1 are known positive numbers, G k and N k It is a known proportional matrix. Predicted gain J k satisfy:

[0022]

[0023] Furthermore, step 4 involves basing the prediction error variance on the upper bound Ω. k+1|k The filter gain K is calculated. k+1 According to K k+1 Obtain state estimate upper bound of error variance Ω k+1|k+1 Specifically:

[0024]

[0025]

[0026] Where λ² and θ² are known positive numbers, Where the filter gain K k+1 satisfy:

[0027]

[0028] Beneficial effects of this invention:

[0029] (1) This invention simultaneously considers the model uncertainty problem with multiplication noise, unknown measurement interference and correlation noise, and has obvious advantages compared with existing algorithms;

[0030] (2) To address the issues of multiplication noise, interference from unknown measurements, and correlated noise, a modeling and design of a spacecraft attitude estimation system was developed. The proposed method is applicable to other systems, such as robots, automotive systems, and sensors. Attached Figure Description

[0031] Figure 1 This is a comparison chart of the root mean square error of attitude angles between the invented RREKF and AEKF and REKF.

[0032] Figure 2 This is a comparison chart of attitude angle error results from a single independent experiment conducted by AEKF;

[0033] Figure 3 This is a comparison chart of attitude angle error results from a single independent experiment conducted by REKF.

[0034] Figure 4 This is a comparison chart of attitude angle error results from a single independent experiment using the invented RREKF.

[0035] Figure 5 This is a flowchart of the method of the present invention. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] Combination Figure 5This invention is a robust filtering method for spacecraft attitude estimation that considers multiplicative noise, correlated noise, and interference from unknown measurements, and includes the following parts:

[0038] 1. Collect the output data of star sensors and gyroscopes during spacecraft operation and use it as a measurement.

[0039] 2. Establish a spacecraft attitude estimation system model with multiplication noise, unknown measurement interference, and correlation noise;

[0040] 2.1 Equations of State

[0041] Choose the attitude quaternion q k and gyroscope drift ρ k State vector Based on the spacecraft's kinematic equations, the discrete-time state equations are established as follows:

[0042]

[0043] q = [q1, q2, q3, q4] T =[ρ, q4] T ; ζ represents the gyroscope's output angular rate; Δt represents the gyroscope's sampling time; v The noise of the gyroscope is measured, with a variance of Δtσ. v I 3×3 ;ζ v The noise is gyroscope drift, with variance Δtσ. u I 3×3 ; ω = [ω1, ω2, ω3] is the gyroscope's triangular rate output vector. w k Zero-mean Gaussian white noise, s = 3; ξ ik B is Gaussian white noise with zero mean and variance of 1; ik For a matrix of appropriate dimension,

[0044] 2.2 Measurement Equation

[0045] To obtain attitude information, a star sensor model with unknown interference and three reference vectors is selected as follows:

[0046]

[0047] Output vector for star sensor; The star sensor vector; Zero-mean Gaussian white noise, And w k and vk For related noise, E[g(x k )g T (x k )]≤Γ k ;φ i =[φ ix φ iy φ iz ] is the unknown measurement interference vector. ζ i =diag(ζ ix ζ ix ζ iy ζ iy ζ iz ζ iz ), Parameter τ ij For positive,

[0048] Three: Assume the state estimate at time k is... The upper bound of the error variance is Ω k|k-1

[0049] Two-step state prediction values ​​are:

[0050]

[0051] The predicted state value is:

[0052]

[0053] J k For predicting gain.

[0054] The state prediction error is:

[0055]

[0056] f(x) k ) and h(x k )exist Perform a Taylor series expansion at this point:

[0057]

[0058]

[0059] in G k and N k It is a known proportional matrix, β k and α k It is an unknown matrix that satisfies

[0060] Based on formulas (6) and (7), formula (5) can be further written as:

[0061]

[0062] The variance of the prediction error is:

[0063]

[0064] In the formula, λ1, τ1, and θ1 are known positive numbers.

[0065] According to formula (9), the upper bound of the prediction error variance is:

[0066]

[0067] The state estimate is:

[0068]

[0069] K k+1 This represents the filter gain.

[0070] The state estimation error is:

[0071]

[0072] h(x) k+1 )exist Perform a Taylor series expansion at this point:

[0073]

[0074] in It is a known proportional matrix. It is an unknown matrix that satisfies

[0075] According to formula (13), formula (12) can be further written as:

[0076]

[0077] The error variance is:

[0078]

[0079] In the formula, λ² and θ² are known positive numbers.

[0080] According to formula (15), the upper bound of the error variance is:

[0081]

[0082] Using the minimum variance theory, let and The optimal prediction gain and filter gain can be obtained:

[0083]

[0084]

[0085] 4. The prediction gain J is obtained according to equation (17). k Based on equations (3) and (4), the one-step prediction estimate is obtained. The upper bound Ω of the prediction error variance is obtained according to equation (10). k+1|k .

[0086] 5. Obtain the filter gain K according to equation (18) k+1 The state estimate is obtained according to equation (11). The upper bound Ω of the error variance is obtained according to equation (16). k+1|k+1 .

[0087] 6. The system runtime is N. If k = N, then attitude estimation is complete, and the estimation result is output. If k < N, then return to step four until the system finishes running.

[0088] The beneficial effects of this invention are described below:

[0089] The robust filtering method for spacecraft attitude estimation proposed in this invention was simulated using MATLAB software, and its estimation performance was compared with that of Additive Extended Kalman Filter (AEKF) and Robust Extended Kalman Filter (REKF). The simulation hardware environment consisted of an Intel(R) Core(TM) i7-10750H CPU (2.60GHz, 2.59GHz) and Windows 10 operating system. Figure 1-4 As shown, the proposed RREKF achieves the best estimation accuracy when the system model simultaneously exhibits multiplicative noise, correlated noise, and interference from unknown measurements. Since AEKF and REKF do not fully consider the impact of these model uncertainties on the system, their filtering effects are poor. The RREKF proposed in this invention maintains better estimation accuracy and robustness because the robust filter fully considers the impact of multiplicative noise, correlated noise, and interference from unknown measurements on the system during its design, demonstrating the effectiveness of our proposed robust filter.

[0090] Based on the following simulation conditions, a simulation experiment was conducted using MATLAB to demonstrate this method:

[0091] Simulation time: 1000s; Standard deviations of gyroscope measurement noise and gyroscope drift noise are respectively and The gyroscope sampling period is Δt = 1s; the angular velocity is set to ω = [-1 / (90 / (2π)×60), 0, 0] rad / s; the initial gyroscope drift is set to ρ = [0.1 0.1 0.1]. T ° / h; the standard deviation of the star sensor measurement noise is set to σ. s =0.005°; initial variance matrix is ​​set to P 0|0 =diag([(0.1°) 2 (0.1°) 2 (0.1°) 2 (0.2° / h) 2 (0.2° / h) 2 (0.2° / h) 2 The initial state estimate is set to x. 0|0 = [0 0 0 1 0 0 0]T; Since the star sensor has high precision, the linearization truncation error can be ignored, that is, let G k =0, N k =0 and The parameters are set as τ1=λ1=λ2=0.1 and θ1=θ2=0.0001; the correlation matrix between state noise and measurement noise is set as M. k =0.5I 3×9 ; a1 = 1, a2 = 0.005; τ ij =5″.

Claims

1. A robust RREKF filtering method for spacecraft attitude estimation under model uncertainty, characterized in that, include: Step 1: Collect the output data of the star sensor and gyroscope during spacecraft operation and use it as a measurement. Step 2: Establish a spacecraft attitude estimation system model with multiplication noise, unknown measurement interference, and correlation noise; The spacecraft attitude estimation system model includes state equations and measurement equations, specifically: Choose the attitude quaternion q k and gyroscope drift State vector The discrete-time state equation is: Where q = [q1, q2, q3, q4] T =[ρ,q4] T ; ζ represents the gyroscope's output angular rate; Δt represents the gyroscope's sampling time; v The noise of the gyroscope is measured, with a variance of Δtσ. v I 3×3 ;ζ v The noise is gyroscope drift, with variance Δtσ. u I 3×3 ; ω = [ω1, ω2, ω3] is the gyroscope's triangular speed output vector. w k Zero-mean Gaussian white noise, s = 3; ξ ik B is Gaussian white noise with zero mean and variance of 1; ik For a matrix of appropriate dimension, The measurement equations for the three reference vectors are as follows: Where i = 1, 2, 3; Output vector for star sensor; The star sensor vector; Zero-mean Gaussian white noise, And w k and v k For related noise, E[g(x k )g T (x k )]≤Γ k ;φ i =[φ ix φ iy φ iz ] is the unknown measurement interference vector. ζ i =diag(ζ ix ζ ix ζ iy ζ iy ζ iz ζ iz ), Parameter τ ij For positive, Step 3: Assume the state estimate at k-1 is The upper bound of the error variance is Ω k|k-1 The predicted gain J is calculated. k According to J k Obtain one-step prediction estimate and the upper bound of the variance of the prediction error Ω k+1|k ; Where λ1 and θ1 are known positive numbers, G k and N k It is a known proportional matrix. Predicted gain J k satisfy: Step 4: Based on the upper bound Ω of the prediction error variance k+1|k The filter gain K is calculated. k+1 According to K k+1 Obtain state estimate upper bound of error variance Ω k+1|k+1 ; Step 5. Determine whether the set system running time N is reached. If k = N, the attitude estimation is completed and the estimation result is output If k < N, return to Step 3 2. The RREKF robust filtering method for spacecraft attitude estimation under model uncertainty as described in claim 1, characterized in that: Step 4 describes the prediction error variance upper bound Ω. k+1|k The filter gain K is calculated. k+1 According to K k+1 Obtain state estimate upper bound of error variance Ω k+1|k+1 Specifically: Where λ² and θ² are known positive numbers, Where the filter gain K k+1 satisfy:

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