Large misalignment angle alignment method of strapdown inertial navigation system based on variational Bayesian filtering

Abstract

The invention belongs to the technical field of inertial navigation, and particularly relates to a large misalignment angle alignment method for a strapdown inertial navigation system based on variational Bayesian filtering. Firstly, the uncertainty of the strapdown inertial navigation system alignment environment is fully considered, and the system state noise and measurement noise are modeled by using a T distribution with a thick-tail characteristic. Then, the Nataf transformation is used to realize the conversion of the original state space into an independent standard normal space, so as to avoid the interference of data correlation in the original state space. Finally, a sparse grid method and a variational Bayesian learning method are combined to realize navigation state estimation, so as to solve the problem that the robustness of a traditional filtering algorithm decreases due to various large error sources in the self-alignment of the strapdown inertial navigation system.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, and in particular relates to a large misalignment angle alignment method of a strapdown inertial navigation system based on variational Bayesian filtering. Background Art

[0002] Modern warfare requires tactical weapons to have rapid response capabilities, and the response efficiency of tactical weapons depends largely on the initial alignment capability of the inertial navigation system. Error propagation model and filtering algorithm are two important issues in the study of initial alignment of strapdown inertial navigation systems.

[0003] In the classic small misalignment angle error model, a small disturbance is usually given to the strapdown inertial navigation system equation to represent the impact of the error factor, thereby deriving a set of linear differential equation error models. The Chinese invention patent with publication number CN109931957A, published on June 25, 2019, "Self-alignment method of SINS strapdown inertial navigation system based on LGMKF", uses Lie group differential equations to establish a linear alignment filter model and improves the alignment accuracy; the Chinese invention patent with publication number CN112857398A, published on May 28, 2021, "A method for rapid initial alignment of ships in a moored state", improves the initial error propagation model and improves the alignment accuracy compared with the traditional error propagation model. The above technology is effective under the assumption that various error sources are small. With the improvement of the application requirements of inertial systems, initial alignment under large misalignment angles is the most representative, and with the development of research on nonlinear filtering estimation technology, the research on strapdown inertial navigation system error models is no longer limited to linear models. The Chinese invention patent with publication number CN107479076B published on August 8, 2017, "A Joint Filtering Initial Alignment Method under a Moving Base", adjusts the error propagation model and filtering algorithm according to the size of the misalignment angle, realizes the adaptive switching of the unscented Kalman filter and the linear Kalman filter algorithm, and shortens the alignment time. The above technologies improve the accuracy of the initial self-alignment and shorten the self-alignment time by improving the error propagation model and filtering algorithm, but they are all based on the Gaussian noise assumption. In fact, since the carrier movement is disturbed by factors such as vibration and temperature, the statistical characteristics of the system noise are often unknown or disturbed by wild values. The Gaussian noise assumption may make it difficult for the transfer alignment filtering algorithm to converge.

[0004] With the increasing uncertainty of the combat environment in modern warfare, a more robust initial self-alignment technique is needed to deal with the problem of unknown or time-varying statistical characteristics of noise. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] The technical problem to be solved by the present invention is: in view of the shortcomings of the prior art, how to provide a strapdown inertial navigation system large loss angle alignment method based on variational Bayesian filtering to improve the robustness of the strapdown inertial navigation system self-alignment.

[0007] (II) Technical solution

[0008] In order to solve the above technical problems, the present invention provides a strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering, the method comprising the following steps:

[0009] Step 1: Collect the angular velocity ω output by the gyroscope and accelerometer b and acceleration f b , and then establish the nonlinear error equation;

[0010] Step 2: Considering environmental uncertainty, the student-t distribution with thick tail characteristics is used to characterize the state noise and measurement noise of the system model, and the probability density function of the state and measurement is obtained;

[0011] Step 3: Since it is difficult to obtain a closed-form solution for the maximum likelihood estimation of the student-t distribution, a variational Bayesian learning method is used to obtain the unknown parameters that characterize the statistical characteristics of the state vector and the measurement vector;

[0012] Step 4: Use Nataf transformation to transform the original state space into an independent standard normal space;

[0013] Step 5: Use the sparse grid method to perform navigation state estimation with nonlinear Kalman filtering.

[0014] Wherein, in the step 2, the state noise and measurement noise of the system model are characterized by using the student-t distribution with a thick tail characteristic to obtain the probability density function of the state and the measurement, including the following steps:

[0015] Step 2-1, based on the nonlinear error equation of the strapdown inertial navigation system, establish the state equation for large misalignment angle alignment:

[0016] x k =f(x k-1 )+g(x k-1 ) k-1

[0017] in, represents the n-dimensional state vector at time k, including the misalignment angle Speed ​​error Gyroscope drift ε b =[ε x ,ε y ,ε z], accelerometer bias f(·) and g(·) are known nonlinear functions, They represent the n-dimensional system noise vector, and their covariance matrix is ​​Q k ;

[0018] Step 2-2, using the velocity error of the strapdown inertial navigation system as the observed quantity, establish the measurement equation for large misalignment angle alignment:

[0019] z k =H k x k +o k

[0020] in, represents the m-dimensional measurement vector at time k, H k is the measurement matrix, o k is the speed error noise, and its covariance matrix R k ;

[0021] Step 2-3, use Q k and R k represents the noise w k and k The covariance matrix of k and k represents the noise w k and v k degrees of freedom, and obtain the probability density function p(x k |x k-1 ) and p(z k |x k ):

[0022]

[0023] Wherein, in step 3, the unknown parameters characterizing the statistical characteristics of state noise and measurement noise are obtained by using a variational Bayesian learning method, including the following steps:

[0024] Step 3-1, replace p(x k |x k-1 ) and p(z k |x k ) are converted into the following integral forms:

[0025]

[0026] Where N(x|μ,∑) is a Gaussian distribution with mean μ and variance ∑, and Gamma(λ|a,b) is a gamma distribution with shape parameter a and scale parameter b.

[0027] Step 3-2, characterize Q using Wishartf distribution k and R k Prior distribution of :

[0028] Q k ~IW(Q k |u0,U0), R k ~IW(R k |c0,C0)

[0029] Among them, u0 and c0 are free parameters, U0 and C0 are inverse scaling matrices;

[0030] Step 3-3, based on Bayesian theory, establish the joint posterior distribution of unknown parameters and navigation state: p(Θ,z k |Ψ,x k-1 ), where Θ = {x k ,Q k ,R k ,ξ k ,λ k},Ψ={u0,U0,c0,C0,ω k ,v k};

[0031] Step 3-4, use the conjugate function q(Θ) to approximate x k ,Q k ,R k ,ξ k ,λ k The approximate posterior distribution of :

[0032] q(Θ)=q(x k )q(Q k )q(R k )q(ξ k )q(λ k );

[0033] Step 3-5, use the expected maximum algorithm to get the expected term

[0034] Wherein, in step 4, the Nataf transformation is used to realize the conversion of the original state space into the independent standard normal space, including the following steps:

[0035] Step 4-1: Establish according to Copula theory The joint probability density function p(x k ) and the marginal probability density function p i (w k,i ) are as follows:

[0036]

[0037] in represents a standard normal random variable, φ(r|ρ) represents the joint probability density function of r, and ρ represents the correlation coefficient matrix;

[0038] Step 4-2, perform Choleskey decomposition on the correlation coefficient matrix ρ: ρ = LL T ;

[0039] Step 4-3, obtain the Jacobian matrix transformed from the original space to the standard normal space:

[0040]

[0041] Wherein, in said step 5, the navigation state estimation of nonlinear Kalman filtering is performed using a sparse grid method, comprising the following steps:

[0042] Step 5-1, initialize the state variable x0, covariance matrix P0, standard deviation vector σ0 and correlation coefficient matrix ρ0:

[0043] Step 5-2, the sparse grid method generates the integration points u in the standard normal space l and integral weight w l , l=1,…,N;

[0044] Step 5-3, time update;

[0045] Step 5-4, measurement update;

[0046] Step 5-5, output the results.

[0047] Wherein, in step 5-3, the time updating process includes the following steps:

[0048] Step 5-3-1, navigation status prediction:

[0049] χ k|k-1,l =f(L k-1 u l ·σ k-1 +x k-1 )

[0050]

[0051] Where, L k-1 is the correlation coefficient matrix ρ k-1 Perform Choleskey decomposition on the lower triangular matrix;

[0052] Step 5-3-2, mean square error matrix prediction:

[0053]

[0054] Wherein, in step 5-4, the measurement update process includes the following steps:

[0055] Step 5-4-1, calculate the gain matrix:

[0056]

[0057] Step 5-4-2, use the measurement information to correct the navigation state and update its covariance matrix:

[0058]

[0059]

[0060] Step 5-4-3, calculate the correlation coefficient matrix:

[0061]

[0062] Among them, in the step 5-5, the output result includes and P k , update k=k+1 and enter the next filtering update.

[0063] (III) Beneficial effects

[0064] Compared with the prior art, the present invention provides a strapdown inertial navigation system large loss angle alignment method based on variational Bayesian filtering, which can improve the robustness of the strapdown inertial navigation system self-alignment. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Schematic diagram of large misalignment angle alignment based on variational Bayesian filtering;

[0066] Figure 2 Schematic diagram of the transformation relationship between the ideal coordinate system (n system) and the actual carrier platform coordinate system (n' system). DETAILED DESCRIPTION

[0067] In order to make the purpose, content, and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below in conjunction with the accompanying drawings and examples.

[0068] In order to solve the above technical problems, the present invention provides a strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering, the method comprising the following steps:

[0069] Step 1: Collect the angular velocity ω output by the gyroscope and accelerometer b and acceleration f b , and then establish the nonlinear error equation;

[0070] Step 2: Considering environmental uncertainty, the student-t distribution with thick tail characteristics is used to characterize the state noise and measurement noise of the system model, and the probability density function of the state and measurement is obtained;

[0071] Step 3: Since it is difficult to obtain a closed-form solution for the maximum likelihood estimation of the student-t distribution, a variational Bayesian learning method is used to obtain the unknown parameters that characterize the statistical characteristics of the state vector and the measurement vector;

[0072] Step 4: Use Nataf transformation to transform the original state space into an independent standard normal space;

[0073] Step 5: Use the sparse grid method to perform navigation state estimation with nonlinear Kalman filtering.

[0074] Wherein, in the step 2, the state noise and measurement noise of the system model are characterized by using the student-t distribution with a thick tail characteristic to obtain the probability density function of the state and the measurement, including the following steps:

[0075] Step 2-1, based on the nonlinear error equation of the strapdown inertial navigation system, establish the state equation for large misalignment angle alignment:

[0076] x k =f(x k-1 )+g(x k-1 ) k-1

[0077] in, represents the n-dimensional state vector at time k, including the misalignment angle Speed ​​error Gyroscope drift ε b =[ε x ,ε y ,ε z ], accelerometer bias f(·) and g(·) are known nonlinear functions, They represent the n-dimensional system noise vector, and their covariance matrix is ​​Q k ;

[0078] Step 2-2, using the velocity error of the strapdown inertial navigation system as the observed quantity, establish the measurement equation for large misalignment angle alignment:

[0079] z k =H k x k +o k

[0080] in, represents the m-dimensional measurement vector at time k, H k is the measurement matrix, o k is the speed error noise, and its covariance matrix R k ;

[0081] Step 2-3, use Q k and R k represents the noise w k and k The covariance matrix of k and k represents the noise w k and v k degrees of freedom, and obtain the probability density function p(x k |x k-1 ) and p(z k |x k ):

[0082]

[0083] Wherein, in step 3, the unknown parameters characterizing the statistical characteristics of state noise and measurement noise are obtained by using a variational Bayesian learning method, including the following steps:

[0084] Step 3-1, replace p(x k |x k-1 ) and p(z k |x k ) are converted into the following integral forms:

[0085]

[0086] Where N(x|μ,∑) is a Gaussian distribution with mean μ and variance ∑, and Gamma(λ|a,b) is a gamma distribution with shape parameter a and scale parameter b.

[0087] Step 3-2, characterize Q using Wishartf distribution k and R k Prior distribution of :

[0088] Q k ~IW(Q k |u0,U0), R k ~IW(R k |c0,C0)

[0089] Among them, u0 and c0 are free parameters, U0 and C0 are inverse scaling matrices;

[0090] Step 3-3, based on Bayesian theory, establish the joint posterior distribution of unknown parameters and navigation state: p(Θ,z k |Ψ,x k-1), where Θ = {x k ,Q k ,R k ,ξ k ,λ k},Ψ={u0,U0,c0,C0,ω k ,v k};

[0091] Step 3-4, use the conjugate function q(Θ) to approximate x k ,Q k ,R k ,ξ k ,λ k The approximate posterior distribution of :

[0092] q(Θ)=q(x k )q(Q k )q(R k )q(ξ k )q(λ k );

[0093] Step 3-5, use the expected maximum algorithm to get the expected item

[0094] Wherein, in step 4, the Nataf transformation is used to realize the conversion of the original state space into the independent standard normal space, including the following steps:

[0095] Step 4-1: Establish according to Copula theory The joint probability density function p(x k ) and the marginal probability density function p i (w k,i ) are as follows:

[0096]

[0097] in represents a standard normal random variable, φ(r|ρ) represents the joint probability density function of r, and ρ represents the correlation coefficient matrix;

[0098] Step 4-2, perform Choleskey decomposition on the correlation coefficient matrix ρ: ρ = LL T ;

[0099] Step 4-3, obtain the Jacobian matrix transformed from the original space to the standard normal space:

[0100]

[0101] Wherein, in said step 5, the navigation state estimation of nonlinear Kalman filtering is performed using a sparse grid method, comprising the following steps:

[0102] Step 5-1, initialize the state variable x0, covariance matrix P0, standard deviation vector σ0 and correlation coefficient matrix ρ0:

[0103] Step 5-2, the sparse grid method generates the integration points u in the standard normal space l and integral weight w l , l=1,…,N;

[0104] Step 5-3, time update;

[0105] Step 5-4, measurement update;

[0106] Step 5-5, output the results.

[0107] Wherein, in step 5-3, the time updating process includes the following steps:

[0108] Step 5-3-1, navigation status prediction:

[0109] X k|k-1,l =f(L k-1 u l ·σ k-1 +x k-1 )

[0110]

[0111] Where, L k-1 is the correlation coefficient matrix ρ k-1 Perform Choleskey decomposition on the lower triangular matrix;

[0112] Step 5-3-2, mean square error matrix prediction:

[0113]

[0114] Wherein, in step 5-4, the measurement update process includes the following steps:

[0115] Step 5-4-1, calculate the gain matrix:

[0116]

[0117] Step 5-4-2, use the measurement information to correct the navigation state and update its covariance matrix:

[0118]

[0119] Step 5-4-3, calculate the correlation coefficient matrix:

[0120]

[0121] Among them, in the step 5-5, the output result includes and P k , update k=k+1 and enter the next filtering update.

[0122] Example 1

[0123] The core content of this embodiment is a strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering, combined with Figure 1 , including the following 5 stages:

[0124] Phase 1: Collecting the angular velocity ω output by the gyroscope and accelerometer b and acceleration f b Then the nonlinear error equation is established.

[0125] (1) Establish the attitude matrix differential equation, velocity differential equation and position differential equation:

[0126]

[0127]

[0128] The operator V× represents the antisymmetric matrix formed by the vector V. and p = {L, λ, h} represent the navigation coordinate system velocity (“northeast” direction) and position (latitude, longitude and altitude), respectively. M and R N are the curvature radii of the local meridian and meridian respectively, It represents the attitude matrix of the carrier system (b system) relative to the navigation coordinate system (n system), is the angular velocity of the carrier coordinate system relative to the navigation coordinate system:

[0129]

[0130] In the above formula, g n =[0,0,-g], g and ω ie They are the local gravitational acceleration and the angular velocity of the Earth's rotation.

[0131] (2) Assume that the angular velocity of the actual carrier platform coordinate system (n' system) relative to the ideal coordinate system (n system) is The misalignment angle can be obtained and The relationship is:

[0132]

[0133] Among them are,

[0134]

[0135] (3) Considering gyro measurement error as well as The calculation error of get The expression is:

[0136]

[0137] in The transformation matrix from n system to n' system is:

[0138]

[0139]

[0140] Substituting equation (8) into equation (6) yields the nonlinear attitude error equation expressed by the large misalignment angle:

[0141]

[0142] (4) Considering the difference between the actual velocity value and the calculated value, as well as the influence of accelerometer measurement error, position error, and attitude error on the velocity solution result, the real velocity navigation solution result is obtained:

[0143]

[0144] in, δf b is the accelerometer measurement error. By subtracting equation (11) from equation (2), we get the velocity error equation:

[0145]

[0146] Among them, the error term and Specifically expressed as:

[0147]

[0148] Since the latitude error δL and the height error δh are small, and there is and Established, equations (13) and (14) are simplified into linear equations about the error, namely:

[0149]

[0150] in,

[0151] (5) Considering the difference between the true position value and the calculated value in equation (3), the position error differential equation is obtained:

[0152]

[0153] in,

[0154] (6) Assuming gyro measurement error Mainly due to the constant drift error ε b and zero-mean Gaussian white noise Composition, accelerometer measurement error δf b Mainly due to the constant bias error and zero-mean Gaussian white noise At the same time, the process of converting the Euler platform error angle to velocity error and then to position error is a "simple direct accumulation" process. Therefore, the attitude error differential equation does not contain velocity error and position error information, and the velocity error differential equation does not contain position error information. The following four vector equations are established:

[0155]

[0156] Phase 2: Considering environmental uncertainty, the student-t distribution with thick tail characteristics is used to characterize the state noise and measurement noise of the system model, and the probability density function of the state and measurement is obtained.

[0157] (1) Let the state vector Noise Vector The equation of state for large misalignment angle alignment is established:

[0158] x k =f(x k-1 )+g(x k-1 ) k-1 (twenty four)

[0159] Among them, f(x k-1 ) and g(x k-1 ) is expressed in terms of formulas (20) to (23);

[0160] (2) With v n As the observed quantity, the measurement equation for large misalignment angle alignment is established:

[0161] z k =H k x k +o k (25)

[0162] Among them, z k =v n , H k=[0 1×3 I 1×3 0 1×6 ] T is the measurement matrix, is the noise of velocity error;

[0163] (3) Use Q k and R k They represent the state noise w k and measurement noise k The covariance matrix of k and k They represent the state noise w k and measurement noise k degrees of freedom, and obtain the probability density function p(x k |x k-1 ) and p(z k |x k ):

[0164]

[0165] p(x k |x k-1 ) and p(z k |x k )The thickness of the tail end is determined by the degree of freedom parameters ω and v respectively. When ω and v = 1, it is a Cauchy distribution, and when ω→∞ and v→∞, it converges to a Gaussian distribution.

[0166] Phase 3: Use variational Bayesian learning methods to obtain unknown parameters that characterize the statistical characteristics of the state vector and the measurement vector.

[0167] (1) Since it is difficult to obtain a closed-form solution for the maximum likelihood estimation of the student-t distribution, we can use p(x k |x k-1 ) and p(z k |x k ) are converted into the following integral forms:

[0168]

[0169] Where N(x|μ,∑) is the Gaussian distribution probability density function with mean μ and variance ∑:

[0170]

[0171] Gamma(λ|a,b) is the probability density function of the gamma distribution with shape parameter a and scale parameter b:

[0172]

[0173] (2) Characterizing Q using Wishartf distribution k and R k Prior distribution of :

[0174]

[0175] Q k ~IW(Q k |u0,U0), R k ~IW(R k |c0,C0), where u0 and c0 are free parameters, U0 and C0 are inverse scaling matrices, Γ n (·) and Γ m (·) denote the gamma function with n and m degrees of freedom, respectively.

[0176] (3) Combining equations (28) to (31), we can obtain the unknown parameters and observed quantities z k The joint probability density function of is:

[0177]

[0178] where Θ = {x k ,Q k ,R k ,ξ k ,λ k},ψ={u0,U0,a0,b0,ω,υ}.

[0179] (4) According to Bayesian theory, the posterior probability density function of the unknown parameters is obtained:

[0180]

[0181] Since the observation at time k is independent of the measurement at any previous time, then p(z k |ψ,ψ) can be expressed as p(z k |Θ), the above formula can be further expressed as:

[0182]

[0183] (5) Use the conjugate function q(Θ) to approximate x k ,Q k ,R k ,ξ k ,λ k The approximate posterior distribution p(Θ|Ψ,x k-1 ). First, the logarithmic marginal likelihood p(z k |Ψ,x k-1 ) is expressed as: lnp(z k |Ψ,x k-1)=F(qΘ))+KLD[q(Θ)||p(Θ|Ψ,x k-1 )] (35) where F(q(Θ)) is the free energy, KLD[q(Θ)||p(Θ|Ψ,x k-1 )] is the relationship between q(Θ) and p(Θ|Ψ,x k-1 ) between the Kullback-Leibler divergence; when KLD[q(Θ)||p(Θ|Ψ,x k-1 )] reaches the minimum value 0, q(Θ) is equal to the true posterior distribution p(Θ|Ψ,x k-1 ), the free energy F(q(Θ)) reaches its maximum value. Define F(q(Θ)) as lnp(Θ|Ψ,x k-1 ), and maximize the lower bound to obtain q(Θ) that is closest to the true posterior. The general solution of q(Θ) can be obtained as:

[0184] lnq(Θ)∝E Θ [p(Θ|Ψ,x k-1 )] (36)

[0185] q(Θ) can be uniquely determined and is formally consistent with the priors of all unknown parameters:

[0186] q(Θ)=q(ξ k )q(Q k )q(λ k )q(R k )q(x k ) (37)

[0187] In the above formula, ξ k The approximate posterior distribution q(ξ k ) are respectively expressed as:

[0188]

[0189] in,

[0190] Q k The approximate posterior distribution q(Q k ) is expressed as:

[0191]

[0192] in,

[0193] λ k The approximate posterior distribution q(λ k ) is expressed as:

[0194]

[0195] in, R k The approximate posterior distribution q(R k ) is expressed as:

[0196]

[0197] in, x k The approximate posterior distribution q(x k ) is expressed as:

[0198]

[0199] in, is x k The posterior estimate of P k|k For prediction Mean square error matrix;

[0200] (6) Obtain the expected terms in equations (39) to (42)

[0201] Stage 4: Use Nataf transformation to transform the original state space into an independent standard normal space:

[0202] (1) For the vector x of the nonlinear state model k ={x k,1 ,…,x k,n} T , using p(x k ) and p i (x k,i )(i=1,…,n) represent the joint probability density function and the marginal probability density function respectively, and establish p(x k ) and p i (x k,i ) are as follows:

[0203]

[0204] in, represents a standard normal random variable, φ(r|ρ) and φ(r i ) are respectively expressed as:

[0205]

[0206] (2) Perform Choleskey decomposition on the correlation coefficient matrix ρ:

[0207] ρ=LL T(50)

[0208] Where L is a lower triangular matrix, from which independent standard normal variables are obtained

[0209] y=L -1 r (51)

[0210] (3) Establish the Jacobian matrix for transforming from the original space to the standard normal space:

[0211]

[0212] Phase 5: Navigation state estimation using nonlinear Kalman filtering using sparse grid method.

[0213] (1) Initialize state variables Covariance matrix P0 standard deviation vector σ0 and correlation coefficient matrix ρ0:

[0214]

[0215] (2) For the n-dimensional state variable x k-1 , select the sparse grid integration points with accuracy level s according to the Smolyak criterion:

[0216]

[0217] in is the tensor product operation, |i|=i1+…+i n , represents the Gaussian integral point in the one-dimensional space of the jth variable, and its weight is expressed as The lth integral point in The corresponding weight w l Calculated as:

[0218]

[0219] (3) Time update of nonlinear Kalman filtering:

[0220] First, get the predicted value of the navigation state:

[0221]

[0222] Among them, L k-1 is the correlation coefficient matrix ρ k-1 Perform Choleskey decomposition on the lower triangular matrix;

[0223] Then, get the predicted amount of the mean squared error matrix:

[0224]

[0225] (4) Perform measurement update of nonlinear Kalman filtering:

[0226] First, calculate the gain matrix:

[0227]

[0228] Then, the navigation state is corrected using the measurement information and its covariance matrix is ​​updated:

[0229]

[0230] From the above formula, we can see that the expected terms in formulas (39) and (41) are:

[0231]

[0232] Finally, calculate the correlation coefficient matrix:

[0233]

[0234] (5) Output and P k , update k=k+1 and enter the next filtering update.

[0235] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering, characterized in that: The method comprises the following steps: Step 1: Collect the angular velocity ω output by the gyroscope and accelerometer b and acceleration f b , and then establish the nonlinear error equation; Step 2: Considering environmental uncertainty, the student-t distribution with thick tail characteristics is used to characterize the state noise and measurement noise of the system model, and the probability density function of the state and measurement is obtained; Step 3: Since it is difficult to obtain a closed-form solution for the maximum likelihood estimation of the student-t distribution, a variational Bayesian learning method is used to obtain the unknown parameters that characterize the statistical characteristics of the state vector and the measurement vector; Step 4: Use Nataf transformation to transform the original state space into an independent standard normal space; Step 5: Use the sparse grid method to perform navigation state estimation with nonlinear Kalman filtering.

2. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 1, characterized in that: In step 2, the state noise and measurement noise of the system model are characterized by using the student-t distribution with a thick tail characteristic to obtain the probability density function of the state and the measurement, including the following steps: Step 2-1, based on the nonlinear error equation of the strapdown inertial navigation system, establish the state equation for large misalignment angle alignment: x k =f(x k-1 )+g(x k-1 )w k-1 in, represents the n-dimensional state vector at time k, including the misalignment angle Speed ​​error Gyroscope drift ε b =[ε x ,ε y ,ε z ], accelerometer bias f(·) and g(·) are known nonlinear functions, They represent the n-dimensional system noise vector, and their covariance matrix is ​​Q k ; Step 2-2, using the velocity error of the strapdown inertial navigation system as the observed quantity, establish the measurement equation for large misalignment angle alignment: z k =H k x k +o k in, represents the m-dimensional measurement vector at time k, H k is the measurement matrix, o k is the speed error noise, and its covariance matrix R k ; Step 2-3, use Q k and R k represents the noise w k and k The covariance matrix of k and k represents the noise w k and v k degrees of freedom, and obtain the probability density function p(x k |x k-1 ) and p(z k |x k ):

3. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 2, characterized in that: In step 3, a variational Bayesian learning method is used to obtain unknown parameters that characterize the statistical characteristics of state noise and measurement noise, including the following steps: Step 3-1, replace p(x k |x k-1 ) and p(z k |x k ) are converted into the following integral forms: Where N(x|μ,∑) is a Gaussian distribution with mean μ and variance ∑, Gamma(λ|a,b) is a gamma distribution with shape parameter a and scale parameter b; Step 3-2, characterize Q using Wishartf distribution k and R k Prior distribution of : Q k ~IW(Q k |u0,U0),R k ~IW(R k |c0, C0) where u0 and c0 are free parameters, and U0 and C0 are inverse scaling matrices; Step 3-3, based on Bayesian theory, establish the joint posterior distribution of unknown parameters and navigation state: p(Θ, z k |Ψ,x k-1 ), where Θ = {x k , Q k , R k ,h k ,λ k }, Ψ = {u0, U0, c0, C0, ω k , v k }; Step 3-4, use the conjugate function q(Θ) to approximate x k , Q k , R k ,ξ k ,λ k The approximate posterior distribution of : q(Θ)=q(x k )q(Q k )q(R k )q(h k )q(λ k ); Step 3-5, use the expected maximum algorithm to get the expected term 4. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 3, characterized in that: In step 4, the Nataf transformation is used to realize the conversion of the original state space into the independent standard normal space, including the following steps: Step 4-1: Establish according to Copula theory The joint probability density function p(x k ) and the marginal probability density function p i (w k,i ) are as follows: in represents a standard normal random variable, φ(r|ρ) represents the joint probability density function of r, and ρ represents the correlation coefficient matrix; Step 4-2, perform Choleskey decomposition on the correlation coefficient matrix ρ: ρ = LL T ; Step 4-3, obtain the Jacobian matrix transformed from the original space to the standard normal space:

5. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 4, characterized in that: In step 5, the navigation state estimation of nonlinear Kalman filtering is performed using a sparse grid method, which includes the following steps: Step 5-1, initialize the state variable x0, covariance matrix P0, standard deviation vector σ0 and correlation coefficient matrix ρ0: Step 5-2, the sparse grid method generates the integration points u in the standard normal space l and integral weight w l , l = 1, ..., N; Step 5-3, time update; Step 5-4, measurement update; Step 5-5, output the results.

6. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 5, characterized in that: In step 5-3, the time update process includes the following steps: Step 5-3-1, navigation status prediction: x k|k - 1，l =f(L k-1 you l ·s k-1 +x k-1 ) Where, L k-1 is the correlation coefficient matrix ρ k-1 Perform Choleskey decomposition on the lower triangular matrix; Step 5-3-2, mean square error matrix prediction:

7. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 6, characterized in that: In step 5-4, the measurement update process includes the following steps: Step 5-4-1, calculate the gain matrix: Step 5-4-2, use the measurement information to correct the navigation state and update its covariance matrix: Step 5-4-3, calculate the correlation coefficient matrix:

8. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 7, characterized in that: In step 5-5, the output result includes and P k , update k=k+1 and enter the next filtering update.

9. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 8, characterized in that: The method can improve the robustness of the self-alignment of the strapdown inertial navigation system.

10. The strapdown inertial navigation system large misalignment angle alignment method based on variational Bayesian filtering as claimed in claim 8, characterized in that: The method belongs to the technical field of inertial navigation.

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