CN105737823B - A kind of GPS/SINS/CNS Combinated navigation methods based on five rank CKF - Google Patents

Abstract

The present invention discloses a kind of GPS/SINS/CNS Combinated navigation methods based on five rank CKF, which is characterized in that includes the following steps：Step 1：Establish the integrated navigation system nonlinearity erron equation based on SINS error equations and linear measurement equation；Step 2：Utilize five rank spherical surface radial direction volume rule criteria constructions, five rank volume Kalman filter；Step 3：SINS is filtered with GPS, CNS information exported using five rank CKF, is merged, the optimal estimation of navigational parameter is obtained.

Description

A GPS/SINS/CNS Integrated Navigation Method Based on Fifth-Order CKF

technical field

The invention relates to the technical field of strapdown inertial navigation and integrated navigation, in particular to a fifth-order CKF-based SINS/GPS/CNS integrated navigation method.

Background technique

In the SINS/GPS/CNS integrated navigation system, GPS can provide accurate speed information at any time, so the speed error of strapdown inertial navigation can be controlled within the precision range of GPS through the combined system. The CNS system can provide accurate attitude angle information, which can improve the measurement accuracy of the attitude angle after being combined. However, due to the limitation of objective conditions, it can only provide heading information intermittently, which requires that the heading error be reduced within the time interval when there is no heading information. Estimates must be stable. Based on the above reasons, it is necessary to introduce a more advanced filtering algorithm into the integrated navigation system to overcome the influence of system model parameters being inaccurate or changing with the environment, so as to improve the adaptability of the system model to the external environment and provide high-precision navigation information.

Therefore, it is of great significance both in theory and in engineering practice to study the CKF filtering method, further improve its filtering performance, and apply it to the nonlinear filtering problem in the SINS/GPS/CNS integrated navigation system.

Contents of the invention

Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a GPS/SINS/CNS integrated navigation method based on 5th-order CKF that improves filtering accuracy and filtering efficiency.

Technical solution: In order to solve the above technical problems, the present invention provides a GPS/SINS/CNS integrated navigation method based on fifth-order CKF, which is characterized in that it includes the following steps:

Step 1: Establish the nonlinear error equation and linear measurement equation of the integrated navigation system based on the SINS error equation;

Step 2: Construct a fifth-order volumetric Kalman filter using the fifth-order spherical radial volume rule criterion;

Step 3: Use the fifth-order CKF to filter and fuse the information output by SINS, GPS, and CNS to obtain the optimal estimation of navigation parameters and correct the speed information, position information and strapdown attitude matrix to obtain accurate navigation information.

Further, the step 1 establishes the nonlinear error equation and the linear measurement equation of the integrated navigation system based on the SINS error equation as follows:

Step 1.1: Select the "Northeast Sky" geographic coordinate system as the navigation coordinate system n; select the "right front upper" coordinate system of the carrier as the carrier coordinate system b; The pulling angle is recorded as the heading angle ψ∈(-π,π], the pitch angle Roll angle γ∈(-π,π]; the attitude matrix between the n system and the b system is denoted as The true attitude angle is denoted as The true speed is denoted as The real geographic coordinate system is P=[L λ H] ^T , where L is the latitude, λ is the longitude, and H is the height; the attitude angle calculated by the SINS solution is recorded as Speed recorded as The geographic coordinate system is The mathematical platform calculated by the SINS solution is denoted as the n′ system, and the attitude matrix between the n’ system and the b system is denoted as Denote the attitude angle error as The velocity error is: The position error is: Then the nonlinear error model is as follows:

in, is the constant value error of the three-axis gyroscope under the b system, is the random error of the three-axis gyro in the b system is a zero-mean white noise process, is the constant value error of the three-axis acceleration under the b system, is the random error of the three-axis acceleration in the n system is a zero-mean white noise process, is the actual output of the accelerometer, is the rotational angular velocity of the mathematical platform under the b system, For the calculated mathematical platform rotation angular velocity, is the angular velocity of the earth's rotation, To solve the calculated mathematical platform relative to the earth's rotational angular velocity, for correspondence calculation error. R _M and R _N are the radius of curvature of the Maoxi circle of the local meridian, respectively, is the inverse matrix of the Euler angle differential equation coefficient matrix; is the attitude matrix between n′ series and n series, C _ω and Specifically:

Step 1.2: The process of establishing the nonlinear error equation and the linear measurement equation is as follows:

select speed error Euler angle platform error angle φ _e , φ _n , φ _u ; position error δL, δλ; accelerometer constant value error under b system and gyro constant error and form a 12-dimensional state vector, H is approximately zero:

and P only take the first two dimensional states, and is a zero-mean white noise process; . The nonlinear state equation can be abbreviated as: Taking the sampling period T as the filtering period, the fourth-order Runge-Kutta integration method can be used to discretize it with T as the step size. The specific steps are as follows:

Assuming that the value x ₀ of the selected state vector at the initial moment is known, and t ₁ =t+T/2, then the following iterative formula can be used to Discrete:

Δx ₁ =[f(x,t)+ω(t)]T

Δx ₂ =[f(x,t ₁ )+Δx ₁ /2+ω(t ₁ )]T

Δx ₃ =[f(x,t ₁ )+Δx ₂ /2+ω(t ₁ )]T

Δx ₄ =[f(x,t+T)+Δx ₃ +ω(t+T)]T

x _k+1 ＝x _k +(Δx ₁ +2Δx ₂ +2Δx ₃ +Δx ₄ )/6

Record the state filter equation after discretization as: x _k ＝f(x _k-1 )+ω _k-1

The process of establishing the linear measurement equation is as follows:

Select GPS Velocity Error M _e and M _n are the components of the speed measurement error item of the GPS receiver on the east-to-north coordinate axis, respectively;

The velocity quantity measurement vector is defined as follows:

In the formula, H _v (t)＝[diag[1,1]0 _2×10 ]

In the strapdown working mode, the attitude information output by the CNS can obtain the three-axis attitude information of the carrier And SINS will also give the three-axis attitude information of the carrier through the inertial navigation solution as Therefore, the three-axis attitude error angle Δφ of the carrier can be obtained by subtracting the two:

Δφ'=M×Δφ

In the formula, M is the attitude error angle transformation matrix:

In the integrated navigation system, Δφ' is used as the observation value to establish the measurement model of the system, and the error of the inertial device in the navigation system is estimated in real time by the method of optimal estimation, and the SINS is corrected accordingly;

The measurement equation is as follows:

In the formula, H _φ ＝[0 _3×2 I _3×3 0 _3×7 ]

From the above analysis, we can see that the measurement equation of the full combination is:

Also take T as the filtering cycle, and use T as the step size for simple discretization.

The following filter equation is composed of the state equation and the measurement equation:

Further, the step 2) constructing a fifth-order volumetric Kalman filter using the fifth-order spherical radial volume rule criterion is specifically:

Step 2.1: The fifth-order spherical radial volume criterion is as follows:

f(x) is an arbitrary function, R ⁿ is the integral area, and the approximate solution of its analytical value is obtained by an approximate method.

Take x=ry and y ^T y=1,r∈[0,∞), so the above integral can be written in the spherical radial coordinate system as:

U _n is an n-dimensional unit sphere, and σ(·) is an element on U _n . The integral I(f) can be separated into Spherical integral and Radial integral:

Assuming an N _s sampling approximation of the Spherica integral S(r):

The N _r sample approximation of the Radial integral Rr:

The N _r ×N _s sampling approximation to obtain I(f) is:

Spherical criterion: The calculation formula of S(r) is as follows:

in [s] _n is the midpoint set of [e] _n , denoted as They are:

The number of vectors in [e] _n and [s] _n is 2n and 2n(n-1) respectively, [e] _i and [s] _i are respectively the i-th column of [e] _n and [s] _n ;

Solutions have to:

Radial rules:

Use the generalized Gauss-Laguerre integral rule to solve the system of equations

Step 2.2: The fifth-order volumetric Kalman filter is constructed as follows:

For the established filter equation:

In the formula, x _k is a 12-dimensional state vector, and each component is independent and obeys Gaussian distribution; z _k is a 5-dimensional observation vector; ω _k-1 and ν _k are process noise and measurement noise respectively, satisfying:

In the formula, _δij is the δ function; Q is the variance matrix of the system noise; R is the variance matrix of the measurement noise.

The fifth-order CKF algorithm is as follows:

Step 2.2.1: Time update:

①Assume the posterior probability distribution at time k-1 Known, Cholesky decomposition:

P _k-1 = S _k-1 S _k-1 ^T

① Calculate the volume point:

In the formula, i=1,2,...,2n; j=1,2,...,2n(n-1)

①Propagate the volume point through the state equation:

x _1,i ^* ＝f(x _1,i ); x _2,i ^* ＝f(x _2,i )

x _3,j ^* ＝f(x _3,j ); x _4,j ^* ＝f(x _4,j )

① Estimate the predicted value of the state and error matrix at time k:

K=3-α;

Step 2.2.2: Measurement update

①Cholesky decomposition P _xx :

① Calculate the volume point:

①Propagate the volume point through the observation equation:

z _1,i =h(y _1,i ), z _2,i =h(y _2,i )

z _3,i =h(y _3,i ), z _4,i =h(y _4,i )

① Estimate the observed and predicted value at time k:

① Calculate the autocorrelation and cross-correlation covariance matrix:

①Use the Guass-Bayes filtering framework to complete the filtering:

Since the measurement equation described is a linear equation, the measurement update is simplified:

①Cholesky decomposition P _xx :

① Calculation of one-step forecast measurement value

① Calculate the autocorrelation and cross-correlation covariance matrix:

①Use the Guass-Bayes filtering framework to complete the filtering:

Further, the step 3) uses the fifth-order CKF to filter and fuse the information output by SINS, GPS and CNS to obtain the optimal estimation of navigation parameters and correct the velocity information, position information and strapdown attitude matrix to obtain accurate The specific navigation information is:

Step 3.1: After the fifth-order CKF filter completes a filter, the estimated value of the 12-dimensional state quantity output by the filter is: Correction of speed information, position information and strapdown attitude matrix.

Step 3.2: According to the obtained in step 3.1 Perform speed information correction:

It is the speed obtained by SINS solution. When the GPS has no signal, the calculated V _GPS is regarded as the real speed information.

Step 3.3: Correct the attitude information according to φ _e , φ _n , φ _u obtained in step 3.1:

Calculate the attitude matrix between the n' system and the n system The calculation method is as follows:

According to the attitude matrix between the n' system and the b system Attitude matrix between the n′ system and the n system Calculate the exact strapdown attitude matrix The calculation method is as follows:

According to the strapdown attitude matrix Calculate the Euler angle, the calculation method is as follows:

Step 3.4: Carry out the following position information correction according to δL and δλ obtained in step 3.1:

in, is the latitude obtained by SINS solution, and L′ is the precise latitude obtained after correction; is the latitude obtained by SINS solution, and λ' is the precise longitude obtained after correction.

Beneficial effect: the present invention has the following advantages over the prior art:

1. The present invention sets up the error model of integrated navigation according to the general principle of SINS, GPS and CNS and respective advantages and disadvantages. Learn from each other's strengths and make full use of their complementarity to complete combined navigation tasks.

2. Traditional CKF based on the third-order volume criterion is greatly limited in improving the accuracy. In order to solve this problem, this paper proposes a fifth-order CKF algorithm based on the analysis of the high-order volume criterion, which effectively improves the accuracy of the CKF algorithm and has a good filter efficiency.

3. The present invention uses GPS to provide speed information, and CNS to improve attitude angle information, which helps to improve the filtering accuracy and convergence speed of the fifth-order CKF.

Description of drawings

Fig. 1 is a pitch angle error diagram of the present invention.

Fig. 2 is a roll angle error diagram of the present invention.

Fig. 3 is a heading angle error diagram of the present invention.

Fig. 4 is an east speed error map of the present invention.

Fig. 5 is a northward speed error diagram of the present invention.

Fig. 6 is a latitude error diagram of the present invention.

Fig. 7 is a longitude error map of the present invention.

Fig. 8 is a path diagram of the aircraft of the present invention.

Fig. 9 is a system scheme diagram of the present invention.

Fig. 10 is a schematic diagram of the present invention based on the fifth-order CKF SINS/GPS/CNS integrated navigation method

Fig. 11 is the fifth-order CKF filter flowchart of the present invention

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

As shown in Fig. 9 and Fig. 10, it is a system scheme diagram and a navigation principle diagram of the present invention.

The SINS strapdown settlement module collects the gyroscope output value and the accelerometer output value output by the inertial measurement unit (IMU) module for strapdown calculation, and obtains information such as attitude angle, attitude matrix, speed, and position; the GPS device outputs the speed information of the carrier ; The CNS equipment outputs attitude information, SINS and GPS, and the information output by CNS is input to the fifth-order CKF filter at the same time, and the information is filtered. The filtering process is as follows:

1. According to the characteristics of SINS/GPS/CNS integrated navigation, select the 12-dimensional state vector:

The equation of state is established:

After discretization, it is written as: x _k ＝f(x _k-1 )+ω _k-1 .

2. Select the velocity and attitude angle as the measurement value, and establish the measurement filter equation:

After discretization, it is written as: x _k ＝f(x _k-1 )+ω _k-1

3. Time update

①Assume the posterior probability distribution at time k-1 Known, Cholesky decomposition:

P _k-1 = S _k-1 S _k-1 ^T

② Calculate the volume point:

In the formula, i=1,2,...,2n; j=1,2,...,2n(n-1)

③Propagate the volume point through the state equation:

x _1,i ^* ＝f(x _1,i ); x _2,i ^* ＝f(x _2,i )

x _3,j ^* ＝f(x _3,j ); x _4,j ^* ＝f(x _4,j )

④ Estimate the predicted value of the state and error matrix at time k:

K=3-α;

4. Measurement update

①Cholesky decomposition P _xx :

②Calculation of one-step forecast measurement value

③ Calculate the autocorrelation and cross-correlation covariance matrix:

④Use the Guass-Bayes filtering framework to complete the filtering:

5. After the fifth-order CKF filter completes a filter, the estimated value of the 12-dimensional state quantity output by the filter is: Correction of speed information, position information and strapdown attitude matrix.

① According to the obtained Perform speed information correction:

It is the speed obtained by SINS solution. When the GPS has no signal, the calculated V _GPS is regarded as the real speed information.

②Perform attitude information correction according to the obtained φ _e , φ _n , φ _u :

Calculate the attitude matrix between the n' system and the n system The calculation method is as follows:

According to the attitude matrix between the n' system and the b system Attitude matrix between the n′ system and the n system Calculate the exact strapdown attitude matrix The calculation method is as follows:

According to the strapdown attitude matrix Calculate the Euler angle, the calculation method is as follows:

③ Correct the position information according to the obtained δL and δλ:

in, is the latitude obtained by SINS solution, and L′ is the precise latitude obtained after correction; is the latitude obtained by SINS solution, and λ' is the precise longitude obtained after correction.

Use the following examples to illustrate the beneficial effects of the present invention:

1) Motion parameter setting:

At the initial moment of the simulation, the aircraft is at 32 degrees north latitude and 118 degrees east longitude; and performs biaxial swing motion around the pitch axis and roll axis respectively with a sinusoidal function, and the swing amplitudes of pitch angle θ and roll angle γ are respectively: 9, 12, the swing periods are: 16s, 20s, the initial heading angle is 30 degrees, and the initial misalignment angles are: Δθ=15°, Δγ=15°, Δψ=100°; /s speed, do uniform motion, the motion path is shown in Figure 8, the speed when turning is 9°/s, and the sailing time is 6000s.

2) Parameter setting of the sensor:

The gyro constant drift of the strapdown system of the aircraft is 0.01°/h:, the gyro random drift is 0.01°/h:, the accelerometer bias is: 50mg, the accelerometer random error is: 50mg, and the GPS output speed error is: 0.1m/s.

The CNS output attitude error is 1 point.

3) Simulation result analysis:

Use the combined navigation method of the SINS/GPS/CNS based on the fifth-order CKF provided by the present invention to simulate, and Fig. 1, 2, 3 are the pitch angle error in the navigation process of the present invention, the roll angle error, and the curve of the heading angle error ; Fig. 4,5 are the speed error curves in the middle east direction and north direction of the navigation process of the present invention; Fig. 6, 7 are the latitude and longitude error curves in the navigation process of the present invention. It can be found that after the aircraft sails for 1000s, the pitch angle basically converges, with an error of about 0.07°; after 500s, the roll angle basically converges, with an error of about 0.07°; after 100s, the heading angle basically converges, with an error of about 0.02°. After 1550s, the eastward velocity basically converges, with an error of 0.12m/s. After 1500s, the northward velocity basically converges, with an error of 0.1m/s. The longitude and latitude error has been very small, the maximum latitude error is 26 minutes, and the maximum longitude error is 0.031 minutes. Through analysis, it is found that after sailing for 6000s, the error of pitch angle is within 0.0002°, the error of roll angle is within 0.0009°, the error of heading angle is within 0.02; the error of eastward speed is within 0.01m/s, and the error of northward speed is 0.033m Within /s, the latitude error is within 1.63 minutes, and the longitude error is within 0.0064 minutes.

The above results show that the fifth-order CKF algorithm used in SINS/GPS/CNS integrated navigation can quickly converge the system error and stabilize it within a small error range.

The preferred embodiments of the present invention have been described in detail above, but the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be carried out to the technical solutions of the present invention. These equivalent transformations All belong to the protection scope of the present invention.

Claims (3)

1. A GPS/SINS/CNS integrated navigation method based on five-order CKF is characterized by comprising the following steps:

step 1: establishing a combined navigation system nonlinear error equation and a linear measurement equation based on an SINS error equation;

step 1.1: selecting a geographical coordinate system of northeast as a navigation coordinate system n; selecting a carrier 'right front upper' coordinate system as a carrier coordinate system b system; n is rotated to b series through 3 times of Euler angles, and the three Euler angles are recorded as course angle psi ∈ (-pi, pi)]Angle of pitchThe roll angle gamma belongs to (-pi, pi)](ii) a The attitude matrix between n and b is recorded asTrue attitude angle is notedTrue velocity is notedThe real geographic coordinate system is P ═ L lambda H]^TWherein L is latitude, lambda is longitude, and H is altitude; the attitude angle calculated by SINS is recorded asVelocity is recorded asThe system of geographic coordinatesThe mathematical platform calculated by SINS is recorded as n 'system, and the attitude matrix between n' system and b system is recorded asError of attitude angle is recorded asThe speed error is:the position error is:the nonlinear error model is then as follows:

wherein,b is the constant error of the lower triaxial gyro,b is a white noise process with zero mean value of random error of the lower triaxial gyro,is a constant error of the acceleration of the lower three axes,the random error of the triaxial acceleration under n is the white noise process with zero mean value,is the actual output of the accelerometer,is b is the angular velocity of the rotation of the mathematical platform,to solve for the calculated mathematical platform rotational angular velocity,is the angular velocity of the rotation of the earth,to solve for the calculated rotational angular velocity of the mathematical platform relative to the earth,to correspond toCalculated error of (2), R_M、R_NRespectively the curvature radius of the meridian quarter mortise and west circle,the inverse matrix of the Euler angle differential equation coefficient matrix is used;is an attitude matrix between n' and n, C_ωAndthe method specifically comprises the following steps:

step 1.2: the nonlinear error equation and the linear measurement equation are established as follows:

error in the selected velocityEuler angle platform error angle phi_e、φ_n、φ_u(ii) a Position errors δ L, δ λ; constant error of accelerometer under b systemAnd gyro constant errorAnd constructing a 12-dimensional state vector,h is approximately zero:

and P takes only the first two-dimensional state,anda zero mean white noise process; this nonlinear equation of state can be simplified as:taking a sampling period T as a filtering period, a fourth-order Runge-Kutta integration method can be used, and T is discretized by taking the step length as follows:

assume the value x of the selected state vector at the initial time instant₀Is known, and let t₁T + T/2, then the following iterative formula will applyDispersing:

Δx₁＝[f(x,t)+ω(t)]T

Δx₂＝[f(x,t₁)+Δx₁/2+ω(t₁)]T

Δx₃＝[f(x,t₁)+Δx₂/2+ω(t₁)]T

Δx₄＝[f(x,t+T)+Δx₃+ω(t+T)]T

x_k+1＝x_k+(Δx₁+2Δx₂+2Δx₃+Δx₄)/6

the state filtering equation after dispersion is recorded as: x is the number of_k＝f(x_k-1)+ω_k-1

The linear measurement equation is established as follows:

selecting GPS velocity errorM_e、M_nThe components of the speed measurement error term of the GPS receiver on an east-north coordinate axis are respectively;

the velocity measurement vector is defined as follows:

in the formula, H_v(t)＝[diag[1,1]0_2×10]

Under the strapdown working mode, the attitude information output by the CNS can obtain the three-axis attitude information of the carrierThe SINS also gives the three-axis attitude information of the carrier through inertial navigation solutionTherefore, subtracting the two to obtain the three-axis attitude error angle Δ Φ of the carrier:

Δφ'＝M×Δφ

wherein M is an attitude error angle transformation matrix:

in the integrated navigation system, a measurement model of the system is established by taking delta phi' as an observed value, the error of an inertial device in the navigation system is estimated in real time by an optimal estimation method, and the SINS is corrected according to the error;

the measurement equation is as follows:

in the formula, H_φ＝[0_3×2I_3×30_3×7]

From the above analysis, the measurement equation of the total combination is:

and taking T as a filtering period, and taking T as a step size to carry out simple discretization,

the following filter equation is composed of a state equation and a measurement equation:

step 2: constructing a fifth-order volume Kalman filter by utilizing a fifth-order spherical radial volume rule;

and step 3: and filtering and fusing information output by the SINS, the GPS and the CNS by utilizing the five-order CKF to obtain optimal estimation of navigation parameters and correct speed information, position information and a strapdown attitude matrix so as to obtain accurate navigation information.

2. The GPS/SINS/CNS integrated navigation method based on fifth-order CKF of claim 1, wherein the step 2) of constructing the fifth-order cubature Kalman filter by using the fifth-order spherical radial cubature rule criterion specifically comprises:

step 2.1: the fifth-order spherical radial volume criterion is as follows:

f (x) is an arbitrary function, RⁿFor the integration area, an approximate solution of the analytic value is obtained by an approximate method,

let x be ry, and y^Ty is 1, r ∈ [0, ∞), so the above integral in the spherical radial coordinate system can be written as:

U_nis an n-dimensional unit sphere, and sigma (-) is U_nThe above element, integral i (f), can be separated into a spherial integral and a Radial integral:

assume that Spherica integrates N of S (r)_sSampling approximation:

n of Radial integral Rr_rSampling approximation:

obtaining N of I (f)_r×N_sThe sampling approximation is as follows:

spherical guidelines: the calculation formula of S (r) is as follows:

wherein[s]_nIs [ e ]]_nIs marked as the midpoint set Respectively as follows:

[e]_nand [ s ]]_nThe number of the inward vectors is 2n and 2n (n-1), [ e ]]_iAnd [ s ]]_iAre each [ e]_nAnd [ s ]]_nThe ith column;

obtaining by solution:

radial rule:

solving the system of equations using a generalized Gauss-Laguerre integration rule

Step 2.2: the construction method of the fifth-order cubature Kalman filter is as follows:

for the established filter equation:

in the formula x_kThe state vector is 12-dimensional, and each component is independent and follows Gaussian distribution; z is a radical of_k5-dimensional observation vectors; omega_k-1V and v_kRespectively, process noise and measurement noise satisfy:

in the formula, delta_ijIs a delta function; q is a variance matrix of the system noise; r is a variance matrix of the measurement noise,

the five-order CKF algorithm is as follows:

step 2.2.1: and (3) time updating:

① hypothesis posterior probability distribution at time k-1As is known, Cholesky decomposition:

P_k-1＝S_k-1S_k-1 ^T

② calculate volume point:

wherein i is 1,2, …,2 n; j-1, 2, …,2n (n-1)

③ propagate volume points through the state equation:

x_1,i ^*＝f(x_1,i)；x_2,i ^*＝f(x_2,i)

x_3,j ^*＝f(x_3,j)；x_4,j ^*＝f(x_4,j)

④ estimating the predicted value of the state and error matrix at the k moment:

step 2.2.2: measurement update

① Cholesky decomposition P_xx：

② calculate volume point:

③ propagate the volume points through the observation equation:

z_1,i＝h(y_1,i)，z_2,i＝h(y_2,i)

z_3,i＝h(y_3,i)，z_4,i＝h(y_4,i)

④ estimate the observed prediction at time k:

⑤ calculating the auto-and cross-correlation covariance matrices:

⑥ Filtering is accomplished using a Guass-Bayes filtering framework:

since the measurement equation is a linear equation, the measurement update is simplified:

① Cholesky decomposition P_xx：

② calculating one-step predicted measurements

③ calculating the auto-and cross-correlation covariance matrices:

④ Filtering is accomplished using a Guass-Bayes filtering framework:

3. the GPS/SINS/CNS integrated navigation method based on five-order CKF according to claim 1, wherein the step 3) utilizes the five-order CKF to filter and fuse the SINS, the GPS and the CNS output information, so as to obtain the optimal estimation of the navigation parameters and modify the velocity information, the position information and the strapdown attitude matrix, so as to obtain the accurate navigation information specifically:

step 3.1: after the five-order CKF filter finishes one-time filtering, according to a 12-dimensional state quantity estimated value output by the filter:correcting the speed information, the position information and the strapdown attitude matrix;

step 3.2: according to what is obtained in step 3.1And speed information correction is carried out:

for SINS-resolved velocity, calculated V is determined when GPS has no signal_GPSAs the true speed information;

step 3.3: according to phi obtained in step 3.1_e、φ_n、φ_uAnd (3) correcting the attitude information:

computing an attitude matrix between the n' and n systemsThe calculation method is as follows:

based on the attitude matrix between the n' system and the b systemAnd the attitude matrix between the n' system and the n systemCalculating accurate strapdown attitude matrixThe calculation method is as follows:

according to the strapdown attitude matrixAnd (3) calculating the Euler angle by the following method:

step 3.4: the following positional information correction is performed based on δ L and δ λ obtained in step 3.1:

wherein,the latitude obtained by SINS resolving is obtained, and the L' is the accurate latitude obtained after correction;is the latitude obtained by SINS solution, and λ' is the precise longitude obtained after correction.