A method for solving a coordinate transformation matrix of inertial navigation with few parameters

Abstract

A method for solving the coordinate transformation matrix of inertial navigation with few parameters and a fixed structure includes: determining m parameters of the coordinate transformation matrix as variables updated in real time, wherein the remaining 9-m parameters can be directly calculated from these m parameters; and based on the m parameters at time t... k The angular velocity value at time t is obtained by integrating and updating the m parameters using trigonometric integral formulas. k+1 The value at time is used to calculate the remaining 9-m parameters of the coordinate transformation matrix, ultimately obtaining an updated coordinate transformation matrix that supports velocity and position updates, thereby improving the accuracy of inertial navigation. This invention uses the angular rate output from a gyroscope orthogonally mounted on the strapdown inertial system as input information, achieving real-time updates to the inertial navigation coordinate transformation matrix while ensuring solution accuracy and simplifying computation.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of inertial navigation few parameter coordinate transformation matrix solving method, applied to the technical field of inertial navigation. BACKGROUND

[0002] Inertial navigation is widely used in spacecraft, aircraft, ships and other fields, and its main function is to determine the position, velocity and attitude information of the carrier relative to the navigation system in real time. The strapdown inertial system is directly connected to the carrier, and the angular velocity is measured by the gyroscope and the coordinate transformation matrix of the carrier coordinate system relative to the navigation system is obtained after mathematical calculation.

[0003] Currently, there are three methods to determine the attitude information: direction cosine kinematics equation, Euler-Krylov angle kinematics equation and quaternion kinematics equation.

[0004] The four quaternion parameters and their differential equations are widely used in engineering, but they have the disadvantage that the four parameters are only intermediate variables, and nine equations are needed to solve the coordinate transformation matrix of the carrier coordinate system relative to the navigation system. In addition, the coordinate transformation matrix described by the quaternion is not a unique correspondence between the four parameters, because a coordinate transformation matrix can correspond to two different quaternions.

[0005] Compared with the above two methods, the Euler-Krylov angle kinematics equation has only three equations, but in the technical field of "Inertial Devices (Part 1)" (China Astronautics Press) on page 46, it is considered that the kinematics equation described by Euler-Krylov angle has singular points and the equation will degenerate. A method for solving the attitude based on Krylov angle is proposed in the patent (CN202010333184.9), which can realize the full attitude motion description of the carrier, but the problem is that when the pitch angle = 90°, the error of the attitude solution is large when discretization is performed, resulting in large errors in the solution of speed and position.

[0006] The method of using direction cosine array to represent the rotational motion relationship between two coordinate systems and the attitude matrix is convenient, intuitive and easy to understand, but the disadvantage is that the parameters of the transformation matrix and their differential equations are nine, and the integral calculation is large. In the technical field of "Inertial Devices (Part 2)" (China Astronautics Press) in Chapter 18, a method for solving the coordinate transformation matrix based on the direction cosine kinematics equation and the quaternion kinematics equation is given.

[0007] Under the premise of full attitude, to realize one-to-one correspondence between the coordinate transformation matrix and the parameters, the method for updating the nine-parameter coordinate transformation matrix based on trigonometric functions is

[0008]

[0009] where, is the coordinate transformation matrix, and I is the identity matrix, is the anti-symmetric matrix of unit angular velocity, and Δθ is the angular increment in the sampling time ΔT.

[0010] The derivation of the above formula is based on linear equations, which can ensure high accuracy of integral solution, but the problem is that the 9 parameters of the direction cosine matrix 9 cause large amount of calculation, so the number of parameters should be reduced. However, the reduction of the number of parameters will make the differential equation a nonlinear equation, for example, the 8-parameter coordinate transformation matrix

[0011]

[0012] The corresponding differential equation is

[0013]

[0014] In the formula, a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 and a 33 are 8 parameters of the coordinate transformation matrix .

[0015] At this time, the update method corresponding to formula (1) cannot be applied to the integral solution of formula (2). Therefore, under the premise of ensuring accuracy, a new solution method of the carrier coordinate system relative to the navigation system is needed to reduce the amount of calculation and improve the rapidity of inertial navigation and flight control. SUMMARY

[0016] The technical problem to be solved by the present application is to overcome the shortcomings of the prior art and provide an inertial navigation few-parameter fixed-structure coordinate transformation matrix solution method.

[0017] The object of the present application is achieved by the following technical solutions:

[0018] An inertial navigation few-parameter fixed-structure coordinate transformation matrix solution method comprises:

[0019] calculating the coordinate transformation matrix of the body coordinate system of the strapdown navigation system relative to the navigation coordinate system at time t k ;

[0020] calculating the angular velocity of the body coordinate system relative to the navigation coordinate system at time t k ; wherein ω x′ , ω y′ and ω z′ are the angular velocities on the x, y and z axes of the body, respectively.

[0021] according to the angular velocity The angular increment Δθ in the sampling time ΔT is calculated, and the calculation formula is

[0022] m parameters are selected from the coordinate transformation matrix to form a to-be-updated parameter vector X m,k The remaining 9-m parameters form a to-be-solved vector

[0023] According to the unit angular velocity skew-symmetric matrix N9 of the 9-parameter coordinate transformation matrix, the unit angular velocity skew-symmetric matrix N corresponding to the m parameters is determined m , the unit complementary angular velocity skew-symmetric matrix , and the unit complementary angular velocity skew-symmetric matrix

[0024] According to the coordinate transformation matrix and the angular velocity, the m parameters are integrated and updated to solve, and the calculation formula is

[0025]

[0026] According to X m,k+1 , the remaining 9-m parameters are solved to obtain an updated coordinate transformation matrix;

[0027] According to the updated coordinate transformation matrix, velocity updating and position updating are performed.

[0028] In an embodiment of the present application, the coordinate transformation matrix of the strapdown navigation system body coordinate system relative to the navigation coordinate system at t k is:

[0029]

[0030] In the formula, a 11,k , a 12,k , a 13,k , a 21,k , a 22,k , a 23,k , a 31,k , a 32,k , and a 33,k are 9 parameters of the coordinate transformation matrix at t k , and the vector X9 formed by the 9 parameters is

[0031]

[0032] , and the unit angular velocity skew-symmetric matrix

[0033]

[0034] In an embodiment of the present application, the m parameters form a to-be-updated parameter vector X m,kThe vector to be solved, along with the remaining 9-m parameters, constitutes the solution vector. The relationship between the vector X9 consisting of 9 parameters is as follows:

[0035]

[0036] Wherein, the selection parameter matrix P and the discard parameter matrix Q are m×9 and 9-m×9 dimension time invariant matrices, respectively, and they satisfy P T P+Q T Q = I.

[0037] In one embodiment of the present invention, the antisymmetric matrix N of unit angular velocity corresponding to m parameters is determined. m antisymmetric matrix of unit coaxial angular velocity and the antisymmetric matrix of unit supplementary angular velocity The specific calculation formula is as follows:

[0038]

[0039] In one embodiment of the present invention, based on X m,k+1 The remaining 9-m parameters are solved using a lookup table method, and the calculation formula is as follows:

[0040]

[0041] In one embodiment of the present invention, when m = 8, 8 parameters a are selected. 12,k a 13,k a 21,k a 22,k a 23,k a 31,k a 32,k and a 33,k ; at the next moment t k+1 =t k The value of +ΔT after integration is a 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The specific calculation formula is as follows:

[0042] (6.1) Determine the values ​​of the selection parameter matrix P and the discard parameter matrix Q, as well as the values ​​of their transpose matrices;

[0043]

[0044] Q = [100000000] 1×9 ;

[0045] The selected parameter vector is

[0046]

[0047] (6.2) The values of the unit angular velocity skew-symmetric matrix N8, the unit coangular velocity skew-symmetric matrix and the unit complementary angular velocity skew-symmetric matrix corresponding to the 8 parameters are calculated;

[0048]

[0049] (6.3) The 8 parameters are integrated and updated to obtain the formula

[0050]

[0051] The values of a k+1 , a 12,k+1 , a 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 and a 33,k+1 at time t 8,k+1 are obtained;

[0052] (6.4) The remaining 1 parameter is solved according to X k+1 , and the formula is

[0053]

[0054] (6.5) The integral update values a 12,k+1 , a 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 and a 33,k+1 at time t k+1 and the solved value a 11,k+1 are substituted into the following formula to obtain the coordinate transformation matrix from the navigation coordinate system to the body coordinate system

[0055]

[0056] In an embodiment of the present application, when m=7, 7 parameters a 13,k , a 21,k , a 22,k , a 23,k , a 31,k , a 32,k and a 33,k are selected; at the next time t k+1 =t kthe integrated value of +ΔT 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 , and a 33,k+1 , the specific calculation formula is:

[0057] (7.1) determine the value of selected parameter matrix P and abandoned parameter matrix Q and the value of their transpose matrix;

[0058]

[0059] The selected parameter vector is

[0060]

[0061] (7.2) calculate the values of the unit angular velocity skew-symmetric matrix N7, the unit complementary angular velocity skew-symmetric matrix and the unit supplementary angular velocity skew-symmetric matrix corresponding to the 7 parameters;

[0062]

[0063] (7.3) integrate and update the calculation of the 7 parameters, the formula is

[0064]

[0065]

[0066] Get the values of a k+1 , a 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 and a 33,k+1 at time t k+1 ;

[0067] (7.4) calculate the remaining two parameters according to X 7,k+1 , the formula is

[0068]

[0069] (7.5) put the integrated and updated values of a 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 and a 33,k+1 at time t k+1 into the calculated values of a 11,k+1 and a21,k+1 Substitute the values into the following formula to solve the coordinate transformation matrix from the navigation coordinate system to the body coordinate system

[0070]

[0071] In an embodiment of the present application, the speed update and the position update are performed according to the updated coordinate transformation matrix, specifically:

[0072] When p is an inertial system, the navigation equation is:

[0073]

[0074] wherein, is the updated coordinate transformation matrix, is the apparent acceleration, is the gravitational acceleration, V is the updated speed, T is the transpose of the matrix, and r is the updated position.

[0075] Compared with the prior art, the present application has the following beneficial effects:

[0076] (1) The present application discloses an inertial navigation few-parameter fixed-structure coordinate transformation matrix solving method, which can cover the cases of 9-parameter coordinate transformation matrix, 8-parameter coordinate transformation matrix and 7-parameter coordinate transformation matrix, and has universality.

[0077] (2) The present application discloses an inertial navigation few-parameter fixed-structure coordinate transformation matrix solving method, which can ensure high precision through trigonometric function integral solving, relative to the non-linear problem of differential equation when the number of parameters is less than 9.

[0078] (3) The present application discloses an inertial navigation few-parameter fixed-structure coordinate transformation matrix solving method, which can reduce the integral calculation amount relative to the differential equation of 9-parameter coordinate transformation matrix, and can realize full-attitude non-singular high-precision solving.

[0079] (4) The present application discloses an inertial navigation few-parameter fixed-structure coordinate transformation matrix solving method, which has simple structure and is easy to implement in engineering. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 is a step flow chart of the inertial navigation few-parameter fixed-structure coordinate transformation matrix solving method of the present application;

[0081] Figure 2 is a schematic diagram of the relationship between the body of the strapdown inertial system and the navigation coordinate system. DETAILED DESCRIPTION

[0082] To make the purpose, technical scheme and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0083] The application discloses a method for solving an inertial navigation few-parameter fixed-structure coordinate transformation matrix, which comprises the following steps: determining m parameters of the coordinate transformation matrix as real-time updated variables, wherein the m parameters can be directly used to solve the remaining 9-m parameters; integrating the m parameters by using a trigonometric function integration formula according to angular velocity values of the m parameters at t k time to obtain values of the m parameters at t k+1 time; calculating the remaining 9-m parameters of the coordinate transformation matrix, and finally obtaining the coordinate transformation matrix update and supporting velocity update and position update, so as to improve the precision of the inertial navigation. The method takes the angular rate output by a gyroscope orthogonally installed on a body of a strapdown inertial system as input information, realizes real-time update of the inertial navigation coordinate transformation matrix, and simplifies the calculation amount while ensuring the solving precision.

[0084] As shown in the step flow chart of the method for solving the inertial navigation few-parameter fixed-structure coordinate transformation matrix in the embodiment of the application, Figure 1 the method for solving the inertial navigation few-parameter fixed-structure coordinate transformation matrix comprises the following steps:

[0085] As shown in the step flow chart of the method for solving the inertial navigation few-parameter fixed-structure coordinate transformation matrix in the embodiment of the application, Figure 2 based on a strapdown inertial system fixed to a carrier, a body coordinate system (b system, as a moving system) corresponding to the strapdown inertial system is Ox′y′z′, a navigation coordinate system (p system, as a fixed system) for describing the rotating motion of the carrier is Oxyz, and the origins of the two coordinate systems coincide. In the rotating process, the angular velocity of the body of the strapdown inertial system relative to the navigation coordinate system is The method for solving the inertial navigation few-parameter fixed-structure coordinate transformation matrix realizes the following steps:

[0086] the coordinate transformation matrix of the body coordinate system of the strapdown navigation system relative to the navigation coordinate system at t k time is calculated;

[0087] the angular velocity of the body coordinate system relative to the navigation coordinate system at t k time is calculated wherein ω x′ , ω y′ and ω z′ are the angular velocities on the x, y and z axes of the body respectively;

[0088] the angular increment Δθ in the sampling time ΔT is calculated according to the angular velocity , and the calculation formula is

[0089] m parameters are selected from the coordinate transformation matrix to form a to-be-updated parameter vector X m,k , and the remaining 9-m parameters form a to-be-solved vector

[0090] According to the unit angular velocity skew-symmetric matrix N9 of the 9-parameter coordinate transformation matrix, the unit angular velocity skew-symmetric matrix N corresponding to the m parameters is determined m , the unit complementary angular velocity skew-symmetric matrix , and the unit supplementary angular velocity skew-symmetric matrix

[0091] According to the coordinate transformation matrix and the angular velocity, the m parameters are integrated to update and solve, and the calculation formula is

[0092]

[0093] According to X m,k+1 , the remaining 9-m parameters are solved to obtain the updated coordinate transformation matrix;

[0094] According to the updated coordinate transformation matrix, the velocity is updated and the position is updated.

[0095] Preferably, the calculation obtains the coordinate transformation matrix of the body coordinate system of the strapdown navigation system relative to the navigation coordinate system at t k , and specifically is:

[0096]

[0097] In the formula, a 11,k , a 12,k , a 13,k , a 21,k , a 22,k , a 23,k , a 31,k , a 32,k , and a 33,k are 9 parameters of the coordinate transformation matrix at t k , and the vector X9 composed of the 9 parameters is

[0098]

[0099] , and the unit angular velocity skew-symmetric matrix

[0100]

[0101] Preferably, the m parameters constitute the to-be-updated parameter vector X m,k , and the remaining 9-m parameters constitute the to-be-solved vector The relationship between the vector X9 composed of the 9 parameters and the vector Xm composed of the m parameters is

[0102]

[0103] Wherein, the selection parameter matrix P and the discard parameter matrix Q are m×9 and 9-m×9 dimension time invariant matrices, respectively, and they satisfy P T P+Q T Q = I.

[0104] Preferably, the unit angular velocity antisymmetric matrix N9 determines the unit angular velocity antisymmetric matrix N corresponding to m parameters. m antisymmetric matrix of unit covariant angular velocity and the antisymmetric matrix of unit supplementary angular velocity The specific calculation formula is as follows:

[0105]

[0106] Preferred, based on X m,k+1 The remaining 9-m parameters are solved, mainly using a lookup table method. The calculation formula is as follows:

[0107]

[0108] Preferably, when m=8, 8 parameters a are selected. 12,k a 13,k a 21,k a 22,k a 23,k a 31,k a 32,k and a 33,k ; at the next moment t k+1 =t k The value of +ΔT after integration is a 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The specific calculation formula is as follows:

[0109] (6.1) Determine the values ​​of the selection parameter matrix P and the discard parameter matrix Q, as well as the values ​​of their transpose matrices;

[0110]

[0111] Q = [100000000] 1×9 ;

[0112] The selected parameter vector is

[0113]

[0114] (6.2) Calculate the antisymmetric matrix N8 of unit angular velocity and the antisymmetric matrix of unit co-angular velocity corresponding to the 8 parameters. and the antisymmetric matrix of unit supplementary angular velocity The value;

[0115]

[0116]

[0117] (6.3) Perform an integral update solution on the eight parameters, using the following formula:

[0118]

[0119] Get t k+1 a of time 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The value of .

[0120] (6.4) Based on X 8,k+1 The remaining parameter is solved using the following formula:

[0121]

[0122] (6.5) Put t k+1 The integral update value a at time t is 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The sum of the calculated values ​​a 11,k+1 Substituting into the following equation, the coordinate transformation matrix from the navigation coordinate system to the body coordinate system is obtained as follows:

[0123]

[0124] Preferably, when m=7, 7 parameters a are selected. 13,k a 21,k a 22,k a 23,k a 31,k a 32,k and a 33,k ; at the next moment t k+1 =t k The value of +ΔT after integration is a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a32,k+1 and a 33,k+1 , the specific formula is:

[0125] (7.1) determine the value of the selected parameter matrix P and the abandoned parameter matrix Q and the value of its transpose matrix;

[0126]

[0127] The selected parameter vector is

[0128]

[0129] (7.2) calculate the values of the unit angular velocity skew-symmetric matrix N7 corresponding to the 7 parameters, the unit complementary angular velocity skew-symmetric matrix and the unit supplementary angular velocity skew-symmetric matrix ;

[0130]

[0131] (7.3) integrate and update the calculation of the 7 parameters, the formula is

[0132]

[0133]

[0134] Get the values of a k+1 , a 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 and a 33,k+1 at time t k+1 .

[0135] (7.4) according to X 7,k+1 , the remaining two parameters are calculated, the formula is

[0136]

[0137] (7.5) put the integral update values a 13,k+1 , a 21,k+1 , a 22,k+1 , a 23,k+1 , a 31,k+1 , a 32,k+1 and a 33,k+1 at time t k+1 and the calculated values a 11,k+1 and a 21,k+1 into the following formula to solve the coordinate transformation matrix from the navigation coordinate system to the body coordinate system

[0138]

[0139] (9) According to the integral updating calculation of the coordinate transformation matrix, the velocity updating and position updating are supported to improve the precision of the inertial navigation. The updated coordinate transformation matrix and the visual acceleration and the gravity acceleration are taken as the input of the velocity differential equation After the integral calculation, the updated velocity V is obtained. The updated velocity V is taken as the input of the position differential equation After the integral calculation, the updated position r is obtained.

[0140] The gyroscopes installed on the body of the strapdown inertial system are three single-degree-of-freedom gyroscopes or two double-degree-of-freedom gyroscopes.

[0141] The contents not described in detail in the specification of the present application are the known technology of the person skilled in the art.

[0142] Although the present application has been disclosed with the above preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not depart from the technical solutions of the present application, shall fall within the protection scope of the technical solutions of the present application.

Claims

1. A method for solving the coordinate transformation matrix of inertial navigation with few parameters and a fixed structure, characterized in that, include: The calculation yields the relative coordinate system of the strapdown navigation system to the navigation coordinate system at time t. k The coordinate transformation matrix at time step; Calculate at t k Angular velocity of the body coordinate system relative to the navigation coordinate system at any given moment Where, ω x′ ω y′ ω z′ These are the angular velocities of the body along the x, y, and z axes, respectively. Based on angular velocity The formula for calculating the angular increment Δθ within the sampling time ΔT is as follows: Select m parameters from the coordinate transformation matrix to form the parameter vector X to be updated. m,k The remaining 9-m parameters constitute the vector to be solved. Based on the antisymmetric matrix N9 of the 9-parameter coordinate transformation matrix, determine the antisymmetric matrix N of the unit angular velocity corresponding to the m parameters. m antisymmetric matrix of unit coaxial angular velocity and the antisymmetric matrix of unit supplementary angular velocity Based on the coordinate transformation matrix and angular velocity, the m parameters are updated by integration, and the calculation formula is as follows: According to X m,k+1 Solve for the remaining 9-m parameters to obtain the updated coordinate transformation matrix; Based on the updated coordinate transformation matrix, the velocity and position are updated. The strapdown navigation system's body coordinate system relative to the navigation coordinate system at t k The coordinate transformation matrix at time t is: In the formula, a 11,k a 12,k a 13,k a 21,k a 22,k a 23,k a 31,k a 32,k and a 33,k For in t k The time coordinate transformation matrix has nine parameters, and the vector X9 formed by these nine parameters is... and the antisymmetric matrix of unit angular velocity The m parameters constitute the parameter vector X to be updated. m,k The vector to be solved, along with the remaining 9-m parameters, constitutes the solution vector. The relationship between the vector X9 consisting of 9 parameters is as follows: Wherein, the selection parameter matrix P and the discard parameter matrix Q are m×9 and 9-m×9 dimension time invariant matrices, respectively, and they satisfy P T P+Q T Q = I; Determine the antisymmetric matrix N of unit angular velocity corresponding to m parameters. m antisymmetric matrix of unit coaxial angular velocity and the antisymmetric matrix of unit supplementary angular velocity The specific calculation formula is as follows:

2. The inertial navigation method for solving the coordinate transformation matrix with few parameters according to claim 1, characterized in that, According to X m,k+1 The remaining 9-m parameters are solved using a lookup table method, and the calculation formula is as follows:

3. The inertial navigation method for solving the coordinate transformation matrix with few parameters according to claim 2, characterized in that, When m = 8, 8 parameters a are selected. 12,k a 13,k a 21,k a 22,k a 23,k a 31,k a 32,k and a 33,k ; at the next moment t k+1 =t k The value of +ΔT after integration is a 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The specific calculation formula is as follows: (6.1) Determine the values ​​of the selection parameter matrix P and the discard parameter matrix Q, as well as the values ​​of their transpose matrices; The selected parameter vector is (6.2) Calculate the antisymmetric matrix N8 of unit angular velocity and the antisymmetric matrix of unit co-angular velocity corresponding to the 8 parameters. and the antisymmetric matrix of unit supplementary angular velocity The value; (6.3) Perform an integral update solution on the eight parameters, using the following formula: Get t k+1 a of time 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The value; (6.4) Based on X 8,k+1 The remaining parameter is solved using the following formula: (6.5) Put t k+1 The integral update value a at time t is 12,k+1 a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The sum of the calculated values ​​a 11,k+1 Substituting into the following equation, the coordinate transformation matrix from the navigation coordinate system to the body coordinate system is obtained as follows:

4. The inertial navigation method for solving the coordinate transformation matrix with few parameters according to claim 2, characterized in that, When m = 7, select 7 parameters a 13,k a 21,k a 22,k a 23,k a 31,k a 32,k and a 33,k ; at the next moment t k+1 =t k The value of +ΔT after integration is a 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The specific calculation formula is as follows: (7.1) Determine the values ​​of the selection parameter matrix P and the discard parameter matrix Q, as well as the values ​​of their transpose matrices; The selected parameter vector is (7.2) Calculate the antisymmetric matrix N7 of unit angular velocity and the antisymmetric matrix of unit co-angular velocity corresponding to the 7 parameters. and the antisymmetric matrix of unit supplementary angular velocity The value; (7.3) Perform an integral update solution on the seven parameters, using the following formula: Get t k+1 a of time 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 The value; (7.4) Based on X 7,k+1 The remaining two parameters are solved using the following formula: (7.5) Put t k+1 The integral update value a at time t is 13,k+1 a 21,k+1 a 22,k+1 a 23,k+1 a 31,k+1 a 32,k+1 and a 33,k+1 With the solution value a 11,k+1 and a 21,k+1 Substituting the values ​​into the following formula, the coordinate transformation matrix from the navigation coordinate system to the body coordinate system is obtained as follows:

5. The inertial navigation method for solving the coordinate transformation matrix with few parameters according to claim 1, characterized in that: The step of updating the velocity and position based on the updated coordinate transformation matrix specifically involves: When p is an inertial frame of reference, the navigation equations are: in, This is the updated coordinate transformation matrix. For apparent acceleration, Let V be the acceleration due to gravity, V be the updated velocity, T be the transpose of the matrix, and r be the updated position.

6. The inertial navigation method for solving the coordinate transformation matrix with few parameters according to claim 1, characterized in that: The gyroscopes installed on the strapdown inertial system body are three single-degree-of-freedom gyroscopes.

7. The inertial navigation method for solving the coordinate transformation matrix with few parameters according to claim 1, characterized in that: The gyroscopes installed on the strapdown inertial system body are two two-degree-of-freedom gyroscopes.

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