A Strapdown Inertial Navigation System-Level Calibration Method Based on Matrix Decomposition

Abstract

The invention discloses a strapdown inertial navigation system-level calibration method based on matrix decomposition, and the steps are: selecting a set of navigation-level fiber optic gyro strapdown inertial navigation system; starting a preheating device for half an hour to stabilize the system; hovering according to six predetermined calibration paths, and staying still for 10 minutes at each position; collecting gyro and accelerometer outputs, performing system-level calibration based on matrix decomposition, and collecting data; inputting the calibrated parameters into the strapdown inertial navigation system to perform static navigation data solution to obtain the final result. The strapdown inertial navigation system-level calibration method based on matrix decomposition of the invention can complete the decoupling and estimation of all installation error matrix parameters, and the calibration accuracy meets the inertial navigation accuracy requirements; by designing different strapdown matrices to perform dimensionality reduction processing on the Kalman filter equation, not only can the decoupling and estimation of all installation error matrix parameters be achieved, but also it has a certain guiding significance for the installation of inertial elements.

Description

Technical Field

[0001] The invention belongs to the technical field of strapdown inertial navigation system calibration, and in particular relates to a strapdown inertial navigation system-level calibration method based on matrix decomposition. Background Art

[0002] There are many sources of error in the strapdown inertial navigation system. One of the most important sources of error is the calibration error of the inertial measurement unit (IMU), which directly affects the navigation accuracy of the system. The solution to the calibration error of the inertial measurement unit is to calibrate it regularly. The most commonly used method is the system-level calibration method. The system-level calibration uses the navigation error as the observed quantity and infers the calibration model parameters through fitting or filtering methods. The difficulty of the study is that the calibration parameters on the non-main diagonal of the error matrix are coupled together and difficult to identify effectively. The coupling of calibration parameters increases the difficulty of designing filters in system-level calibration, reduces the accuracy of calibration parameter estimation, and seriously restricts the widespread application and development of strapdown inertial navigation systems.

[0003] In order to solve the problems of system-level calibration parameter coupling and long filtering time, the following solutions are currently proposed: First, starting from the IMU calibration error model, the calibration error model is simplified. The installation error matrix in the IMU calibration model is defined as an upper triangular matrix or the model parameters are simplified by assuming that one axis of the two coordinate systems coincides. This method reduces the accuracy of the calibration model at the expense of the IMU calibration accuracy and the navigation accuracy of the inertial navigation system; second, the installation error is introduced into the rotating inertial navigation system model by taking advantage of the fact that the rotating inertial navigation system (RINS) can rotate around one or more axes, but the general inertial navigation system does not have the rotation function of RINS; third, a multi-position rotation scheme is designed by using gravity and the angular velocity of the earth's rotation or the angular velocity of the turntable to stimulate the IMU calibration parameter error, and the calibration parameters are estimated by using methods such as Kalman filtering or unscented Kalman filtering; fourth, only some parameters are quickly calibrated according to the needs of the use and environment of the inertial navigation system, and all parameters cannot be calibrated.

[0004] Therefore, it is of great significance to design a calibration method with high precision that can reduce the design difficulty of the filter in the calibration. Summary of the invention

[0005] Based on the above deficiencies in the prior art, the technical problem solved by the present invention is to provide a strapdown inertial navigation system-level calibration method based on matrix decomposition, which can complete the decoupling and estimation of all installation error matrix parameters, and the calibration accuracy meets the inertial navigation accuracy requirements.

[0006] In order to solve the above technical problems, the present invention is implemented by the following technical solutions:

[0007] The strapdown inertial navigation system-level calibration method based on matrix decomposition of the present invention comprises the following steps:

[0008] Step S1: Select a navigation-grade fiber optic gyro strapdown inertial navigation system;

[0009] Step S2: start the preheating device for half an hour to stabilize the system;

[0010] Step S3: hovering along the six predetermined calibration paths, and staying still for 10 minutes at each position;

[0011] Step S4: collecting gyro and accelerometer outputs, performing system-level calibration based on matrix decomposition, and collecting data;

[0012] Step S5: input the calibrated parameters into the strapdown inertial navigation system to perform static navigation data solution to obtain the final result.

[0013] Further, in step S4, according to the conversion model between the gyro and accelerometer output pulses and the angular rate and specific force and the relationship between the output vectors in different coordinate systems, a strapdown inertial navigation system calibration mathematical model is established as follows:

[0014]

[0015]

[0016] Where N g and N a is the gyro pulse output and accelerometer pulse output; K g and K a is the gyro scale factor and accelerometer scale factor; ω g and f a is the gyro angular rate and accelerometer relative force; D0 and is the gyro zero position and accelerometer bias.

[0017] Furthermore, in step S4, the matrix decomposition principle is introduced to transform the matrix Decompose into the sum of the skew-symmetric error matrix and the symmetric error matrix:

[0018]

[0019] in: is the coordinate transformation matrix from b system to g(a) system; express The skew-symmetric matrix in ; express The symmetric matrix in can be further obtained:

[0020]

[0021]

[0022] Furthermore, the error model of the strapdown inertial navigation system caused by the calibration error under the static base is established:

[0023]

[0024]

[0025] Where δv is the velocity error; φ is the attitude error; f n is the specific force vector in the navigation system; is the transformation matrix from the carrier coordinate system to the navigation coordinate system; δf b is the specific force error in carrier coordinates; is the projection of the Earth's rotation angular velocity under navigation; δω b is the angular rate error in the carrier coordinate system; calibration error and angular rate error δω b , specific force error δf b The relationship between them is:

[0026] δω b =E g ω b +ε

[0027] In the formula Similarly:

[0028] δf b =E a f b +Δ.

[0029] Furthermore, in step S3, a strapdown inertial navigation system error equation is established:

[0030]

[0031]

[0032] According to the matrix decomposition principle, E g It can be decomposed into a skew-symmetric matrix and the symmetric matrix

[0033]

[0034] Where: The relationship between the accelerometer calibration error and the specific force error can be written as:

[0035]

[0036] Furthermore, in step 4, for the Kalman filter system-level calibration with velocity error and attitude error as observation quantities, a Kalman filter system with a 30-dimensional state vector is established. By designing a multi-position IMU calibration path and merging the IMU calibration error parameters, the 30-dimensional state vector is reduced to 12 dimensions, thereby achieving fast and high-precision calibration of the strapdown inertial navigation system.

[0037] From the above, the strapdown inertial navigation system-level calibration method based on matrix decomposition of the present invention has at least the following beneficial effects:

[0038] First, by deriving the physical cause of the installation error matrix, the installation error matrix is ​​decomposed into a skew-symmetric matrix and a symmetric matrix;

[0039] 2. Design the system-level calibration path based on the velocity error equation and attitude error equation of the inertial navigation system;

[0040] 3. By changing the strapdown matrix The value of , separates the installation error matrix coupling parameters;

[0041] 4. Achieve complete estimation of calibration parameters.

[0042] 5. By designing different strapdown matrices to reduce the dimension of the Kalman filter equation, and then performing algebraic decoupling calculations on the calibration parameters coupled together at different positions, not only can the decoupling and estimation of all installation error matrix parameters be achieved, but also it has certain guiding significance for the installation of inertial components.

[0043] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following is a detailed description in combination with the preferred embodiments and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solution of the embodiment of the present invention, the drawings of the embodiment are briefly introduced below.

[0045] Figure 1 To design the calibration path diagram, the three axes point to sky-east-north, earth-west-north, east-sky-south, east-earth-north, east-north-sky, and east-south-earth.

[0046] Figure 2 This is the simulation experiment result diagram of position 1;

[0047] Figure 3 This is the simulation experiment result diagram for position 2;

[0048] Figure 4 This is the simulation experiment result diagram of position 3;

[0049] Figure 5 This is the simulation experiment result diagram of position 4;

[0050] Figure 6 This is the simulation experiment result diagram of position 5;

[0051] Figure 7 This is the simulation experiment result diagram of position 6;

[0052] Figure 8 Figure 1 is a diagram of the experimental setup;

[0053] Fig. 9 The present invention is a flow chart of the strapdown inertial navigation system-level calibration method based on matrix decomposition. DETAILED DESCRIPTION

[0054] like Figures 1 to 9 As shown, the strapdown inertial navigation system-level calibration method based on matrix decomposition of the present invention comprises the following steps:

[0055] The first step is to select a navigation-grade fiber optic gyro strapdown inertial navigation system;

[0056] Step 2: Start the preheating device for half an hour to stabilize the system;

[0057] Step 3: Hover along the six predetermined calibration paths and stay still for 10 minutes at each position;

[0058] Step 4: Collect gyro and accelerometer outputs, perform system-level calibration based on matrix decomposition, and collect data;

[0059] Step 5: Input the calibrated parameters into the strapdown inertial navigation system to solve the static navigation data and obtain the final result.

[0060] When solving the strapdown inertial navigation system, the output of the gyro and the output of the accelerometer must be converted to the carrier coordinate system. Therefore, the key to the mathematical modeling of the strapdown inertial navigation system calibration is the coordinate system conversion problem between the gyro coordinate system (g system) and the accelerometer coordinate system (a system) and the carrier coordinate system (b system). According to the conversion model between the output pulses of the gyro and accelerometer and the angular rate and specific force, and the relationship between the output vectors in different coordinate systems.

[0061] The calibration mathematical model of the strapdown inertial navigation system is:

[0062]

[0063]

[0064] Among them, Ng and N a is the gyro pulse output and accelerometer pulse output; K g and K a is the gyro scale factor and accelerometer scale factor; ω g and f a is the gyro angular rate and accelerometer relative force; D0 and is the gyro zero position and accelerometer bias.

[0065] According to the matrix decomposition principle, the matrix Decompose into the sum of the skew-symmetric error matrix and the symmetric error matrix.

[0066]

[0067] in: is the coordinate transformation matrix from b system to g(a) system; express The skew-symmetric matrix in ; express The symmetric matrix in . Further, we can get:

[0068]

[0069]

[0070] The error model of the strapdown inertial navigation system caused by the calibration error under the static base is:

[0071]

[0072]

[0073] Among them, δv is the velocity error; φ is the attitude error; f n is the specific force vector in the navigation system; is the transformation matrix from the carrier coordinate system to the navigation coordinate system; δf b is the specific force error in carrier coordinates; is the projection of the Earth's rotation angular velocity under navigation; δω b is the angular velocity error in the carrier coordinate system. The calculated calibration parameters

[0074]

[0075]

[0076]

[0077]

[0078] Introduce into the strapdown inertial navigation system calibration mathematical model:

[0079]

[0080]

[0081] Substituting (4) into (5) yields:

[0082]

[0083] make:

[0084]

[0085]

[0086] get:

[0087] δω b =E g ω b +ε (9)

[0088] δf b =E a f b +Δ (10)

[0089] Based on this, the error equation of the strapdown inertial navigation system is obtained:

[0090]

[0091]

[0092] E g Decompose into a skew-symmetric matrix and the symmetric matrix

[0093]

[0094]

[0095] The relationship between the accelerometer calibration error and the specific force error is:

[0096] δf b =E a f b +Δ

[0097]

[0098] The new system-level calibration scheme is divided into two steps for the decoupling design of calibration parameter errors: first, the dimension of the Kalman filter is reduced, and the calibration parameters are merged and estimated by taking advantage of the characteristics of calibration error parameter coupling; second, the matrix is ​​changed by calibration path design. Decouples coupled parameters that were merged together. Figure 1 To design the calibration path diagram, the three axes point to sky-east-north, earth-west-north, east-sky-south, east-earth-north, east-north-sky, and east-south-earth.

[0099] The specific design idea is: to simplify the calculation, the turntable is kept stationary. The elements in are only 1, 0 and -1. At this time, f b ,ω b The elements are 0, ±g, in is the geographical latitude, Abbreviated as ω c , Abbreviated as ω s Combined with the error coupling characteristics of calibration parameters, the calibration parameters are separated by designing different positions. a 、E g Separate from Δ and ε, and then separate E a 、E g Parameters in . We get:

[0100]

[0101]

[0102] Table 1 shows the design of various positions in the system-level calibration path. f b ,ω b value.

[0103] Table 1 System level calibration path

[0104]

[0105]

[0106] According to the designed calibration path, 6 positions are obtained and the system error equation is:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Perform Kalman filter calculation and design the jth (j=1~12) parameter of the ith (i=1~6)th position as The 1st to 6th state quantities of Kalman filtering are The 7th to 12th state variables of Kalman filtering for:

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

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[0149]

[0150] By using formulas (22) to (27) to establish the state vectors at different positions, we can get 6 positions x7 to x 12 The filtered steady-state estimate of The calibration parameter errors of the strapdown inertial navigation system, such as the scale factor, installation error and zero position, are coupled together, and 24 calibration error parameters are decoupled and calculated. Decoupling equations (22) to (27):

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] So far, the strapdown inertial navigation system-level calibration based on matrix decomposition has been completed. The strapdown inertial navigation system-level calibration method based on matrix decomposition is simulated and the initial value of the Kalman filter state vector X(0) = 0 12×1 , initial covariance matrix initial value System noise variance matrix and the measurement noise variance matrix R = diag[(0.01) 2 ,(0.01) 2 ,(0.01) 2 ,(0.01°) 2 ,(0.01°) 2 ,(0.01°) 2 ], Table 2 is the simulation parameter design.

[0164] Table 2 Simulation parameter design

[0165]

[0166] Figure 2 The simulation results for position 1 are as follows: Figure 3 The simulation results for position 2 are as follows: Figure 4 The simulation results for position 3 are as follows: Figure 5 This is the simulation experiment result of position 4. Figure 6 This is the simulation result of position 5. Figure 7 This is the simulation result of position 6. According to the simulation results, we can know the state quantities of the 6 positions can all be estimated. Substituting the estimated results into formula (28), the 24 parameters to be calibrated of the strapdown inertial navigation system are calculated as follows: It is found that the relative error of the gyro calibration parameters in the strapdown inertial navigation system is between 0.03% and 0.55%, and the relative error of the accelerometer calibration parameters is between 0.01% and 0.24%, as shown in Table 3.

[0167] Table 3. Errors of parameters to be calibrated in the strapdown inertial navigation system

[0168]

[0169] Calibration and navigation experiments were performed on the navigation-grade fiber optic gyro strapdown inertial navigation system. Figure 8 This is a diagram of the experimental device. Hovering experiments were carried out at the positions of sky-east-north, ground-west-north, east-sky-south, east-ground-north, east-north-sky, and east-south-ground, and the navigation and positioning results under different calibration methods were compared. The three navigation positioning errors based on the traditional system-level calibration method were 0.757n mile / h, 0.773n mile / h, and 0.778n mile / h, respectively. The three navigation positioning errors based on the matrix decomposition system-level calibration method were 0.522n mile / h, 0.515n mile / h, and 0.541n mile / h, respectively. The positioning errors of the strapdown inertial navigation system in the three experiments were reduced by 31%, 33%, and 30%, respectively.

[0170] The strapdown inertial navigation system-level calibration method based on matrix decomposition of the present invention can effectively identify the parameters coupled together in the strapdown inertial navigation system-level calibration, and on this basis, a Kalman filter dimensionality reduction processing method is designed, which includes the following parts:

[0171] First, by deriving the physical cause of the installation error matrix, the installation error matrix is ​​decomposed into a skew-symmetric matrix and a symmetric matrix;

[0172] 2. Design the system-level calibration path based on the velocity error equation and attitude error equation of the inertial navigation system;

[0173] 3. By changing the strapdown matrix The value of , separates the installation error matrix coupling parameters;

[0174] 4. Achieve complete estimation of calibration parameters.

[0175] The present invention reduces the dimension of the Kalman filter equation by designing different strapdown matrices, and then performs algebraic decoupling calculation on calibration parameters coupled together at different positions, which can not only realize the decoupling and estimation of all installation error matrix parameters, but also has certain guiding significance for the installation of inertial elements.

[0176] The above is only a preferred embodiment of the present invention, which certainly cannot be used to limit the scope of rights of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and changes can be made without departing from the principle of the present invention, and these improvements and changes are also regarded as the protection scope of the present invention.

Claims

1. A strapdown inertial navigation system-level calibration method based on matrix decomposition, characterized in that: The following steps are involved: Step S1: Select a navigation-grade fiber optic gyro strapdown inertial navigation system; Step S2: start the preheating device for half an hour to stabilize the system; Step S3: hovering along the six predetermined calibration paths, and staying still for 10 minutes at each position; Step S4: collecting gyro and accelerometer outputs, performing system-level calibration based on matrix decomposition, and collecting data; Step S5: input the calibrated parameters into the strapdown inertial navigation system to perform static navigation data solution to obtain the final result; In step S4, the matrix decomposition principle is introduced to transform the matrix Decompose into the sum of the skew-symmetric error matrix and the symmetric error matrix: in: is the coordinate transformation matrix from b system to g(a) system; express The skew-symmetric matrix in ; express The symmetric matrix in can be further obtained: In step S3, the strapdown inertial navigation system error equation is established: According to the matrix decomposition principle, E g Decompose into a skew-symmetric matrix and the symmetric matrix Where: The relationship between the accelerometer calibration error and the specific force error can be written as:

2. The strapdown inertial navigation system-level calibration method based on matrix decomposition as claimed in claim 1, characterized in that: In step S4, according to the conversion model between the gyro and accelerometer output pulses and the angular rate and specific force and the relationship between the output vectors in different coordinate systems, a strapdown inertial navigation system calibration mathematical model is established as follows: Where N g and N a is the gyro pulse output and accelerometer pulse output; K g and K a is the gyro scale factor and accelerometer scale factor; ω g and f a is the gyro angular rate and accelerometer relative force; D0 and is the gyro zero position and accelerometer bias.

3. The strapdown inertial navigation system-level calibration method based on matrix decomposition as claimed in claim 1, characterized in that: Establish the error model of strapdown inertial navigation system caused by calibration error under static base: Where δv is the velocity error; φ is the attitude error; f n is the specific force vector in the navigation system; is the transformation matrix from the carrier coordinate system to the navigation coordinate system; δf b is the specific force error in carrier coordinates; is the projection of the Earth's rotation angular velocity under navigation; δω b is the angular rate error in the carrier coordinate system; calibration error and angular rate error δω b , specific force error δf b The relationship between them is: here b =E g oh b +e In the formula Similarly: δf b =E a f b +Δ。 4. The strapdown inertial navigation system-level calibration method based on matrix decomposition as claimed in claim 1, characterized in that: In step 4, for the Kalman filter system-level calibration with velocity error and attitude error as observation quantities, a Kalman filter system with a 30-dimensional state vector is established. By designing a multi-position IMU calibration path and merging the IMU calibration error parameters, the 30-dimensional state vector is reduced to 12 dimensions, thereby achieving fast and high-precision calibration of the strapdown inertial navigation system.

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