Error calibration method of resonant inertial navigation system with four gyroscopes in conical configuration

Abstract

The present invention relates to a resonant inertial navigation error calibration method for a four-gyroscope conical configuration, comprising the following steps: 1. constructing an error compensation model based on the conversion relationship between the gyroscope sensitive axis and the inertial navigation system coordinate system B, and determining error compensation parameters in the error compensation model that affect the output of the resonant inertial navigation system; 2. solving the error compensation parameters in step 1, substituting the solution results into the error compensation model, and solving the error compensation model. The method comprises the following steps: 2.1 fixing the resonant inertial navigation system with the four-gyroscope conical configuration on a three-axis turntable, rotating it, and obtaining output data of the resonant inertial navigation system; 2.2 using the output data of the resonant inertial navigation system obtained in step 2.1 in combination with the least squares method to solve the error compensation parameters determined in step 1; and 2.3 using the error compensation parameters obtained in step 2.2 to solve the error compensation model. The present invention greatly simplifies the error compensation process, improves error compensation efficiency, and creates basic conditions for achieving high precision in resonant inertial navigation.

Description

Technical Field

[0001] The present invention relates to the field of resonant inertial navigation technology, and in particular to a resonant inertial navigation error calibration method for four gyroscopes in a conical configuration. Background Art

[0002] Multi-gyroscope configurations are a key technical approach to achieving high precision in resonant inertial navigation systems. Considering factors such as system cost, size, and weight, a four-gyroscope conical configuration is the optimal solution for resonant inertial navigation systems. The gyroscopes in this conical configuration are non-orthogonally mounted, and their error compensation model differs from that of traditional three-gyroscope orthogonal inertial navigation systems. Research on the error compensation parameters for this conical configuration is lacking, necessitating the development of a model for the error compensation of inertial navigation systems using this configuration and the design of a corresponding discrete error compensation model approach to lay the foundation for subsequent system navigation solutions. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a resonant inertial navigation error calibration method for a four-gyroscope conical configuration. This method can directly establish the conversion relationship between the four gyroscope sensitive axes and the inertial navigation system coordinate system B, obtain the error compensation parameters for each gyroscope, and then convert the four gyroscope sensitive angular velocities to the inertial navigation system coordinate system B. This method is simple and direct, requiring no intermediate conversion steps, greatly simplifying the error compensation process and improving error compensation efficiency.

[0004] The above-mentioned purpose of the present invention is achieved through the following technical solutions:

[0005] A method for calibrating the error of a resonant inertial navigation system with four gyroscopes arranged in a conical configuration, characterized in that it comprises the following steps:

[0006] Step 1: Based on the conversion relationship between the gyroscope sensitive axis and the inertial navigation system coordinate system B, an error compensation model is constructed to determine the error compensation parameters that affect the output of the resonant inertial navigation system in the error compensation model;

[0007] Step 2: Solve the error compensation parameters in step 1 and substitute the solution into the error compensation model to solve the error compensation model, including:

[0008] 2.1 The resonant inertial navigation system with four gyroscopes in a conical configuration is fixedly mounted on a three-axis turntable and rotated to obtain the resonant inertial navigation system output data;

[0009] 2.2 Using the output data of the resonant inertial navigation system obtained in step 2.1, the error compensation parameters determined in step 1 are solved by the least squares method;

[0010] 2.3 Use the error compensation parameters obtained in step 2.2 to solve the error compensation model.

[0011] Further: Step 1 includes:

[0012] 1.1. Arbitrarily distribute four gyroscopes on the same conical surface. The ideal sensitive axis of the gyroscope is G i (i=1,2,3,4), the inertial navigation system coordinate system b is OX b Y b Z b ; The ideal azimuth angle α of the i-th (i=1,2,3,4) gyroscope i G i In OX b Y b Plane projection and OX b The angle between the axes, the ideal pitch angle β i G i With flat OX b Y b The angle between

[0013] Due to the existence of installation error, the actual sensitive axis G of the gyroscope i ′ and the ideal sensitive axis G i The small angle installation error is δα i and δβ i , then G i ′ corresponds to the actual azimuth α i ′ and actual pitch angle β i ′ can be expressed as:

[0014]

[0015] 1.2. Define the actual input angular velocity of the four gyroscopes as M′=[m1′m2′m3′m4′] T , the input angular velocity of the inertial navigation system coordinate system b is ω=[ω x ω y ω z ] T , the output pulses of the four gyroscopes are N g =[N g1 N g2 N g3 N g4 ] T , the scaling factor is K = diag([k1k2k3k4] T ), the error compensation model is established through the relationship between the output pulse and the error compensation parameter:

[0016] N g =KM′=K(H+δα·P+δβ·Q)ω

[0017] in,

[0018]

[0019]

[0020]

[0021] δα=diag([δα1δα2δα3δα4] T )

[0022] δβ=diag([δβ1δβ2δβ3δβ4] T )

[0023] Where H is the measurement matrix, P is the azimuth conversion matrix, Q is the elevation conversion matrix, δα is the azimuth installation error matrix, δβ is the elevation installation error matrix, and k i , δα i , δβ i (i=1, 2, 3, 4) are the error compensation parameters that affect the output of the resonant inertial navigation system and are also the error compensation parameters to be determined.

[0024] Further, step 2.1 is: fix the resonant inertial navigation system with four gyroscopes in a conical configuration on a three-axis turntable, and make the inertial navigation system coordinate system b coincide with the turntable coordinate system t; rotate the turntable, and the specific rotation order is as follows:

[0025] 1) Rotate the turntable so that the inertial navigation system coordinate system b system OZ b Axis and turntable frame axis Z t Coincidentally, make the turntable outer frame axis (Z t ) rotates forward for n circles, then reverse for n circles, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and

[0026] 2) Rotate the turntable so that the inertial navigation system coordinate system b system OY b Axis and turntable frame axis Z t Coincident, around the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and

[0027] 3) Rotate the turntable so that the inertial navigation system coordinate system b is OX b Axis and turntable frame axis Z t Coincident, around the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and

[0028] Further: Step 2.2 is: calculate the error compensation parameters using the least squares method:

[0029] The least squares calculation model of error compensation parameters is established as follows:

[0030] Ax i =B

[0031] in,

[0032]

[0033]

[0034]

[0035] The error compensation parameters are calculated using the least squares algorithm

[0036] x i =(A T A) -1 A T B,

[0037] Substitute i (i = 1, 2, 3, 4) into the above formula to obtain the i (i = 1, 2, 3, 4) gyroscope error compensation parameter matrix x i Where x i It is k i , δα i , δβ i The matrix of .

[0038] The present invention has the following advantages and positive effects:

[0039] This invention designs a resonant inertial navigation error calibration method for four gyroscopes in a conical configuration. This method is applicable to resonant inertial navigation systems with four gyroscopes in a conical configuration distributed in arbitrary spatial positions. This method directly establishes a conversion relationship between the four gyroscope sensitive axes and the inertial navigation system coordinate system B, obtains error compensation parameters for each gyroscope, and then converts the four gyroscope sensitive angular velocities to the inertial navigation system coordinate system B. This method is simple and direct, requiring no intermediate conversion steps, greatly simplifying the error compensation process and improving error compensation efficiency, creating the foundation for achieving high-precision resonant inertial navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a conical configuration diagram of the four gyroscopes of the present invention. DETAILED DESCRIPTION

[0041] The structure of the present invention will be further described below with reference to the accompanying drawings and through examples. It should be noted that the present examples are descriptive rather than restrictive.

[0042] A resonant inertial navigation error calibration method for a four-gyroscope conical configuration can directly establish the conversion relationship between the four gyroscope sensitive axes and the inertial navigation system coordinate system B, obtain the error compensation parameters of each gyroscope, and then convert the four gyroscope sensitive angular velocities to the inertial navigation system coordinate system B. This method is simple and direct, without the need for intermediate conversion links, greatly simplifying the error compensation process and improving error compensation efficiency. The four-gyroscope conical configuration diagram of the present invention is shown in FIG. Figure 1 shown.

[0043] Step 1: Construct an error compensation model and determine the error compensation parameters that affect the output of the resonant inertial navigation system in the error compensation model.

[0044] First, construct the conversion model between the gyroscope sensitive axis and the inertial navigation system coordinate system B. Specifically:

[0045] The four gyroscopes are randomly distributed on the same conical surface, and the ideal sensitive axis of the gyroscope is G i (i=1,2,3,4), the inertial navigation system coordinate system b is OX b Y b Z b The ideal azimuth angle α of the i-th (i=1,2,3,4) gyroscope i G i In OX b Y b Plane projection and OX b The angle between the axes, the ideal pitch angle β i G i With flat OX b Y b Angle.

[0046] In actual situations, due to the existence of installation errors, it is impossible to guarantee the actual sensitive axis G of the gyroscope. i ′ and the ideal sensitive axis G i Strictly coincide. Set the two to have a small angle installation error δα i and δβ i , then G i ′ corresponds to the actual azimuth α i ′ and actual pitch angle β i ′ can be expressed as:

[0047]

[0048] Define the actual input angular velocity of the four gyroscopes as M′=[m1′m2′m3′m4′] T , the input angular velocity of the inertial navigation system coordinate system b is ω=[ω x ω y ω z ] T , the output pulses of the four gyroscopes are Ng =[N g1 N g2 N g3 N g4 ] T , the scaling factor is K = diag([k1k2k3k4] T ), the error compensation model is established through the relationship between the output pulse and the error compensation parameter:

[0049] N g =KM′=K(H+δα·P+δβ·Q)ω

[0050] in,

[0051]

[0052]

[0053]

[0054] δα=diag([δα1δα2δα3δα4] T )

[0055] δβ=diag([δβ1δβ2δβ3δβ4] T )

[0056] Where H is the measurement matrix, P is the azimuth conversion matrix, Q is the elevation conversion matrix, δα is the azimuth installation error matrix, δβ is the elevation installation error matrix, and k i , δα i , δβ i (i=1, 2, 3, 4) are the error compensation parameters that affect the output of the resonant inertial navigation system and are also the error compensation parameters to be determined.

[0057] Step 2: Solve the error compensation parameters in step 1 and substitute the solution into the error compensation model to solve the error compensation model:

[0058] The resonant inertial navigation system with four gyroscopes in a conical configuration is fixed on a three-axis turntable. The coordinate system b of the inertial navigation system coincides with the coordinate system t of the turntable. The turntable is rotated in the following order:

[0059] (1) Rotate the turntable so that the inertial navigation system coordinate system b system OZ b Axis and turntable frame axis Z t Coincidentally, make the turntable outer frame axis (Z t ) rotates forward for n circles, then reverse for n circles, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and

[0060] (2) Rotate the turntable so that the inertial navigation system coordinate system b system OY b Axis and turntable frame axis Z t Coincident, around the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and

[0061] (3) Rotate the turntable so that the inertial navigation system coordinate system b system OX b Axis and turntable frame axis Z t Coincident, around the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and

[0062] The error compensation parameters are calculated using the least squares method:

[0063] The least squares calculation model of error compensation parameters is established as follows:

[0064] A i x i =B i

[0065] in,

[0066]

[0067]

[0068]

[0069] The error compensation parameters are calculated using the least squares algorithm

[0070] x=(A T A) -1 A T B,

[0071] Substitute i (i = 1, 2, 3, 4) into the above formula to obtain the i (i = 1, 2, 3, 4) gyroscope error compensation parameter matrix x i Where x i It is k i , δα i , δβ i In this way, the quad-gyroscope resonant inertial navigation error compensation model can be solved.

[0072] Please add examples:

[0073] like Figure 1 As shown, four gyroscopes G i(i=1,2,3,4) are evenly distributed on the conical surface. The ideal azimuth angles are α1=0°, α2=90°, α3=180°, α4=270°, and the ideal pitch angle is β i =60°(i=1,2,3,4). Through the error model in step 1, we can get

[0074]

[0075]

[0076]

[0077] According to the test method in step 2, use the three-axis turntable to rotate, rotating 5 times in the forward direction and 5 times in the reverse direction each time, to obtain the cumulative output of the four gyroscopes:

[0078]

[0079]

[0080] According to the least squares algorithm, the four gyroscope error compensation parameter matrices can be obtained using the above data:

[0081]

[0082]

[0083]

[0084]

[0085] A novel error compensation modeling method for a resonant inertial navigation system (RIS) with four gyroscopes arranged in a conical configuration has been developed. This method is applicable to RINS systems with four gyroscopes arranged in a conical configuration regardless of spatial distribution. This method directly establishes a transformation relationship between the four gyroscopes' sensitive axes and the INS coordinate system's B-frame, deriving error compensation parameters for each gyroscope. The error compensation parameters are then converted to the INS coordinate system's B-frame. This simple and direct method, requiring no intermediate conversion steps, significantly simplifies the error compensation process and improves its efficiency, creating the foundation for achieving high-precision RINS.

[0086] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will understand that various replacements, changes and modifications are possible without departing from the spirit of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for calibrating the error of a resonant inertial navigation system with four gyroscopes arranged in a conical configuration, comprising the following steps: Step 1: Based on the conversion relationship between the gyroscope sensitive axis and the inertial navigation system coordinate system B, an error compensation model is constructed to determine the error compensation parameters that affect the output of the resonant inertial navigation system in the error compensation model; including: 1.

1. Arbitrarily distribute four gyroscopes on the same conical surface. The ideal sensitive axis of the gyroscope is G i (i=1,2,3,4), the inertial navigation system coordinate system b is OX b Y b Z b ; The ideal azimuth angle α of the i-th (i=1,2,3,4) gyroscope i G i In OX b Y b Plane projection and OX b The angle between the axes, the ideal pitch angle β i G i With flat OX b Y b Angle; Due to the existence of installation error, the actual sensitive axis G of the gyroscope i ′ and the ideal sensitive axis G i The small angle installation error is δα i and δβ i , then G i ′ corresponds to the actual azimuth α i ′ and actual pitch angle β i ′ can be expressed as: 1.

2. Define the actual input angular velocity of the four gyroscopes as M′=[m1′m2′m3′m4′] T , the input angular velocity of the inertial navigation system coordinate system b is ω=[ω x ω y ω z ] T , the output pulses of the four gyroscopes are N g =[N g1 N g2 N g3 N g4 ] T , the scaling factor is K = diag([k1 k2 k3 k4] T ), the error compensation model is established through the relationship between the output pulse and the error compensation parameter: N g =KM′=K(H+δα·P+δβ·Q)ω in, δα=diag([δα1δα2δα3δα4] T ) δβ=diag([δβ1δβ2δβ3δβ4] T ) Where H is the measurement matrix, P is the azimuth conversion matrix, Q is the elevation conversion matrix, δα is the azimuth installation error matrix, δβ is the elevation installation error matrix, and k i , δα i ,δβ i (i=1,2,3,4) are the error compensation parameters that affect the output of the resonant inertial navigation system and are also the error compensation parameters to be determined; Step 2: Solve the error compensation parameters in step 1 and substitute the solution into the error compensation model to solve the error compensation model, including: 2.1 The resonant inertial navigation system with four gyroscopes in a conical configuration is fixedly mounted on a three-axis turntable and rotated to obtain the resonant inertial navigation system output data; 2.2 Using the output data of the resonant inertial navigation system obtained in step 2.1, the error compensation parameters determined in step S1 are solved by the least squares method; 2.3 Use the error compensation parameters obtained in step 2.2 to solve the error compensation model.

2. The method for calibrating the error of a resonant inertial navigation system with a conical configuration of four gyroscopes according to claim 1, characterized in that: Step 2.1: Mount the resonant inertial navigation system (IRN) with four gyroscopes in a conical configuration on a three-axis turntable. The IR system coordinate system b coincides with the turntable coordinate system t. Rotate the turntable in the following order: 1) Rotate the turntable so that the inertial navigation system coordinate system b is OZ b Axis and turntable frame axis Z t Coincidentally, make the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and 2) Rotate the turntable so that the inertial navigation system coordinate system b system OY b Axis and turntable frame axis Z t Coincident, around the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and 3) Rotate the turntable so that the inertial navigation system coordinate system b is OX b Axis and turntable frame axis Z t Coincident, around the turntable outer frame axis (Z t ) rotates forward n times, then reversely rotates n times, and records the cumulative sum of the output pulses of the four gyroscopes in the forward and reverse directions. and 3. The method for calibrating the error of a resonant inertial navigation system with a conical configuration of four gyroscopes according to claim 2, characterized in that: The error compensation parameters are calculated using the least squares method: The least squares calculation model of error compensation parameters is established as follows: Ax i =B in, The least squares algorithm is used to calculate the error compensation parameters: x i =(A T A) -1 A T B, Substitute i (i = 1, 2, 3, 4) into the above formula to obtain the i (i = 1, 2, 3, 4) gyroscope error compensation parameter matrix x i ; where x i It is k i , δα i , δβ i The matrix of .

Images