A wavelet transform-based integrated navigation initial alignment method and system

Abstract

The present invention proposes a combined navigation initial alignment method and system based on wavelet transform, which belongs to the field of navigation and positioning technology. The method comprises: obtaining the acceleration observation value at the initial stage of the combined navigation system, using wavelet transform to denoise the acceleration observation value to obtain the acceleration measurement value, which is used to eliminate the influence of the base shaking on the acceleration; using the acceleration measurement value, based on the rough alignment of the inertial system of the attitude matrix to obtain the first initial attitude matrix of the combined navigation, which is used to eliminate the influence of the shaking on the gyroscope measurement value; after completing the rough alignment, the first initial attitude matrix is ​​finely aligned by Kalman filtering to realize the initial alignment of the combined navigation. Based on this method, the present invention also proposes a combined navigation initial alignment system based on wavelet transform. The present invention can avoid the influence of various shaking or vibration interference in micro-dynamic conditions, solve the initial alignment problem of typical application scenarios such as ship-borne mooring state, and provide accurate initial values ​​for the combined navigation system.

Description

Technical Field

[0001] The invention belongs to the technical field of navigation and positioning, and in particular relates to a combined navigation initial alignment method and system based on wavelet transform. Background Art

[0002] The shipborne integrated navigation system needs initial alignment before entering the working state. Determining the attitude array of the system at the initial moment as quickly and accurately as possible is a problem that must be solved in the initial alignment of the inertial navigation system. The accuracy of the initial alignment directly affects the working performance of the system. When the survey ship is under mooring or low dynamic conditions, due to the influence of the marine environment on the ship's own movement, the inertial navigation system is under dynamic conditions, and various harmful interferences will have an adverse effect on the alignment at sea. This requires the comprehensive use of various measurement information and means to seek effective methods to achieve the initial alignment of the inertial navigation in the ocean sloshing environment.

[0003] The first alignment method used in the prior art is the dual-antenna assisted transfer alignment method, which requires accurate measurement of the coordinates of the dual antennas in the carrier coordinate system, and the two antennas need to maintain a fixed connection, which is difficult to adapt to the working environment of different survey ships, making the ship-borne multi-sensor island and reef comprehensive measurement system not universal. The second alignment method used in the prior art is the shore static self-alignment method, which is difficult to apply to engineering practice after the alignment is completed and then transported to the ship for measurement operations. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes an integrated navigation initial alignment method and system based on wavelet transform, which can avoid the influence of various shaking or vibration interference in micro-dynamic conditions and provide accurate initial values ​​for the integrated navigation system.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A wavelet transform-based integrated navigation initial alignment method comprises the following steps:

[0007] Acquire the acceleration observation value at the initial stage of the integrated navigation system, and use wavelet transform to denoise the acceleration observation value to obtain the acceleration measurement value;

[0008] Using the acceleration measurement value, the first initial attitude matrix of the integrated navigation is obtained based on the rough alignment of the inertial system of the attitude matrix;

[0009] After the coarse alignment is completed, Kalman filtering fine alignment is performed on the first initial attitude matrix to achieve initial alignment of the integrated navigation.

[0010] The present invention also proposes a wavelet transform-based integrated navigation initial alignment system, comprising a denoising module, a coarse alignment module and a fine alignment module;

[0011] The denoising module is used to obtain the acceleration observation value of the integrated navigation system at the initial stage, and denoise the acceleration observation value by using wavelet transform to obtain the acceleration measurement value;

[0012] The coarse alignment module is used to obtain a first initial attitude matrix of the integrated navigation by using the acceleration measurement value and coarse alignment of the inertial system based on the attitude matrix;

[0013] The fine alignment module is used to perform Kalman filter fine alignment on the first initial attitude matrix after completing the rough alignment to achieve initial alignment of the integrated navigation.

[0014] The effects provided in the content of the invention are only the effects of the embodiments, not all the effects of the invention. One of the above technical solutions has the following advantages or beneficial effects:

[0015] The present invention proposes a combined navigation initial alignment method and system based on wavelet transform, belonging to the field of navigation and positioning technology. The method comprises the following steps: obtaining the acceleration observation value at the initial stage of the combined navigation system, using wavelet transform to denoise the acceleration observation value to obtain the acceleration measurement value, which is used to eliminate the influence of the base shaking on the acceleration; using the acceleration measurement value, based on the inertial system rough alignment of the attitude matrix to obtain the first initial attitude matrix of the combined navigation, which is used to eliminate the influence of the shaking on the gyroscope measurement value; after completing the rough alignment, performing Kalman filter fine alignment on the first initial attitude matrix to realize the initial alignment of the combined navigation. Based on a combined navigation initial alignment method based on wavelet transform, the present invention also proposes a combined navigation initial alignment system based on wavelet transform. The present invention adopts wavelet transform denoising to propose the influence of the shaking base on the acceleration, and adopts inertial system alignment to avoid the influence of the shaking on the gyroscope, thereby ensuring the accuracy of the data used for rough alignment. After completing the rough alignment, performing Kalman filter fine alignment, thereby realizing the process of initial alignment. The present invention can avoid the influence of various shaking or vibration interference in micro-dynamic conditions, solve the initial alignment problem in typical application scenarios such as ship-borne mooring status, and provide accurate initial values ​​for the integrated navigation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flow chart of an integrated navigation initial alignment method based on wavelet transform proposed in Example 1 of the present invention;

[0017] Figure 2 The process of wavelet transform denoising in the wavelet transform-based combined navigation initial alignment method proposed in Embodiment 1 of the present invention;

[0018] Figure 3 This is a schematic diagram of an integrated navigation initial alignment system based on wavelet transform proposed in Example 2 of the present invention. DETAILED DESCRIPTION

[0019] In order to clearly illustrate the technical features of the present solution, the present invention is described in detail below through specific implementation methods and in conjunction with the accompanying drawings. The disclosure below provides many different embodiments or examples for realizing different structures of the present invention. In order to simplify the disclosure of the present invention, the components and settings of specific examples are described below. In addition, the present invention may repeat reference numbers and / or letters in different examples. This repetition is for the purpose of simplification and clarity, and does not itself indicate the relationship between the various embodiments and / or settings discussed. It should be noted that the components illustrated in the accompanying drawings are not necessarily drawn to scale. The present invention omits the description of known components and processing techniques and processes to avoid unnecessary limitations on the present invention.

[0020] Example 1

[0021] Embodiment 1 of the present invention proposes a combined navigation initial alignment method based on wavelet transform, which is used to solve the initial alignment problem in typical application scenarios such as ship-borne mooring status in the prior art.

[0022] Embodiment 1 of the present invention proposes an implementation process of an integrated navigation initial alignment method based on wavelet transform, including: using wavelet transform denoising to propose the influence of shaking base on acceleration, using inertial system alignment to avoid the influence of shaking on gyroscope, so as to ensure the accuracy of data used for coarse alignment. After completing the coarse alignment, Kalman filter fine alignment is performed to achieve the process of initial alignment.

[0023] Figure 1 A flow chart of an integrated navigation initial alignment method based on wavelet transform proposed in Example 1 of the present invention;

[0024] In step S10, the process starts.

[0025] In step S11, the acceleration measurement values ​​measured by the accelerometer in the shipborne integrated navigation system are collected, and the acceleration observation values ​​are denoised using wavelet transform to obtain acceleration measurement values ​​for eliminating the influence of base shaking on acceleration.

[0026] The present invention is based on the research idea of ​​canonical orthogonal basis, which expresses the original signal or function as the weighted sum of a family of wavelet basis functions, which are obtained by translating and scaling a mother function, that is, using a family of functions to approximate a certain signal or function. It can retain the transient characteristic information of the real signal while removing most of the noise. The appropriate wavelet basis and decomposition layer number are selected, and the data collected by the accelerometer are pre-processed by wavelet to filter out the interference signal, and then the filtered data is used for coarse alignment, which effectively improves the alignment accuracy under the inertial system.

[0027] Given a basic function ,make

[0028] ;

[0029] In the formula, are constants, and .

[0030] Obviously, It is a basic function The family of functions obtained by first translating and then scaling is called wavelet basis functions.

[0031] is called the mother wavelet. Given a square-integrable signal ,but The wavelet transform of is defined as

[0032] ; In the formula, Represents the conjugate of a complex number.

[0033] Assume that a one-dimensional signal model containing noise is:

[0034] ;

[0035] In the formula, is the original signal; is a noisy signal, for noise; represents the sequence of observations, Represents the scale, Represents time.

[0036] In this application, the one-dimensional signal containing noise is the acceleration observation value.

[0037] The process of denoising the acceleration observation value by using wavelet transform includes: using wavelet basis function to perform wavelet transform on the acceleration observation value signal, determining the scale N of wavelet decomposition, and then performing N-scale wavelet decomposition on the acceleration observation value signal; selecting the target threshold to perform threshold quantization processing on the high-frequency coefficients of each scale; performing inverse wavelet transform based on the low-frequency coefficients of the Nth scale after wavelet decomposition and the coefficients after threshold quantization processing to obtain the denoised acceleration measurement value.

[0038] The selection of wavelet basis function has an important influence on the denoising process. The wavelet basis functions used in the present invention are: Haar wavelet, Daubechies (dbN) wavelet, Symlet (symN) wavelet, etc. At the same time, the number of wavelet decomposition layers is also selected according to actual needs. According to the test, the number of wavelet decomposition layers is selected as 5, which means that the signal is decomposed into a series of spaces with different frequencies. Different numbers of decomposition layers can show the characteristics of different frequencies. Each decomposition decomposes the signal into two parts, low frequency and high frequency. The low frequency part is further decomposed to obtain low frequency and high frequency parts on a higher scale. The more decomposition layers there are, the lower the frequency obtained, but the more the better is not necessarily true.

[0039] The key to the quality of wavelet denoising lies in how to select the threshold and quantify the threshold. The selection of the threshold is divided into two methods: soft threshold and hard threshold according to the different threshold functions. Both soft threshold and hard threshold compare the absolute value of the corresponding wavelet coefficient with the given threshold. The former sets the coefficient greater than the threshold to the difference between it and the threshold, and sets the coefficient less than or equal to the threshold to zero. The latter keeps the coefficient greater than the threshold unchanged and sets the others to zero. In effect, the former will have a larger deviation and produce a smoother filtering result, while the latter will produce a larger variance, but it retains the local characteristics of the signal well. The threshold selection method is a fixed threshold. Other optional typical threshold selection methods include adaptive threshold selection based on Stein's unbiased likelihood estimation principle, heuristic threshold selection, and maximum and minimum threshold selection. In order to extract a relatively pure gravitational acceleration, Figure 2 This is the process of wavelet transform denoising in the wavelet transform-based integrated navigation initial alignment method proposed in Example 1 of the present invention.

[0040] In step S12, the acceleration measurement value is used to obtain a first initial attitude matrix of the integrated navigation based on the rough alignment of the inertial system of the attitude matrix, so as to eliminate the influence of the shaking on the gyroscope measurement value;

[0041] The process of rough alignment of the inertial system based on the attitude matrix in this application includes:

[0042] The first initial posture matrix is ​​decomposed into the form of multiplication of multiple posture matrices; wherein the first initial posture matrix is Tie to The coordinate system transformation matrix of the system; multiple posture matrices include: Tie to The coordinate transformation matrix of the system, Tie to The coordinate transformation matrix of the system, Department and The transformation matrix between the systems and Department and The transformation matrix between the systems; Represents the navigation coordinate system; represents the carrier coordinate system; represents the Earth-centered Earth-fixed coordinate system; represents the inertial coordinate system; is the carrier inertial coordinate system at the initial moment, and is Departments overlap;

[0043] Assume that the longitude and latitude of the alignment location are The idea of ​​rough alignment of the inertial system based on the attitude matrix is ​​to decompose the direction cosine matrix from the carrier coordinate system to the navigation coordinate system into the form of multiplication of four relatively small attitude matrices, that is, to decompose the first initial attitude matrix into the form of multiplication of multiple attitude matrices, which is specifically expressed as:

[0044] ; (1)

[0045] in, represent Tie to The coordinate system transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; for Department and Transformation matrix between systems; for Department and Transformation matrix between systems; is the unit matrix, and The posture array of the moment The output of the gyroscope Relative The angular motion information of the system is obtained through the strapdown inertial navigation attitude update algorithm. In addition, for the matrix is known, and can be obtained from the geographical location of the carrier and the rough alignment time Sure.

[0046] in, ; (2)

[0047] ; (3)

[0048] ; (4)

[0049] in, The longitude of the alignment point; To align the location's latitude; Indicates that the Earth has an angular rate of rotation around its polar axis; For time.

[0050] For the transformation matrix ,in:

[0051]

[0052]

[0053] And for for Department and The transformation matrix between the systems is Department and The system is fixed to the inertial space, so the transformation matrix is ​​a constant matrix, so the attitude matrix is ​​solved The key is to solve the constant matrix .

[0054] Solution Department and Transformation matrix between systems Determine the attitude matrix at the end of the rough alignment; the specific process includes:

[0055] Assumptions Time transformation matrix for , the corresponding transformation quaternion is , Time transformation matrix for , the corresponding transformation quaternion is ; and ; for Time transformation matrix for , the corresponding transformation quaternion is ;

[0056] Assumptions Time to The angular increment of the gyro output at the moment is , using the equivalent rotation vector single sample algorithm, we can get Relative to From Time to The transformation quaternion at this moment is:

[0057] ; (5)

[0058] This allows the quaternion update solution to be performed: ;

[0059] Assumptions , then according to the relationship between the transformation quaternion and the transformation matrix, we can calculate Transformation matrix at time ;

[0060] in, , , and are all real numbers, represents the real part of the quaternion, Represented in quaternion The imaginary part of the axis; Represented in quaternion Axis imaginary part; Represented in quaternion The imaginary part of the axis;

[0061] ; (6)

[0062] pass The solution of determines the attitude matrix at the end of the rough alignment. Transformation matrix The update solution enables the coarse alignment to track the angular motion of the carrier, that is, the attitude matrix at the end of the coarse alignment is obtained.

[0063] Solution Department and Transformation matrix between systems , and then calculate the first initial attitude matrix to complete the rough alignment of the inertial system based on the attitude matrix.

[0064] On the rocking base, the output of the accelerometer mainly includes the acceleration of gravity, the interference acceleration caused by the hull's vertical, longitudinal, lateral and vibration, and the zero bias of the accelerometer.

[0065] On the rocking base, the output of the accelerometer is used to calculate the carrier coordinate system at the initial moment. The projection is:

[0066] ; (7)

[0067] in, Represents the carrier coordinate system at the initial moment and The attitude transfer matrix between systems; Represents the scale vector measured by the accelerometer; represents the identity matrix; is the scale factor error matrix of the accelerometer; is the installation error matrix of the accelerometer; Represents the gravity vector in the carrier coordinate system Projection in Represents acceleration zero bias; represents the disturbance acceleration; represents the error factor;

[0068] represents the acceleration bias, Represents the acceleration zero bias on the x-axis component, Represents the acceleration zero bias on the y-axis component, Represents the acceleration zero bias in the z-axis component.

[0069] is the scale factor error matrix of the accelerometer;

[0070] in, is the scale factor error matrix of the accelerometer, where , and Represent the scale factor error coefficient of the accelerometer on the x-axis, y-axis and z-axis respectively.

[0071] Put both sides of formula (7) in The inner integral is:

[0072] ; (8)

[0073] Represents the integral result of the acceleration output, that is, Always Speed ​​information of the system;

[0074] Formula (8) can be simplified into the following form:

[0075] ; (9)

[0076] in, ; (10)

[0077] Represents the error term caused by shaking; Represents the carrier coordinate system at the initial moment arrive The transformation matrix of the system; represent Tie to The transformation matrix of the system;

[0078] Depend on We can get:

[0079] ; (11)

[0080] in, Represents the gravity vector in the inertial frame Projection in Represents the inertial coordinate system at the initial moment arrive The transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; Represents the gravity vector in the system Projection in

[0081] right Both sides at the same time The inner integral can be obtained:

[0082] ; (12)

[0083] in, represents the gravitational constant, represent Inertial frame at all times Speed ​​information of the system;

[0084] In the formula ;

[0085] Will After processing, we can get:

[0086] ; (13)

[0087] represent Inertial frame at all times The real speed information of the system; Represents the carrier coordinate system and inertial coordinate system at the initial moment The attitude transfer matrix between them;

[0088] According to the principle of dual-vector attitude determination, select and time, and ,have

[0089] ; (14)

[0090] ; (15)

[0091] Constructing the cross product vector gives:

[0092] ; (16)

[0093] Finally we get:

[0094] ; (17)

[0095] in, Represents the inertial coordinate system The attitude transfer matrix between the carrier coordinate system at the initial moment is obtained The first initial posture matrix can be finally determined , thus completing all the rough alignment tasks.

[0096] In step S13, after the coarse alignment is completed, Kalman filtering fine alignment is performed on the first initial attitude matrix to achieve initial alignment of the integrated navigation.

[0097] Coarse alignment provides an initial attitude matrix that meets the requirements for fine alignment. By processing the output signals of inertial instruments (accelerometers and gyroscopes) and external observation information, the misalignment angle is continuously calculated, so that the calculated geographic coordinate system approaches the real geographic coordinate system, thereby establishing an accurate initial transformation matrix. Fine alignment is a key stage to ensure the accuracy of autonomous initial alignment. The self-alignment filter model in two states is constructed, and the algorithm flow of initial alignment is summarized.

[0098] The purpose of fine alignment is to accurately estimate the platform error angle based on rough alignment. , in order to obtain a more accurate first initial posture matrix The first step is to use Kalman filtering to convert the initial error angle of the inertial navigation platform to The first step is to estimate the inertial device error (gyroscope drift and accelerometer zero offset) as much as possible; the second step is to eliminate the platform error angle based on the result and compensate for the inertial device error.

[0099] The specific process includes: using Kalman filtering to calculate the initial error angle of the inertial navigation platform and the error of the inertial device; the inertial device includes a gyroscope and an accelerometer; using the initial error angle to correct the first initial attitude matrix, and feedback correction of the error of the inertial device to achieve precise alignment of the integrated navigation.

[0100] The process of using Kalman filtering to calculate the initial error angle of the inertial navigation platform and the error of the inertial device includes:

[0101] The northeast sky geographic coordinate system is used as the navigation coordinate system, and the error equation of the static system is:

[0102] ; (18)

[0103] in, represents the eastward velocity error; represents the north speed; represents the north misalignment angle; Represents acceleration Axis zero offset; represents the north velocity error; represents the eastward speed; represents the east misalignment angle; Represents acceleration Axis zero offset; Represents acceleration Axis zero offset; Represents the east misalignment angle error; Represents the north misalignment angle error; Indicates the celestial misalignment angle; Represents the angular error of the azimuth; Represents gyroscope Axis zero offset; Represents gyroscope Axis zero offset; Represents gyroscope Axis zero offset; represents the gravitational constant.

[0104] The initial error angle corrects the first initial attitude matrix and feedback corrects the error of the inertial device to achieve the precise alignment of the integrated navigation. The process includes:

[0105] For strapdown inertial navigation systems:

[0106] ; (19)

[0107] ; (20)

[0108] in, Represents the east component of the accelerometer zero bias in the navigation coordinate system; Represents the accelerometer zero bias in the navigation coordinate system north component and Represents the celestial component of the accelerometer zero bias in the navigation coordinate system; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the east component of the gyroscope zero bias in the navigation coordinate system; Represents the north component of the gyroscope zero bias in the navigation coordinate system; Represents the antenna component of the gyroscope zero bias in the navigation coordinate system; Represents the gyroscope zero bias in the carrier coordinate system Axis component; Represents the gyroscope zero bias in the carrier coordinate system Axis component; Represents the gyroscope zero bias in the carrier coordinate system Axis component;

[0109] The state vector obtained after expansion is:

[0110] ;(twenty one)

[0111] The state equation of the expanded stationary base strapdown inertial navigation system is:

[0112] ;(twenty two)

[0113] represents the state transfer matrix; represents the noise driven array; represents the system noise vector; and is the observed quantity, and the measurement equation of the system is:

[0114] ;(twenty three)

[0115] in, is the observation matrix; ; is the observation noise vector.

[0116] In step S14, the self-alignment of the strapdown inertial navigation system is completed and the process ends.

[0117] The combined navigation initial alignment method based on wavelet transform proposed in Example 1 of the present invention can avoid the influence of various shaking or vibration interference in micro-dynamic conditions, solve the initial alignment problem in typical application scenarios such as ship-borne mooring status, and provide accurate initial values ​​for the combined navigation system.

[0118] Example 2

[0119] Based on the integrated navigation initial alignment method based on wavelet transform proposed in embodiment 1 of the present invention, embodiment 2 of the present invention further proposes an integrated navigation initial alignment system based on wavelet transform. Figure 3 This is a schematic diagram of an integrated navigation initial alignment system based on wavelet transform proposed in Example 2 of the present invention. The system includes: a denoising module, a coarse alignment module and a fine alignment module;

[0120] The denoising module is used to obtain the acceleration observation value at the initial stage of the integrated navigation system, and denoise the acceleration observation value by using wavelet transform to obtain the acceleration measurement value;

[0121] The coarse alignment module is used to obtain a first initial attitude matrix of the integrated navigation by using the acceleration measurement value and coarse alignment of the inertial system based on the attitude matrix;

[0122] The fine alignment module is used to perform Kalman filter fine alignment on the first initial attitude matrix after completing the rough alignment to achieve initial alignment of the integrated navigation.

[0123] The process of implementing the denoising module includes: using the wavelet basis function to perform wavelet transform on the acceleration observation value signal, determining the scale N of the wavelet decomposition, and then performing N-scale wavelet decomposition on the acceleration observation value signal;

[0124] Select the target threshold to perform threshold quantization on the high-frequency coefficients of each scale;

[0125] The inverse wavelet transform is performed based on the low-frequency coefficients of the Nth scale after wavelet decomposition and the coefficients after threshold quantization processing to obtain the acceleration measurement value after noise reduction.

[0126] Given a basic function ,make

[0127] ;

[0128] In the formula, are constants, and .

[0129] Obviously, It is a basic function The family of functions obtained by first translating and then scaling is called wavelet basis functions.

[0130] is called the mother wavelet. Given a square-integrable signal ,but The wavelet transform of is defined as

[0131] ; In the formula, Represents the conjugate of a complex number.

[0132] Assume that a one-dimensional signal model containing noise is:

[0133]

[0134] In the formula, is the original signal; is a noisy signal, for noise; represents the sequence of observations, Represents the scale, Represents time.

[0135] In this application, the one-dimensional signal containing noise is the acceleration observation value.

[0136] In the coarse alignment module, the process of coarse alignment of the inertial system based on the attitude matrix includes:

[0137] The first initial posture matrix is ​​decomposed into the form of multiplication of multiple posture matrices; wherein the first initial posture matrix is Tie to The coordinate system transformation matrix of the system; multiple posture matrices include: Tie to The coordinate transformation matrix of the system, Tie to The coordinate transformation matrix of the system, Department and The transformation matrix between the systems and Department and The transformation matrix between the systems; Represents the navigation coordinate system; represents the carrier coordinate system; represents the Earth-centered Earth-fixed coordinate system; represents the inertial coordinate system; is the carrier inertial coordinate system at the initial moment;

[0138] Solution Department and The transformation matrix between the systems determines the attitude matrix at the end of the rough alignment;

[0139] Solution Department and The transformation matrix between the systems is calculated, and then the first initial attitude matrix is ​​calculated to complete the rough alignment of the inertial system based on the attitude matrix.

[0140] Solution Department and Transformation matrix between systems The process of determining the attitude matrix at the end of coarse alignment includes:

[0141] Assumptions Time transformation matrix for , the corresponding transformation quaternion is , Time transformation matrix for , the corresponding transformation quaternion is ; and ; for Time transformation matrix for , the corresponding transformation quaternion is ;

[0142] Assumptions Time to The angular increment of the gyro output at the moment is , using the equivalent rotation vector single sample algorithm, we can get Relative to From Time to The transformation quaternion at this moment is:

[0143] ; (5)

[0144] This allows the quaternion update solution to be performed: ;

[0145] Assumptions , then according to the relationship between the transformation quaternion and the transformation matrix, we can calculate Transformation matrix at time ;

[0146] in, , , and are all real numbers, represents the real part of the quaternion, Represented in quaternion The imaginary part of the axis; Represented in quaternion Axis imaginary part; Represented in quaternion The imaginary part of the axis;

[0147] ; (6)

[0148] pass The solution determines the attitude matrix at the end of the rough alignment.

[0149] Solution Department and Transformation matrix between systems The process includes:

[0150] On the rocking base, the output of the accelerometer is used to calculate the carrier coordinate system at the initial moment. The projection is:

[0151] ; (7)

[0152] in, Represents the carrier coordinate system at the initial moment and The attitude transfer matrix between systems; Represents the scale vector measured by the accelerometer; represents the identity matrix; is the scale factor error matrix of the accelerometer; is the installation error matrix of the accelerometer; Represents the gravity vector in the carrier coordinate system Projection in Represents acceleration zero bias; represents the disturbance acceleration; represents the error factor;

[0153] Put both sides of formula (7) in The inner integral is:

[0154] ; (8)

[0155] Represents the integral result of the acceleration output, that is, Always Speed ​​information of the system;

[0156] Formula (8) can be simplified into the following form:

[0157] ; (9)

[0158] in, ; (10)

[0159] Represents the error term caused by shaking; Represents the carrier coordinate system at the initial moment arrive The transformation matrix of the system; represent Tie to The transformation matrix of the system;

[0160] Depend on We can get:

[0161] ; (11)

[0162] in, Represents the gravity vector in the inertial frame Projection in Represents the inertial coordinate system at the initial moment arrive The transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; Represents the gravity vector in the system Projection in

[0163] right Both sides at the same time The inner integral can be obtained:

[0164] ; (12)

[0165] in, represents the gravitational constant, represent Inertial frame at all times Speed ​​information of the system; ;

[0166] Will After processing, we can get:

[0167] ; (13)

[0168] represent Inertial frame at all times The real speed information of the system; Represents the carrier coordinate system and inertial coordinate system at the initial moment The attitude transfer matrix between them;

[0169] According to the principle of dual-vector attitude determination, select and time, and ,have

[0170] ; (14)

[0171] ; (15)

[0172] Constructing the cross product vector gives:

[0173] ; (16)

[0174] Finally we get:

[0175] ; (17)

[0176] in, Represents the inertial coordinate system The attitude transfer matrix between the carrier coordinate system at the initial moment.

[0177] The process performed by the fine alignment module includes: using Kalman filtering to calculate the initial error angle of the inertial navigation platform and calculating the error of the inertial device; the inertial device includes a gyroscope and an accelerometer;

[0178] The first initial attitude matrix is ​​corrected by utilizing the initial error angle, and the error of the inertial device is feedback-corrected to achieve precise alignment of the integrated navigation.

[0179] The northeast sky geographic coordinate system is used as the navigation coordinate system, and the error equation of the static system is:

[0180] ; (18)

[0181] in, represents the eastward velocity error; represents the north speed; represents the north misalignment angle; Represents acceleration Axis zero offset; represents the north velocity error; represents the eastward speed; represents the east misalignment angle; Represents acceleration Axis zero offset; Represents acceleration Axis zero offset; Represents the east misalignment angle error; Represents the north misalignment angle error; Indicates the celestial misalignment angle; Represents the angular error of the azimuth; Represents gyroscope Axis zero offset; Represents gyroscope Axis zero offset; Represents gyroscope Axis zero offset; represents the gravitational constant.

[0182] The process of correcting the first initial attitude matrix by using the initial error angle and performing feedback correction on the error of the inertial device to achieve precise alignment of the integrated navigation includes:

[0183] For strapdown inertial navigation systems:

[0184] ; (19)

[0185] ; (20)

[0186] in, Represents the east component of the accelerometer zero bias in the navigation coordinate system; Represents the accelerometer zero bias in the navigation coordinate system north component and Represents the celestial component of the accelerometer zero bias in the navigation coordinate system; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the east component of the gyroscope zero bias in the navigation coordinate system; Represents the north component of the gyroscope zero bias in the navigation coordinate system; Represents the antenna component of the gyroscope zero bias in the navigation coordinate system; Represents the gyroscope zero bias in the carrier coordinate system Axis component; Represents the gyroscope zero bias in the carrier coordinate system Axis component; Represents the gyroscope zero bias in the carrier coordinate system Axis component;

[0187] The state vector obtained after expansion is:

[0188] ;(twenty one)

[0189] The state equation of the expanded stationary base strapdown inertial navigation system is:

[0190] ;(twenty two)

[0191] represents the state transfer matrix; represents the noise driven array; represents the system noise vector; and is the observed quantity, and the measurement equation of the system is:

[0192] ;(twenty three)

[0193] in, is the observation matrix; ; is the observation noise vector.

[0194] The combined navigation initial alignment system based on wavelet transform proposed in Example 2 of the present invention can avoid the influence of various shaking or vibration interference in micro-dynamic conditions, solve the initial alignment problem in typical application scenarios such as ship-borne mooring status, and provide accurate initial values ​​for the combined navigation system.

[0195] The description of the relevant parts of the combined navigation initial alignment system based on wavelet transform provided in Example 2 of the present application can be found in the detailed description of the corresponding parts of the combined navigation initial alignment method based on wavelet transform provided in Example 1 of the present application, and will not be repeated here.

[0196] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the term "include", "comprise" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or equipment that includes a series of elements are inherent to the elements. In the absence of more restrictions, the elements limited by the sentence "comprise one..." do not exclude the presence of other identical elements in the process, method, article or equipment that includes the elements. In addition, the above-mentioned technical solution provided in the embodiment of the present application is consistent with the corresponding technical solution in the prior art in principle, and the part is not described in detail, so as not to repeat too much.

[0197] Although the above describes the specific implementation of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. For those skilled in the art, other different forms of modifications or deformations can be made on the basis of the above description. It is not necessary and impossible to list all the implementation methods here. On the basis of the technical solution of the present invention, various modifications or deformations that can be made by those skilled in the art without creative work are still within the scope of protection of the present invention.

Claims

1. A wavelet transform-based integrated navigation initial alignment method, characterized in that: The following steps are involved: Acquire the acceleration observation value at the initial stage of the integrated navigation system, and use wavelet transform to denoise the acceleration observation value to obtain the acceleration measurement value; The process of denoising the acceleration observation value by using wavelet transform includes: performing wavelet transform on the acceleration observation value signal by using wavelet basis function, determining the scale N of wavelet decomposition, and then performing N-scale wavelet decomposition on the acceleration observation value signal; selecting a target threshold to perform threshold quantization processing on the high-frequency coefficient of each scale; performing inverse wavelet transform on the low-frequency coefficient of the Nth scale after wavelet decomposition and the coefficient after threshold quantization processing to obtain the acceleration measurement value after noise reduction; Using the acceleration measurement value, the first initial attitude matrix of the integrated navigation is obtained based on the rough alignment of the inertial system of the attitude matrix; After the coarse alignment is completed, the first initial attitude matrix is ​​finely aligned by Kalman filtering to realize the initial alignment of the integrated navigation; the process of finely aligning the first initial attitude matrix by Kalman filtering to realize the initial alignment of the integrated navigation after the coarse alignment is completed includes: using Kalman filtering to calculate the initial error angle of the inertial navigation platform and the error of the inertial device; the inertial device includes a gyroscope and an accelerometer; using the initial error angle to correct the first initial attitude matrix, and feedback correction is performed on the error of the inertial device to realize the fine alignment of the integrated navigation.

2. The integrated navigation initial alignment method based on wavelet transform according to claim 1 is characterized in that: The process of rough alignment of the inertial system based on the attitude matrix includes: The first initial posture matrix is ​​decomposed into the form of multiplication of multiple posture matrices; the first initial posture matrix is Tie to The coordinate system transformation matrix of the system; multiple posture matrices include: Tie to The coordinate transformation matrix of the system, Tie to The coordinate transformation matrix of the system, Department and The transformation matrix between the systems and Department and The transformation matrix between the systems; Represents the navigation coordinate system; represents the carrier coordinate system; represents the Earth-centered Earth-fixed coordinate system; represents the inertial coordinate system; is the carrier inertial coordinate system at the initial moment; Solution Department and The transformation matrix between the systems determines the attitude matrix at the end of the rough alignment; Solution Department and The transformation matrix between the systems is calculated, and then the first initial attitude matrix is ​​calculated to complete the rough alignment of the inertial system based on the attitude matrix.

3. The integrated navigation initial alignment method based on wavelet transform according to claim 2 is characterized in that: The decomposition of the first initial posture matrix into a multiplication of multiple posture matrices is specifically expressed as follows: ；（1） in, represent Tie to The coordinate system transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; for Department and Transformation matrix between systems; for Department and Transformation matrix between systems; in, ; (2) ；（3） ；（4） in, The longitude of the alignment point; To align the location's latitude; Indicates that the Earth has an angular rate of rotation around its polar axis; For time.

4. The integrated navigation initial alignment method based on wavelet transform according to claim 3 is characterized in that: Solution Department and Transformation matrix between systems The process of determining the attitude matrix at the end of coarse alignment includes: Assumptions Time transformation matrix for , the corresponding transformation quaternion is , Time transformation matrix for , the corresponding transformation quaternion is ; and ; for Time transformation matrix for , the corresponding transformation quaternion is ; Assumptions Time to The angular increment of the gyro output at the moment is , using the equivalent rotation vector single sample algorithm, we can get Relative to From Time to The transformation quaternion at this moment is: ；（5） This allows the quaternion update solution to be performed: ; Assumptions , then according to the relationship between the transformation quaternion and the transformation matrix, we can calculate Transformation matrix at time ; in, , , and are all real numbers, represents the real part of the quaternion, Represented in quaternion The imaginary part of the axis; Represented in quaternion Axis imaginary part; Represented in quaternion The imaginary part of the axis; ；（6） pass The solution determines the attitude matrix at the end of the rough alignment.

5. The integrated navigation initial alignment method based on wavelet transform according to claim 4 is characterized in that: Solution Department and Transformation matrix between systems The process includes: On the rocking base, the output of the accelerometer is used to calculate the carrier coordinate system at the initial moment. The projection is: ；（7） in, Represents the carrier coordinate system at the initial moment and The attitude transfer matrix between systems; Represents the scale vector measured by the accelerometer; represents the identity matrix; is the scale factor error matrix of the accelerometer; is the installation error matrix of the accelerometer; Represents the gravity vector in the carrier coordinate system Projection in Represents acceleration zero bias; represents the disturbance acceleration; represents the error factor; Put both sides of formula (7) in The inner integral is: ；（8） Represents the integral result of the acceleration output, that is, Always Speed ​​information of the system; Formula (8) can be simplified into the following form: ；（9） in, ; (10) Represents the error term caused by shaking; Represents the carrier coordinate system at the initial moment arrive The transformation matrix of the system; represent Tie to The transformation matrix of the system; Depend on We can get: ；（11） in, Represents the gravity vector in the inertial frame Projection in Represents the inertial coordinate system at the initial moment arrive The transformation matrix of the system; represent Tie to The coordinate system transformation matrix of the system; Represents the gravity vector in the system Projection in right Both sides at the same time The inner integral can be obtained: ；（12） in, represents the gravitational constant, represent Inertial frame at all times Speed ​​information of the system; ; Will After processing, we can get: ；（13） represent Inertial frame at all times The real speed information of the system; Represents the carrier coordinate system and inertial coordinate system at the initial moment The attitude transfer matrix between them; According to the principle of dual-vector attitude determination, select and time, and ,have ；（14） ；（15） Constructing the cross product vector gives: ；（16） Finally we get: ；（17） in, Represents the inertial coordinate system The attitude transfer matrix between the carrier coordinate system at the initial moment.

6. The integrated navigation initial alignment method based on wavelet transform according to claim 1 is characterized in that: The process of using Kalman filtering to calculate the initial error angle of the inertial navigation platform and the error of the inertial device includes: The northeast sky geographic coordinate system is used as the navigation coordinate system, and the error equation of the static system is: ；（18） in, represents the eastward velocity error; represents the north speed; represents the north misalignment angle; Represents acceleration Axis zero offset; represents the north velocity error; represents the eastward speed; represents the east misalignment angle; Represents acceleration Axis zero offset; Represents acceleration Axis zero offset; Represents the east misalignment angle error; Represents the north misalignment angle error; Indicates the celestial misalignment angle; Represents the angular error of the celestial direction; Represents gyroscope Axis zero offset; Represents gyroscope Axis zero offset; Represents gyroscope Axis zero offset; represents the gravitational constant.

7. The integrated navigation initial alignment method based on wavelet transform according to claim 6 is characterized in that: The process of correcting the first initial attitude matrix by using the initial error angle and performing feedback correction on the error of the inertial device to achieve precise alignment of the integrated navigation includes: For strapdown inertial navigation systems: ；（19） ；（20） in, Represents the east component of the accelerometer zero bias in the navigation coordinate system; Represents the accelerometer zero bias in the navigation coordinate system north component and Represents the celestial component of the accelerometer zero bias in the navigation coordinate system; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the accelerometer zero bias in the carrier coordinate system Axis component; Represents the east component of the gyroscope zero bias in the navigation coordinate system; Represents the north component of the gyroscope zero bias in the navigation coordinate system; Represents the antenna component of the gyroscope zero bias in the navigation coordinate system; Represents the gyroscope zero bias in the carrier coordinate system Axis component; Represents the gyroscope zero bias in the carrier coordinate system Axis component; Represents the gyroscope zero bias in the carrier coordinate system Axis component; The state vector obtained after expansion is: ；（21） The state equation of the expanded stationary base strapdown inertial navigation system is: ；（22） represents the state transfer matrix; represents the noise driven array; represents the system noise vector; and is the observed quantity, and the measurement equation of the system is: ；（23） in, is the observation matrix; ; is the observation noise vector.

8. An integrated navigation initial alignment system based on wavelet transform, used to execute an integrated navigation initial alignment method based on wavelet transform according to any one of claims 1 to 7, characterized in that: It includes a denoising module, a coarse alignment module and a fine alignment module; The denoising module is used to obtain the acceleration observation value of the integrated navigation system at the initial stage, and denoise the acceleration observation value by using wavelet transform to obtain the acceleration measurement value; The coarse alignment module is used to obtain a first initial attitude matrix of the integrated navigation by using the acceleration measurement value and coarse alignment of the inertial system based on the attitude matrix; The fine alignment module is used to perform Kalman filter fine alignment on the first initial attitude matrix after completing the rough alignment to achieve initial alignment of the integrated navigation.

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