A method for improving the output accuracy of inertial guidance system based on non-significant component estimation

Abstract

The present invention relates to a method for improving the output accuracy of an inertial guidance system based on non-significant component estimation. This method introduces a correlation test based on the traditional principal component estimation method. By selecting principal components and combining interrelated guidance tool errors, it overcomes the disadvantage of insufficient rank in the environment function matrix while also increasing the confidence level of the separated parameters. The method is simple, fast, easy to implement, and valuable for practical engineering applications.

Description

Technical Field

[0001] The invention relates to a method for improving output accuracy of an inertial guidance system based on non-significant component estimation, and belongs to the technical field of data processing. Background Art

[0002] Current inertial navigation systems for spacecraft primarily utilize strapdown or platform systems composed of gyroscopes and accelerometers. Prior to live-fire flight, the error coefficients of the gyroscopes and accelerometers must be calibrated on the ground. Error compensation based on the calibration results can effectively improve the accuracy of inertial navigation. Currently, even with ground-calibrated inertial devices, during actual flight navigation tests, the theoretical velocity and position values ​​calculated from telemetry data still exhibit significant deviations from the actual flight velocity and position values ​​obtained through field measurements, resulting in a so-called "ground-ground inconsistency." Analysis has shown that this inconsistency is caused by insufficient precision in the ground-based calibration and data processing methods, leading to error accumulation during actual flight and reduced flight accuracy. Therefore, the error models and data processing methods used in ground-based calibration need to be verified and corrected.

[0003] In the multiple linear regression model, the linear equation can be written in matrix form as:

[0004]

[0005] in, is the parameter to be measured; is the observation vector; C n is the environmental function matrix; ε is the measurement noise.

[0006] When C n When the column is full rank, (C n T C n ) -1 Exists, and the parameter estimate is obtained by the least squares method:

[0007]

[0008] But the premise for the solution of the above equation is that C n is a full rank column, and when C n When the column is not full rank, the parameter estimation calculated according to the above formula has a very large deviation, and even has no solution due to singularity.

[0009] C nThe situation of not having full column rank is often encountered in reality. For example, when calculating the error coefficient of the remote measurement and separation guidance tool of a ballistic missile, the problem of inverting the ill-conditioned matrix cannot be fundamentally avoided. In the book "Precision Analysis and Evaluation of Inertial Guided Weapons" (National University of Defense Technology Press), principal component estimation and partial least squares regression are given. However, none of the above methods can fundamentally solve the problem of C. n When the column is not full rank, we can solve the problem accurately. Taking principal component estimation as an example, we can perform eigenvalue decomposition on the information matrix and have the relationship

[0010] Φ=C n T C n =PDP T (3)

[0011] Where D is the eigenvalue diagonal matrix and P is the transformation matrix.

[0012] Make the same transformation on the model parameter X and get the new model parameter α as

[0013] α=P T X (4)

[0014] According to the significance level of each parameter to be tested, it is divided into two groups α A and α B , where the principal component is α B , and its corresponding eigenvector is P B Let the minor component α A The related terms are zero, and the above formula is simplified to

[0015]

[0016] because The column is not full rank, so it needs to be processed for non-correlation in order to solve the above equation.

[0017] In addition, a least squares method for significance testing is presented in the book "System Identification and Adaptive Control (Volume 1)" (Harbin Institute of Technology Press). The article "Error Separation Method for Rocket Sled Tests of Inertial Measurement Units" in the Journal of Chinese Inertial Technology (Volume 22, Issue 1) also applies this method to rocket sled test error separation. However, the main drawback of this method is that it does not perform a correlation test, resulting in the retained significant error coefficients being correlated parameters, which deviates from the actual situation.

[0018] According to the definition of correlation, the vector group C n The calculation formula for the correlation coefficient ρ of any two vectors in is

[0019]

[0020] Among them, c i∈C n , c j ∈C n (i=1,2,...,n;j=1,2,...,n;i≠j), n is the vector group C n The number of columns. When the column vectors c1, c2, ..., c n-1 The structure matrix [c1 c2 … c n-1 ] is non-singular, if there exists a c i (i<n), which is the same as c n The correlation coefficient ρ i ' ,n ≈1, defining this situation as strong correlation, then

[0021] c n =r1c1+r2c2+…+r n-1 c n-1 ≈r i c i (7)

[0022] But the above equation is only valid for the structure matrix [c1 c2 … c n-1 ] is non-singular, and the structure matrix [c1 c2 …c n-1 ] is not true when it is singular. For example, c n ≈r i c i , c i ≈r ij c j When ρ′ i,n ≈1,ρ′ j,i ≈1, the structure matrix is ​​singular, and the above formula does not hold.

[0023] Patent No. 202010334359.8, "A Method for Improving Inertial Guidance Accuracy by Combining Correlation and Significance Testing," proposes a method for addressing correlation. The core idea is to find uncorrelated combinations of basis vectors that can be used to represent the remaining column vectors. However, this method is computationally complex and requires multiple iterations to find the basis vectors.

[0024] Therefore, it is necessary to find a parameter identification method that can quickly solve X under relevant conditions to meet the requirements of fast and accurate valuation. Summary of the Invention

[0025] The technical problem solved by the present invention is to overcome the deficiency of the current principal component estimation that only considers significance and ignores correlation, and provide a method for improving the output accuracy of the inertial guidance system based on non-significant component estimation. This method can not only solve the situation where the linear system structure matrix does not have full column rank, but also meet the requirements of correlation analysis, realize dimensionality reduction, and simplify and quickly calculate, thereby improving the output accuracy of the inertial guidance system.

[0026] The technical solution of the present invention is: a method for improving the output accuracy of an inertial guidance system based on non-significant component estimation, wherein the method performs the following steps for each telemetry measurement in each operation cycle:

[0027] S1. Calculate the current output period telemetry and external difference observation value y according to the telemetry value and external measurement value corresponding to the current output period of the inertial guidance system. i and its corresponding environment function vector

[0028] [u i1 u i2 … u im ], the current output period remote heterodyne observation quantity y i and its corresponding environment function vector [u i1 u i2 … u im ] is added to the environment function matrix and remote differential observation matrix of the inertial guidance system to form a new environment function matrix C and remote differential observation matrix Y, and to construct the inertial guidance tool error model;

[0029] The initial value of the remote difference observation matrix Y is [y1], y1 is the remote difference observation obtained in the first operation cycle, and the initial value of the environment function matrix C is [u 11 u 12 … u 1m ] is the environmental function vector corresponding to the remote difference observation y1;

[0030] S2, determine whether the environment function matrix C meets the column full rank condition, if it meets the condition, go to step S3, if not, go to step S4;

[0031] S3. Use the least squares estimation method to obtain the estimated value of the inertial guidance tool error coefficient

[0032] S4, using the non-significant component estimation method, the information matrix Φ = C T C performs eigenvalue decomposition and selects non-significant components according to the eigenvalues, that is, selects zero eigenvalue and its corresponding eigenvector set P A , and then P A Select the principal component and, based on the principal component, solve the estimated value of the inertial guidance tool error coefficient

[0033] S5. Estimated value of the inertial guidance tool error coefficient Substitute into the inertial guidance tool error model and calculate the estimated value of the remote difference observation Extracting estimates of remote difference observations The last element in The telemetry data is compensated and the telemetry data corresponding to the telemetry quantity in the current output cycle is updated. The compensated telemetry data is the output of the inertial guidance system with improved accuracy.

[0034] Preferably, the inertial guidance tool error model is a linear equation, specifically as follows:

[0035] Y=CX

[0036] Among them, Y is the remote difference observation matrix, X is the inertial guidance tool error coefficient vector, and C is the environment function matrix;

[0037] y1, y2, ..., y n is a sequence of tele-differential observations of the inertial guidance system constructed according to the output period. The tele-differential observation refers to the difference between the telemetered value and the external measurement value. The number of rows of Y increases with the number of tele-differential observations. The last row of data is the additional tele-differential observation value. n is the number of tele-differential observations.

[0038] x1, x2, ..., x m is the error coefficient of the inertial device that affects the telemetry value in the inertial guidance system, including initial alignment, zero bias of gyroscope and accelerometer, scale factor, etc., and m is the number of inertial guidance tool error coefficients;

[0039] The i-th row data [u i1 u i2 … u im ] is the remote heterodyne observation quantity y i The number of rows of C increases with the increase of output data, and the last row of data is the additional environment function vector.

[0040] Preferably, the method for determining whether the environment function matrix C satisfies the column full rank condition is as follows:

[0041] Calculate the information matrix Φ = C T The rank r of C, if r = m, then the environment function matrix C is considered to satisfy the column full rank condition, if r ≠ m, then the environment function matrix C is considered to not satisfy the column full rank condition.

[0042] Preferably, the calculation formula of step S3 is:

[0043]

[0044] Preferably, the step S4 is specifically as follows:

[0045] S4.1. Information matrix Φ = C T C performs eigenvalue decomposition:

[0046] C T C=PDP T

[0047] Where D is a diagonal matrix, and each element on its diagonal is Φ=C T The eigenvalue of C, P is the orthogonal transformation matrix;

[0048] S4.2. Based on the corresponding zero and nonzero eigenvalues ​​in the diagonal matrix D, write P as follows:

[0049] P=[P A P B ]

[0050] Among them, P A is the set of eigenvectors corresponding to zero eigenvalues ​​in the diagonal matrix D, P B is the set of eigenvectors corresponding to the non-zero eigenvalues ​​in the diagonal matrix D;

[0051] S4.3. The set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A Select the pivot and get the row transformation matrices C1 and C2, so that:

[0052]

[0053]

[0054] Among them, P A1 is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A After row exchange, the diagonally dominant square matrix, P A2 is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A After row exchange, except for P A1 The remaining rows except P′ A is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A The matrix after row transformation; is the matrix P′ A The transposed matrix of

[0055] S4.4. Calculate the error coefficient X corresponding to the row transformation matrix C1 A1 The error coefficient X corresponding to the row transformation matrix C2 A2 :

[0056] X A1 =0

[0057]

[0058] Among them, X A1 =C1X,X A2 =C2X, X A1 represents the error coefficient corresponding to the row transformation matrix C1, X A2 represents the error coefficient corresponding to the row transformation matrix C2, R represents the intermediate transformation matrix, D B represents the diagonal matrix composed of non-zero eigenvalues ​​in the diagonal matrix D;

[0059] S4.5. Calculate the estimated value of the inertial device error coefficient A special solution of :

[0060]

[0061] Preferably, step S4.3 is specifically implemented as follows:

[0062] First, find the main element: the eigenvector set P corresponding to the zero eigenvalue in D A Take the absolute value of each element, and select the element with the largest absolute value column by column as the main element of the corresponding column;

[0063] Secondly, use the unit matrix to restore the process of finding the main element and determine the row transformation matrix C1 and row transformation matrix C2;

[0064] Finally, calculate P A The rearranged block matrix P A1 、P A2 , the calculation formula is:

[0065] P A1 =C1P A

[0066] P A2 =C2P A

[0067] Preferably, the specific implementation method of selecting the pivot is:

[0068] S1.1、P A Take the absolute value of each element in and add a column of label vector G to get a new matrix F A ,Right now:

[0069]

[0070] P A (i',j') is the eigenvector set P corresponding to the zero eigenvalue A The elements in ; m is the number of error coefficients of the inertial guidance tool;

[0071] Initialize i to 1, and loop through steps S1.2 to S1.3 until i reaches mr, then proceed to step S1.4;

[0072] S1.2, from F ASelect the row corresponding to the maximum value in column i and record the last number in the row as g i ;

[0073] S1.3, from F A Remove the g i The new matrix formed after the row is updated matrix F A , add 1 to i and update i;

[0074] S1.4, g1, g2, g3, ..., g m-r Determine the eigenvector set P corresponding to the zero eigenvalue A The row number of each column pivot is the latest matrix F A The last column of elements is defined as the vector [g m-r+1 、g r+2 ,...,g m ].

[0075] Preferably, the specific steps of determining the row transformation matrix C1 and the row transformation matrix C2 are:

[0076] S2.1. Given an identity matrix I with dimension m×m;

[0077] S2.2, select g1, g2, g3, ..., g in the unit matrix I in turn. m-r The rows constitute the row transformation matrix C1;

[0078] S2.3, select the gth m-r+1 、g m-r+2 ,…,g m The rows constitute the row transformation matrix C2.

[0079] Another technical solution of the present invention is: an electronic device, the device comprising:

[0080] Memory: used to store computer-readable instructions; and

[0081] The processor is configured to run the computer-readable instructions to execute the above-mentioned method for improving the output accuracy of the inertial guidance system based on non-significant component estimation.

[0082] Another technical solution of the present invention is: a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-mentioned method for improving the output accuracy of an inertial guidance system based on non-significant component estimation.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] (1) The present invention introduces the correlation test of the environment function matrix. By combining the measures of strongly correlated parameters, the shortcoming of the traditional least squares method that cannot solve the situation where the environment function matrix is ​​not full rank is overcome, and the confidence of the separation parameters is improved;

[0085] (2) The present invention is conducive to simplification and greatly reduces the dimension of the model by integrating the interrelated tool error coefficients, and is also conducive to real-time online calculation of the inertial guidance tool error coefficient, which has the advantages of being simple, fast and easy to implement;

[0086] (3) The present invention provides a method that includes the traditional least squares method. That is, the traditional least squares method is a special case of the present invention patent and has a wider range of applications and engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 The present invention is a flowchart of a method for improving the output accuracy of an inertial guidance system based on non-significant component estimation. DETAILED DESCRIPTION

[0088] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments:

[0089] The present invention provides a method for improving the output accuracy of an inertial guidance system based on non-significant component estimation. The method performs the following steps for each telemetry measurement in each operation cycle:

[0090] S1. Calculate the current output period telemetry and external difference observation value y according to the telemetry value and external measurement value corresponding to the current output period of the inertial guidance system. i and its corresponding environment function vector [u i1 u i2 … u im ], the current output period remote heterodyne observation quantity y i and its corresponding environment function vector [u i1 u i2 … u im ] is added to the environment function matrix and remote differential observation matrix of the inertial guidance system to form a new environment function matrix C and remote differential observation matrix Y, and to construct the inertial guidance tool error model;

[0091] The initial value of the remote difference observation matrix Y is [y1], y1 is the remote difference observation obtained in the first operation cycle, and the initial value of the environment function matrix C is [u 11 u 12 … u 1m ] is the environmental function vector corresponding to the remote difference observation y1;

[0092] y1, y2, ..., yn is a sequence of tele-differential observations of the inertial guidance system constructed according to the output period. The tele-differential observation refers to the difference between the telemetered value and the external measurement value. The number of rows of Y increases with the number of tele-differential observations. The last row of data is the additional tele-differential observation value. n is the number of tele-differential observations.

[0093] x1, x2, ..., x m is the error coefficient of the inertial device that affects the telemetry value in the inertial guidance system, including initial alignment, zero bias of gyroscope and accelerometer, scale factor, etc., and m is the number of inertial guidance tool error coefficients;

[0094] The i-th row data [u i1 u i2 … u im ] is the remote heterodyne observation quantity y i The number of rows of C increases with the increase of output data, and the last row of data is the additional environment function vector.

[0095] S2, determine whether the environment function matrix C meets the column full rank condition, if it meets the condition, go to step S3, if not, go to step S4;

[0096] The method for judging whether the environment function matrix C satisfies the column full rank condition is as follows:

[0097] Calculate the information matrix Φ = C T The rank r of C, if r = m, then the environment function matrix C is considered to satisfy the column full rank condition, if r ≠ m, then the environment function matrix C is considered to not satisfy the column full rank condition.

[0098] S3. Use the least squares estimation method to obtain the estimated value of the inertial guidance tool error coefficient

[0099] The calculation formula is:

[0100]

[0101] S4, using the improved principal component estimation method, the information matrix Φ = C T C performs eigenvalue decomposition and selects non-significant components according to the eigenvalues, that is, selects zero eigenvalue and its corresponding eigenvector set P A , and then P A Select the principal component and, based on the principal component, solve the estimated value of the inertial guidance tool error coefficient

[0102] The details are as follows:

[0103] S4.1. Information matrix Φ = CT C performs eigenvalue decomposition:

[0104] C T C=PDP T

[0105] Where D is a diagonal matrix, and each element on its diagonal is Φ=C T The eigenvalue of C, P is the orthogonal transformation matrix;

[0106] S4.2. Based on the corresponding zero and nonzero eigenvalues ​​in the diagonal matrix D, write P as follows:

[0107] P=[P A P B ]

[0108] Among them, P A is the set of eigenvectors corresponding to zero eigenvalues ​​in the diagonal matrix D, P B is the set of eigenvectors corresponding to the non-zero eigenvalues ​​in the diagonal matrix D;

[0109] S4.3. The set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A Select the pivot and get the row transformation matrices C1 and C2, so that:

[0110]

[0111]

[0112] Among them, P A1 is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A After row exchange, the diagonally dominant square matrix, P A2 is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A After row exchange, except for P A1 The remaining rows except P′ A is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A The matrix after row transformation; is the matrix P′ A The transposed matrix of

[0113] Step S4.3 is specifically implemented as follows:

[0114] First, find the main element: the eigenvector set P corresponding to the zero eigenvalue in D A Take the absolute value of each element, and select the element with the largest absolute value column by column as the main element of the corresponding column;

[0115] The specific implementation method of selecting the pivot is:

[0116] S1.1、PA Take the absolute value of each element in and add a column of label vector G to get a new matrix F A ,Right now:

[0117]

[0118] P A (i',j') is the eigenvector set P corresponding to the zero eigenvalue A The elements in ; m is the number of error coefficients of the inertial guidance tool;

[0119] Initialize i to 1, and loop through steps S1.2 to S1.3 until i reaches mr, then proceed to step S1.4;

[0120] S1.2, from F A Select the row corresponding to the maximum value in column i and record the last number in the row as g i ;

[0121] S1.3, from F A Remove the g i The new matrix formed after the row is updated matrix F A , add 1 to i and update i;

[0122] S1.4, g1, g2, g3, ..., g m-r Determine the eigenvector set P corresponding to the zero eigenvalue A The row number of each column pivot is the latest matrix F A The last column of elements is defined as the vector [g m-r+1 、g r+2 ,...,g m ].

[0123] Specifically:

[0124] (a) From F A Select the row corresponding to the maximum value in column 1 and record the last number in the row as g1;

[0125] (b) From F A In the new matrix formed by removing the g1th row, select the row corresponding to the maximum value in the second column, and record the last number of the row as g2;

[0126] (c) From F A In the new matrix formed by removing rows g1 and g2, select the row corresponding to the maximum value in the third column and record the last number of the row as g3;

[0127] (d) Similarly, from F A Remove g1, g2, g3, ..., g m-r-1In the new matrix formed after the row, select the row corresponding to the maximum value in the mr column and record the last number of the row as g m-r ;

[0128] Secondly, use the unit matrix to restore the process of finding the main element and determine the row transformation matrix C1 and row transformation matrix C2;

[0129] The specific steps for determining the row transformation matrix C1 and the row transformation matrix C2 are:

[0130] S2.1. Given an identity matrix I with dimension m×m;

[0131] S2.2, select g1, g2, g3, ..., g in the unit matrix I in turn. m-r The rows constitute the row transformation matrix C1;

[0132] S2.3, select the gth m-r+1 、g m-r+2 ,...,g m The rows constitute the row transformation matrix C2.

[0133] Finally, calculate P A The rearranged block matrix P A1 、P A2 , the calculation formula is:

[0134] P A1 =C1P A

[0135] P A2 =C2P A

[0136] S4.4. Calculate the error coefficient X corresponding to the row transformation matrix C1 A1 The error coefficient X corresponding to the row transformation matrix C2 A2 :

[0137] X A1 =0

[0138]

[0139] Among them, X A1 =C1X,X A2 =C2X, X A1 represents the error coefficient corresponding to the row transformation matrix C1, X A2 represents the error coefficient corresponding to the row transformation matrix C2, R represents the intermediate transformation matrix, D B represents the diagonal matrix composed of non-zero eigenvalues ​​in the diagonal matrix D;

[0140] S4.5. Calculate the estimated value of the inertial device error coefficient A special solution of :

[0141]

[0142] S5. Estimated value of the inertial guidance tool error coefficient Substitute into the inertial guidance tool error model and calculate the estimated value of the remote difference observation Extracting estimates of remote difference observations The last element in The telemetry data is compensated and the telemetry data corresponding to the telemetry quantity in the current output cycle is updated. The compensated telemetry data is the output of the inertial guidance system with improved accuracy.

[0143] The error model of the inertial guidance tool is a linear equation, as follows:

[0144] Y=CX

[0145] Wherein, Y is the remote difference observation matrix, X is the inertial guidance tool error coefficient vector, and C is the environment function matrix. The present invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the following is achieved: Figure 1 The steps of the method.

[0146] The present invention provides an electronic device, comprising a memory and a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the following Figure 1 The steps of the method.

[0147] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage and optical storage, etc.) containing computer-usable program code.

[0148] The present invention is described with reference to the flowcharts and / or block diagrams of the methods, systems, and computer program products of the embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as the combination of processes and / or blocks in the flowcharts and / or blocks, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1means for performing functions specified in one or more processes and / or one or more blocks.

[0149] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0150] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0151] Example 1:

[0152] Assume that the inertial guidance environment function matrix is

[0153]

[0154] The true value of the inertial guidance tool error coefficient vector is

[0155]

[0156] The remote difference observation matrix is

[0157]

[0158] The solution process is as follows:

[0159] (1) According to the given linear equation Y = CX, calculate the information matrix Φ = C T rank r of C;

[0160] r=rank(C T C)=4

[0161] (2) It can be seen that r≠m=6, so for the information matrix Φ=C T C performs eigenvalue decomposition, and we have

[0162] C T C=PDP T

[0163] in,

[0164]

[0165]

[0166] (3) According to the corresponding zero eigenvalues ​​and non-zero eigenvalues ​​in D, P is written as

[0167] P=[P A P B ]

[0168] in,

[0169]

[0170]

[0171] The diagonal matrix D corresponding to the non-zero eigenvalues ​​in D B for

[0172]

[0173] (4) When using the traditional principal component method to solve, there is

[0174]

[0175] Then the estimated value of the inertial guidance error coefficient is

[0176]

[0177] It can be seen that this method cannot estimate the true value of the inertial guidance estimation error coefficient and cannot guarantee the correctness of the inertial guidance compensation.

[0178] When the method of the present invention is used, the above steps (1) to (3) are completed first, and the subsequent solution process is as follows:

[0179] (4.1) For P A Select the main element to obtain the row transformation matrix C1, C2, so that

[0180]

[0181]

[0182] in,

[0183]

[0184]

[0185] (4.2) Using the method of the present invention, the estimated value of the inertial device error coefficient can be estimated A special solution of X A1 =0,

[0186]

[0187]

[0188] (5) The value obtained above is the error coefficient of the inertial guidance tool. The error coefficient is used to compensate the inertial guidance telemetry data, thereby improving the accuracy of the inertial guidance system output.

[0189] Therefore, the method of the present invention ensures that Y=CX, so that the output fitting residual value after compensation is zero, reduces the guidance tool error, and improves the output accuracy of the inertial guidance system.

[0190] The above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

[0191] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

Claims

1. A method for improving the output accuracy of an inertial guidance system based on non-significant component estimation, characterized in that For each telemetry value, the following steps are performed in each calculation cycle: S1. Calculate the current output period telemetry and external difference observation value y according to the telemetry value and external measurement value corresponding to the current output period of the inertial guidance system. i and its corresponding environment function vector [u i1 u i2 …u im ], the current output period remote heterodyne observation quantity y i and its corresponding environment function vector [u i1 u i2 …u im ] is added to the environment function matrix and remote differential observation matrix of the inertial guidance system to form a new environment function matrix C and remote differential observation matrix Y, and the inertial guidance tool error model is constructed; m is the number of inertial guidance tool error coefficients; S2, determine whether the environment function matrix C meets the column full rank condition, if it meets the condition, go to step S3, if not, go to step S4; S3. Use the least squares estimation method to obtain the estimated value of the inertial guidance tool error coefficient S4, using the non-significant component estimation method, the information matrix Φ = C T C performs eigenvalue decomposition and selects non-significant components according to the eigenvalues, that is, selects zero eigenvalue and its corresponding eigenvector set P A , and then P A Select the principal component and, based on the principal component, solve the estimated value of the inertial guidance tool error coefficient S5. Estimated value of the inertial guidance tool error coefficient Substitute into the inertial guidance tool error model and calculate the estimated value of the remote difference observation Extracting estimates of remote difference observations The last element in The telemetry data is compensated and the telemetry data corresponding to the telemetry quantity in the current output cycle is updated. The compensated telemetry data is the output of the inertial guidance system with improved accuracy.

2. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 1, characterized in that The error model of the inertial guidance tool is a linear equation, as follows: Y=CX Among them, Y is the remote difference observation matrix, X is the inertial guidance tool error coefficient vector, and C is the environment function matrix; y1, y2, ..., y n is a sequence of tele-differential observations of the inertial guidance system constructed according to the output period. The tele-differential observation refers to the difference between the telemetered value and the external measurement value. The number of rows of Y increases with the number of tele-differential observations. The last row of data is the additional tele-differential observation value. n is the number of tele-differential observations. x1, x2, ..., x m The error coefficients of inertial devices that affect telemetry values ​​in the inertial guidance system include initial alignment, zero bias of gyroscopes and accelerometers, and scale factors; The i-th row data [u i1 u i2 …u im ] is the remote heterodyne observation quantity y i The number of rows of C increases with the increase of output data, and the last row of data is the additional environment function vector.

3. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 1, characterized in that The method for judging whether the environment function matrix C satisfies the column full rank condition is as follows: Calculate the information matrix Φ = C T The rank r of C, if r = m, then the environment function matrix C is considered to satisfy the column full rank condition, if r ≠ m, then the environment function matrix C is considered to not satisfy the column full rank condition.

4. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 1, characterized in that The calculation formula of step S3 is:

5. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 3, characterized in that The step S4 is specifically as follows: S4.

1. Information matrix Φ = C T C performs eigenvalue decomposition: C T C=PDP T Where D is a diagonal matrix, and each element on its diagonal is Φ=C T The eigenvalue of C, P is the orthogonal transformation matrix; S4.

2. Based on the corresponding zero and nonzero eigenvalues ​​in the diagonal matrix D, write P as follows: P=[P A P B ] Among them, P A is the set of eigenvectors corresponding to zero eigenvalues ​​in the diagonal matrix D, P B is the set of eigenvectors corresponding to the non-zero eigenvalues ​​in the diagonal matrix D; S4.

3. The set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A Select the pivot and get the row transformation matrices C1 and C2, so that: Among them, P A1 is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A After row exchange, the diagonally dominant square matrix, P A2 is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A After row exchange, except for P A1 The remaining rows except P' A is the set of eigenvectors P corresponding to the zero eigenvalues ​​in the diagonal matrix D A The matrix after row transformation; is the matrix P' A The transposed matrix of S4.

4. Calculate the error coefficient X corresponding to the row transformation matrix C1 A1 The error coefficient X corresponding to the row transformation matrix C2 A2 : X A1 ＝0 Among them, X A1 =C1X,X A2 =C2X, X A1 represents the error coefficient corresponding to the row transformation matrix C1, X A2 represents the error coefficient corresponding to the row transformation matrix C2, R represents the intermediate transformation matrix, D B represents the diagonal matrix composed of non-zero eigenvalues ​​in the diagonal matrix D; S4.

5. Calculate the estimated value of the inertial device error coefficient A special solution of :

6. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 5, characterized in that Step S4.3 is specifically implemented as follows: First, find the main element: the eigenvector set P corresponding to the zero eigenvalue in D A Take the absolute value of each element, and select the element with the largest absolute value column by column as the main element of the corresponding column; Secondly, use the unit matrix to restore the process of finding the main element and determine the row transformation matrix C1 and row transformation matrix C2; Finally, calculate P A The rearranged block matrix P A1 、P A2 , the calculation formula is: P A1 =C1P A P A2 =C2P A 。 7. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 6, characterized in that The specific implementation method of selecting the pivot is: S1.1、P A Take the absolute value of each element in and add a column of label vector G to get a new matrix F A ,Right now: P A (i',j') is the eigenvector set P corresponding to the zero eigenvalue A The elements in ; m is the number of error coefficients of the inertial guidance tool; Initialize i to 1, and loop through steps S1.2 to S1.3 until i reaches mr, then proceed to step S1.4; S1.2, from F A Select the row corresponding to the maximum value in column i and record the last number in the row as g i ; S1.3, from F A Remove the g i The new matrix formed after the row is updated matrix F A , add 1 to i and update i; S1.4, g1, g2, g3, ..., g m-r Determine the eigenvector set P corresponding to the zero eigenvalue A The row number of each column pivot is the latest matrix F A The last column of elements is defined as the vector [g m-r+1 、g r+2 ,...,g m ].

8. The method for improving the output accuracy of an inertial guidance system based on non-significant component estimation according to claim 7, characterized in that The specific steps for determining the row transformation matrix C1 and the row transformation matrix C2 are: S2.

1. Given an identity matrix I with dimension m×m; S2.2, select g1, g2, g3, ..., g in the unit matrix I in turn. m-r The rows constitute the row transformation matrix C1; S2.3, select the gth m-r+1 、g m-r+2 ,...,g m The rows constitute the row transformation matrix C2.

9. An electronic device, characterized in that: include: Memory: used to store computer-readable instructions; as well as A processor is configured to execute the computer-readable instructions to perform the method according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that A computer program is stored thereon, and when the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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