A method for improving inertial guidance precision based on least square method

Abstract

This invention discloses a method for improving the accuracy of inertial guidance based on the least squares method, comprising: constructing a recursive formula for the least squares method according to the guidance tool error model; and applying the difference y between k-dimensional guidance telemetry observations at the current recursive time in real time. n+ 1. Combining the recursive formula of the least squares method, the estimated value of the guidance tool error coefficient at the current recursive time is determined. This estimated value is then used to compensate for the k-dimensional guidance telemetry observations at the current recursive time. The specific method for constructing the recursive formula of the least squares method includes: determining the value of the constant p. When the constant p is used as the iteration number, the recursive formula of the least squares method is an iterative recursive least squares recursive formula; when the constant p is used as the order, the recursive formula of the least squares method is a polynomial recursive least squares recursive formula. This invention can significantly improve the estimation accuracy and has a wider range of applications and higher engineering value.

Description

Technical Field

[0001] This invention relates to a method for improving the accuracy of inertial guidance based on the least squares method, belonging to the field of inertial navigation technology. Background Technology

[0002] Currently, inertial navigation in spacecraft primarily employs strapdown systems or platform systems composed of gyroscopes and accelerometers. Before live-fire flights, the error coefficients of the gyroscopes and accelerometers need to be calibrated on the ground. Error compensation based on the calibration results can effectively improve the accuracy of inertial navigation. However, even after ground calibration, in actual flight navigation tests, the theoretical values ​​of velocity and position calculated from telemetry data still deviate significantly from the actual flight velocity and position values ​​obtained from external measurements, resulting in a so-called "ground-to-ground inconsistency." Analysis reveals that this inconsistency is caused by insufficient precision in the ground calibration and data processing methods, leading to error accumulation during actual flight and consequently, decreased flight accuracy. Therefore, it is necessary to correct the error model and data processing methods used in ground calibration.

[0003] The commonly used method is to identify parameters using the least squares method, which has the advantage of providing the sum of squares of the output error. The minimum value is obtained, and the estimated value of the parameter X can be obtained in a single calculation. However, the downside is that as the amount of data accumulates, the amount of computation increases.

[0004] To reduce computational load, recursive least squares method is used in engineering, the core idea of ​​which is to use the estimated value from the previous time step. With the current observation y n+1 Solve for the estimated time of occurrence. The advantage is reduced computational load, meeting real-time requirements. The formula for recursive least squares is as follows:

[0005] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0006]

[0007] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0008]

[0009] Among them, I k It is a k-dimensional identity matrix.

[0010] However, it should be noted that there is a problem with the above recursive least squares method: It's not the smallest. For example, when the noise is zero, according to the formula of the recursive least squares method, we have...

[0011]

[0012] This means that the estimated value is biased, making thereby Not the minimum. To overcome the bias... The information inverse matrix Γ can be made n The value of approaches infinity, but no matter what value it takes, there will always be .

[0013] Therefore, a new method is needed to eliminate this bias in order to improve the accuracy of inertial guidance. Summary of the Invention

[0014] The purpose of this invention is to overcome the above-mentioned defects and provide a method for improving the accuracy of inertial guidance based on the least squares method. This invention solves the technical problem that the traditional least squares method has unavoidable biases that lead to low accuracy in inertial guidance. This invention can significantly improve the estimation accuracy and has a wider range of applications and higher engineering value.

[0015] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0016] A method for improving the accuracy of inertial guidance based on the least squares method includes:

[0017] Based on the difference between inertial guidance telemetry and observations and the flight environment function, a guidance tool error model is constructed, which satisfies a linear relationship.

[0018] Based on the guidance tool error model, a recursive formula for the least squares method is constructed;

[0019] Based on the difference between the k-dimensional guidance telemetry observations at the current recursive time and the recursive formula of the least squares method, the estimated value of the guidance tool error coefficient at the current recursive time is determined, and the estimated value of the guidance tool error coefficient is used to compensate for the k-dimensional guidance telemetry observations at the current recursive time.

[0020] The specific methods for constructing the recursive formula for the least squares method include:

[0021] Determine the value of the constant p, and use the constant p as the number of iterations or the order;

[0022] When the constant p is used as the iteration number, the recursive formula for the least squares method is the iterative recursive least squares method recursive formula. Combining the iterative recursive least squares method recursive formula, the guidance tool error coefficient estimate obtained in the p-th iteration at time n+1 is determined as the guidance tool error coefficient estimate at time n+1. The current guidance tool error coefficient estimate is obtained based on the guidance tool error coefficient estimate obtained in the previous iteration;

[0023] When the constant p is the order, the recursive formula for the least squares method is the polynomial recursive least squares recursive formula. Combining the polynomial recursive least squares recursive formula, based on the estimated value of the guidance tool error coefficient at time n in the recursion... The p-order polynomial feedback matrix K at recursive time n+1 n+1,p Determine the estimated value of the guidance tool error coefficient at time n+1.

[0024] n is an integer ≥ 0, and k is an integer ≥ 1.

[0025] Furthermore, the guidance tool error model is as follows:

[0026] y n+1 =c n+1 X+v

[0027] Among them, y is the difference y between the k-dimensional guided telemetry observations at time n+1 in the recursive step. n+1 =y 遥,n+1 -y 外,n+1 , where y 遥,n+1 For the k-dimensional guided telemetry observations at time n+1, y 外,n+1 For the k-dimensional guided external observations at time n+1; c n+1 Let X be the flight environment function matrix at time n+1, X be the constant error coefficient of the guidance tool, and v be the noise.

[0028] The guidance tool error model includes either a telemetry velocity error model or a telemetry position error model, which consists of gyroscope error and accelerometer error.

[0029] Furthermore, when the constant p is used as the number of iterations, the recursive formula for the least squares method is:

[0030] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0031]

[0032] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0033] Among them, K n+1 Let Γ be the feedback matrix at time n+1 of the recursion. n ,Γ n+1 These are the information inverse matrices at recursion time n and recursion time n+1, respectively. k For a k-dimensional identity matrix, Let c represent the estimated guidance tool error coefficient obtained in the i-th iteration at time n+1, where i = 1, 2, ..., p, c n+1 Let y be the flight environment function matrix at time n+1. n+1 It represents the difference between the k-dimensional guided telemetry observations at time n+1.

[0034] Furthermore, when the constant p is used as the order, the recursive formula for the least squares method is:

[0035] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0036] K n+1,p =K n+1 [I k -(I k -c n+1 K n+1 ) p ](c n+1 K n+1 ) -1

[0037]

[0038] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0039] Among them, K n+1 Let Γ be the feedback matrix at time n+1 of the recursion. n ,Γ n+1These are the information inverse matrices at recursion time n and recursion time n+1, respectively. k For a k-dimensional identity matrix, c n+1 Let n+1 be the flight environment function matrix at recursive time n.

[0040] Furthermore, the value of the constant p ranges from 3 to 10.

[0041] Furthermore, n = 0 represents the initial time, Γ0 and For the given known quantities.

[0042] Furthermore, the k-dimensional guidance telemetry observations at the current recursive time are compensated using the estimated error coefficients of the guidance tool according to the following compensation formula:

[0043]

[0044] in, For the compensated guidance telemetry observations.

[0045] Furthermore, at each recursive time step, the binding value of the tool error is calculated using a determined tool error coefficient. Corrections are made to compensate for inertial guidance telemetry observations.

[0046] Furthermore, before determining the tool error coefficient at each recursive time, it is determined whether the difference between the inertial guidance telemetry observations at the current recursive time is abnormal. If there is no abnormality, processing continues; otherwise, the telemetry observations from the previous recursive time are used to replace the telemetry observations at the current recursive time for subsequent processing.

[0047] Furthermore, before determining the estimated value of the tool error coefficient at each recursive time step, it is determined whether the difference between the current inertial guidance telemetry observations is abnormal. If there is no abnormality, the subsequent processing continues. Otherwise, it is further determined that the dimension of the abnormal data is located, and the relevant recursion of that dimension is isolated from the recursion formula of the least squares method at the current recursive time step, while the other dimensions continue to be processed.

[0048] Compared with the prior art, the present invention has at least one of the following advantages:

[0049] (1) This invention creatively proposes a method to improve the accuracy of inertial guidance based on the least squares method. Without changing the feedback matrix and the information inverse matrix, the estimation accuracy can be significantly improved by adding a state update equation or by adding a polynomial feedback matrix.

[0050] (2) The method of the present invention can select an appropriate number of iterations or polynomial order to find the best match between real-time performance and accuracy, based on the accuracy requirements of inertial navigation.

[0051] (3) The method of the present invention can cover the traditional recursive least squares method. The traditional recursive least squares method is a special case of the present invention. The present invention has a wider range of applications and higher engineering value. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the iterative recursive least squares method used to derive the recursive formula in this invention.

[0053] Figure 2 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 1;

[0054] Figure 3 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 2;

[0055] Figure 4 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 3;

[0056] Figure 5 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 4.

[0057] Figure 6 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 5.

[0058] Figure 7 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 6;

[0059] Figure 8 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 7.

[0060] Figure 9 The output fitting residual is calculated using the recursive least squares method when the number of iterations p = 8.

[0061] Figure 10 To output the sum of squared residuals Q p The relationship between the iteration number p and the number of iterations.

[0062] Figure 11 This is a flowchart illustrating the polynomial recursive least squares method used in this invention.

[0063] Figure 12 The output fitting residual is calculated using the polynomial least squares method when the order p = 1.

[0064] Figure 13 The output fitting residuals are calculated using the polynomial least squares method when the order is p=2.

[0065] Figure 14The output fitting residuals calculated by polynomial least squares method for order p=3;

[0066] Figure 15 The output fitting residuals are calculated using the polynomial least squares method when the order is p=4.

[0067] Figure 16 The output fitting residuals calculated by polynomial least squares method for order p=5;

[0068] Figure 17 The output fitting residuals calculated by polynomial least squares method for order p=6;

[0069] Figure 18 The output fitting residuals calculated by the polynomial least squares method for order p=7;

[0070] Figure 19 The output fitting residuals calculated by the polynomial least squares method for order p=8;

[0071] Figure 20 To output the sum of squared residuals Q p The relationship between order p and order p. Detailed Implementation

[0072] The features and advantages of the present invention will become clearer and more explicit from the following detailed description.

[0073] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0074] This invention provides a method for reducing the estimation bias of the recursive least squares method, so as to improve the accuracy of inertial guidance as much as possible while satisfying real-time requirements. The method of this invention includes the following steps:

[0075] (1) Based on the difference between inertial guidance telemetry observations and the flight environment function, a guidance tool error model is constructed. The guidance tool error model satisfies the linear relationship y n+1 =c n+1 X+v; where y n+1 Let X be the difference between k-dimensional guided telemetry observations at time n+1, and let X be the tool constant error coefficient. n+1 Let v be the flight environment function matrix, and v be the noise; the error compensation model is...

[0076] (2) Perform recursive initialization, that is, set the information inverse matrix Γ. nInitial values ​​and estimated values ​​of parameter X The initial value of parameter X is the tool constant error coefficient in the guidance tool error model;

[0077] (3) Process the error model of the guidance tool to determine the least squares recursive formula. The specific method can be the first or the second form of the least squares recursive formula.

[0078] The first form is the iterative recursive least squares recursive formula. Given the number of iterations p, the iterative recursive least squares recursive formula is as follows:

[0079] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0080]

[0081] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0082] Among them, I k It is a k-dimensional identity matrix; K n+1 For feedback matrix; The calculated value for the first iteration, The calculated value for the second iteration, The calculated value for the third iteration, ... This is the calculated value for the p-th iteration;

[0083] The second form is the recursive formula for polynomial recursive least squares. Given the order p of the polynomial, the recursive formula for polynomial recursive least squares is as follows:

[0084] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0085]

[0086]

[0087]

[0088] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0089] Among them, I k It is a k-dimensional identity matrix; K n+1 For the feedback matrix; K n+1,p It is a p-order polynomial feedback matrix; A new estimate for parameter X; Γ n+1 This is the new information inverse matrix;

[0090] When the p-values ​​in the first and second forms of the least squares recursive formula are equal, the result obtained through the first and second forms... equal.

[0091] (4) Based on the current difference y between inertial guidance telemetry observations and the aforementioned recursive formula, determine the tool error coefficient corresponding to each recursive time. Use this tool error coefficient to evaluate the inertial guidance telemetry observation y. 遥 Compensation will be provided, and the compensation formula is as follows: Used for subsequent guidance.

[0092] Preferably, the guidance tool error model includes a telemetry velocity error model or a telemetry position error model composed of gyroscope error and accelerometer error.

[0093] Preferably, the initialization in step (2) is performed at time zero Γ0. Given a known quantity, and at the remaining times Γ n and It is necessary to pass through the Γ of the previous moment. n-1 and Perform recursive calculations.

[0094] Preferably, the compensation in step (4) is to correct the binding value of the tool error using a determined tool error coefficient at each recursive time, thereby achieving compensation for the inertial guidance telemetry observation.

[0095] Preferably, before determining the tool error coefficient at each recursive time step, it is determined whether the difference between the current inertial guidance telemetry observations is abnormal. If there is no abnormality, the processing continues; otherwise, the telemetry observations from the previous recursive time step are used to replace the current telemetry observations for subsequent processing.

[0096] Preferably, before determining the tool error coefficient at each recursive time, it is determined whether the difference between the current inertial guidance telemetry observations is abnormal. If there is no abnormality, the subsequent processing continues. Otherwise, the dimension of the abnormal data is further determined, and the relevant recursion of that dimension is isolated from the recursion formula in step (2) at the current recursive time. The remaining dimensions continue to be processed.

[0097] Example:

[0098] When a ballistic missile uses telemetry data to separate tool errors, the model structure of the velocity error equation in the x-axis direction is as follows:

[0099]

[0100] In the formula, δv x k represents the telemetry velocity error in the x-axis direction. 0x k 0y k 0z Zero bias of the accelerometers along the x, y, and z axes; δk y k yz D represents the first-order error coefficients of the y- and z-axis accelerometers. Fz This refers to the zero-order drift of the z-axis gyroscope; This is the environment function for the x-axis velocity error.

[0101] For ease of analysis, the errors were normalized to make k 0x =1, k 0y =1, k 0z =1, δk y =1, k yz =1, D Fz =1, meaning the tool constant error coefficient is

[0102]

[0103] Because there is a set of numbers in each external measurement cycle, namely the velocity error δv in the x-axis direction. x And the environmental function of the x-axis velocity error during the external measurement period. Then the first 10 sets of remote telemetry observations y = δv x and environment function matrix

[0104]

[0105] The corresponding value is

[0106] (1) Let c1 = [7 26 6 28 13 60] and y1 = c1X = 140 when n+1 = 1;

[0107] (2) Suppose that when n+1=2, c2=[1 29 15 4 16 52] and y2=c2X=117;

[0108] (3) When n+1=3, c3=[11 56 8 44 19 20] and y3=c3X=158;

[0109] (4) When n+1=4, c4=[11 31 8 44 19 47] and y4=c4X=160;

[0110] (5) When n+1=5, c5=[7 52 6 28 13 33] and y5=c5X=139;

[0111] (6) When n+1=6, c6=[11 55 9 44 20 22] and y6=c6X=161;

[0112] (7) When n+1=7, c7=[3 71 17 12 20 6] and y7=c7X=129;

[0113] (8) When n+1=8, c8=[1 31 22 4 23 44] and y8=c8X=125;

[0114] (9) When n+1=9, c9=[2 54 18 8 20 22] and y9=c9X=124;

[0115] (10) Let c be the value when n+1 = 10. 10 =[21 47 4 84 25 26] and y 10 =c 10 X = 207.

[0116] Let the initial value of the tool constant error X be...

[0117] The initial value of the information inverse matrix is ​​Γ0 = 10. 4 I6. Below, the iterative recursive least squares method is used to calculate the output fitting residuals with convergent accuracy based on different iteration numbers p.

[0118]

[0119] And the sum of squared residuals of the output fitting Q = δY T δY. In the formula, This is the estimated result when the calculation is repeated up to n+1=1, ..., n+1=10.

[0120] like Figure 1 As shown, the calculation is performed using the iterative recursive least squares method recursive formula:

[0121] (1) p = 1

[0122] The recurrence formula for the iterative recursive least squares method is the same as that for the traditional recursive least squares method, as follows:

[0123] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0124]

[0125] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0126]

[0127] The calculated result for δY1 is -1.1 × 10⁻⁶. -5 ~6×10 -6 Magnitude, such as Figure 2 As shown. The output is the sum of squared residuals Q1 = δY1. T δY1=1.98347×10 -10 .

[0128] (2) p = 2

[0129] The recursive formula for the least squares method with one iteration is as follows:

[0130] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0131]

[0132] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0133]

[0134] The calculated δY² result is -1.0 × 10⁻⁶. -6 ~1×10 -6 Magnitude, such as Figure 3 As shown. The output is the sum of squared residuals Q2 = δY2. T δY2=2.3455×10 -12 .

[0135] (3) p = 3

[0136] The recurrence formula for the least squares method with two iterations is as follows:

[0137] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0138]

[0139] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0140]

[0141] The calculated δY3 result is -3.8 × 10⁻⁶. -7 ~2.3×10 -7 Magnitude, such as Figure 4 As shown. The output is the sum of squared residuals Q3 = δY3. T δY3=2.4998×10 -13 .

[0142] (4) p = 4

[0143] The recurrence formula for the three-iteration recursive least squares method is as follows:

[0144] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0145]

[0146] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0147]

[0148] The calculated δY4 result is -2.1 × 10⁴. -7 ~0.6×10 -7 Magnitude, such as Figure 5 As shown. The output is the sum of squared residuals Q4 = δY4. T δY4=4.98471×10 -14 .

[0149] (5) p = 5

[0150] The recurrence formula for the four-iteration recurrence least squares method is as follows:

[0151] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0152]

[0153] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0154]

[0155] The calculated δY5 result is -1.2 × 10⁵. -7 ~1.8×10 -8 Magnitude, such as Figure 6 As shown. The output is the sum of squared residuals Q5 = δY5. T δY5=1.38216×10 -14 .

[0156] (6) p = 6

[0157] The recursive formula for the least squares method with 5 iterations is as follows:

[0158] K n+1 =Γ n c n+1 T[I k +c n+1 Γ n c n+1 T ] -1

[0159]

[0160] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0161]

[0162] The calculated δY6 result is -6.4 × 10⁶. -8 ~0.2×10 -8 Magnitude, such as Figure 7 As shown. The output is the sum of squared residuals Q6 = δY6. T δY6=4.19427×10 -15 .

[0163] (7) p = 7

[0164] The recurrence formula for the 6-iteration recursive least squares method is as follows:

[0165] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0166]

[0167] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0168]

[0169] The calculated δY7 result is -3.6 × 10⁷. -8 ~0.3×10 -8 Magnitude, such as Figure 8 As shown. The output is the sum of squared residuals Q7 = δY7. T δY7=1.29823×10 -15 .

[0170] (8)p=8

[0171] The recurrence formula for the 7-iteration recurrence least squares method is as follows:

[0172] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0173]

[0174] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0175]

[0176] The calculated δY8 result is -2.0 × 10⁸. -8 ~0.2×10 -8 Magnitude, such as Figure 9 As shown. The output is the sum of squared residuals Q8 = δY8. T δY8=4.03785×10 -16 .

[0177] Plot Q1, Q2, ..., Q8 as follows Figure 10 As shown in the figure, it can be seen that the sum of squared residuals Q of the output fitting is... p The relationship between the iteration number p and the number of iterations is exponentially decaying, verifying that the iterative recursive least squares method proposed in this invention has high accuracy. In engineering implementation, a suitable iteration number p needs to be selected to strike a trade-off between computational complexity and accuracy.

[0178] like Figure 11 The calculation is performed using the polynomial recursive least squares method recursive formula:

[0179] (1) p = 1

[0180] The recurrence formula for the polynomial recursive least squares method is the same as that for the traditional recursive least squares method, as follows:

[0181] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n cn+1 T ] -1

[0182]

[0183] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0184]

[0185] The calculated result for δY1 is -1.1 × 10⁻⁶. -5 ~6×10 -6 Magnitude, such as Figure 12 As shown. The output is the sum of squared residuals Q1 = δY1. T δY1=1.98347×10 -10 .

[0186] (2) p = 2

[0187] The recurrence formula for the least squares method for second-order polynomials is as follows:

[0188] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0189]

[0190]

[0191] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0192]

[0193] The calculated δY² result is -1.0 × 10⁻⁶. -6 ~1×10 -6 Magnitude, such as Figure 13 As shown. The output is the sum of squared residuals Q2 = δY2. T δY2=2.3455×10 -12 .

[0194] (3) p = 3

[0195] The recursive formula for the least squares method of recursion for a third-order polynomial is as follows:

[0196] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0197]

[0198]

[0199] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0200]

[0201] The calculated δY3 result is -3.8 × 10⁻⁶. -7 ~2.3×10 -7 Magnitude, such as Figure 14 As shown. The output is the sum of squared residuals Q3 = δY3. T δY3=2.4998×10 -13 .

[0202] (4) p = 4

[0203] The recurrence formula for the fourth-order polynomial recursive least squares method is as follows:

[0204] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0205]

[0206]

[0207] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0208]

[0209] The calculated δY4 result is -2.1 × 10⁴. -7 ~0.6×10 -7 Magnitude, such as Figure 15 As shown. The output is the sum of squared residuals Q4 = δY4. T δY4=4.98471×10 -14 .

[0210] (5) p = 5

[0211] The recursive formula for the least squares method of recursion for a 5th-order polynomial is as follows:

[0212] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0213]

[0214]

[0215] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0216]

[0217] The calculated δY5 result is -1.2 × 10⁵. -7 ~1.8×10 -8 Magnitude, such as Figure 16 As shown. The output is the sum of squared residuals Q5 = δY5. T δY5=1.38216×10 -14 .

[0218] (6) p = 6

[0219] The recursive formula for the least squares method of recursion for a 6th-order polynomial is as follows:

[0220] K n+1 =Γ n c n+1 T [I k +c n+1 Γ nc n+1 T ] -1

[0221]

[0222]

[0223] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0224]

[0225] The calculated δY6 result is -6.4 × 10⁶. -8 ~0.2×10 -8 Magnitude, such as Figure 17 As shown. The output is the sum of squared residuals Q6 = δY6. T δY6=4.19427×10 -15 .

[0226] (7) p = 7

[0227] The recursive formula for the 7th-order polynomial recursive least squares method is as follows:

[0228] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0229]

[0230]

[0231] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0232]

[0233] The calculated δY7 result is -3.6 × 10⁷. -8 ~0.3×10 -8 Magnitude, such as Figure 18 As shown. The output is the sum of squared residuals Q7 = δY7. TδY7=1.29823×10 -15 .

[0234] (8)p=8

[0235] The recursive formula for the least squares method of recursion for an 8th-order polynomial is as follows:

[0236] K n+1 =Γ n c n+1 T [I k +c n+1 Γ n c n+1 T ] -1

[0237]

[0238]

[0239] Γ n+1 =Γ n -K n+1 c n+1 Γ n

[0240]

[0241] The calculated δY8 result is -2.0 × 10⁸. -8 ~0.2×10 -8 Magnitude, such as Figure 19 As shown. The output is the sum of squared residuals Q8 = δY8. T δY8=4.03785×10 -16 .

[0242] Plot Q1, Q2, ..., Q8 as follows Figure 20 As shown in the figure, it can be seen that the sum of squared residuals Q of the output fitting is... p The exponential decay relationship between the polynomial order p and the polynomial order verifies that the proposed polynomial recursive least squares method has high accuracy. In engineering implementation, a suitable polynomial order p needs to be selected to strike a trade-off between computational complexity and accuracy.

[0243] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0244] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for improving the accuracy of inertial guidance based on the least squares method, characterized in that, include: Based on the difference between inertial guidance telemetry and observations and the flight environment function, a guidance tool error model is constructed, which satisfies a linear relationship. Based on the guidance tool error model, a recursive formula for the least squares method is constructed; Real-time based on the current recursive time k By combining the difference between the guided telemetry observations and the recursive formula of the least squares method, the estimated value of the guidance tool error coefficient at the current recursive time is determined. This estimated value of the guidance tool error coefficient is then used to calculate the error coefficient at the current recursive time. k Compensation is performed on guided telemetry observations; The specific methods for constructing the recursive formula for the least squares method include: Determine constants p The value of the constant p As the number of iterations or the order; n For integers ≥ 0, k It is an integer greater than or equal to 1; When constant p When the number of iterations is used, the recurrence relation for the least squares method is: in, K n+1 for n The feedback matrix at recursive time +1 , They are respectively n Recursive time sum n +1 information inverse matrix at recursive time step for k 1D identity matrix express n +1 recursive time i The estimated error coefficients of the guidance tool obtained in the next iteration. i =1, 2, ... p , for n +1 recursive time-time flight environment function matrix, for n +1 recursive time k The difference between the external observations of the guided telemetry system; When constant p When the order is used, the recursive formula for the least squares method is: in, K n+1 for n The feedback matrix at recursive time +1 , They are respectively n Recursive time sum n +1 information inverse matrix at recursive time step for k 1D identity matrix for n +1 recursive time-time flight environment function matrix; Before determining the estimated value of the tool error coefficient at each recursive time step, it is determined whether the difference of the current inertial guidance telemetry observation is abnormal. If there is no abnormality, the subsequent processing continues. Otherwise, it is further determined that the dimension of the abnormal data is located, and the relevant recursion of that dimension is isolated from the recursion formula of the least squares method at the current recursive time step. The remaining dimensions continue to be processed.

2. The method for improving inertial guidance accuracy based on the least squares method according to claim 1, characterized in that, The guidance tool error model is as follows: in, n +1 recursive time k Difference between remotely guided observations ,in, for n +1 recursive time k 3D guided telemetry observations for n +1 recursive time k External observation and measurement for guided navigation; for n +1 recursive time-time flight environment function matrix, For guidance tools, the constant error coefficient is... For noise; The guidance tool error model includes either a telemetry velocity error model or a telemetry position error model, which consists of gyroscope error and accelerometer error.

3. The method for improving inertial guidance accuracy based on least squares method according to claim 1, characterized in that, constant p The value range is 3 to 10.

4. The method for improving inertial guidance accuracy based on least squares method according to claim 1, characterized in that, n =0 represents the initial time. and For the given known quantities.

5. A method for improving inertial guidance accuracy based on the least squares method according to claim 2, characterized in that, According to the following compensation formula, the estimated error coefficient of the guidance tool is used to calculate the error at the current recursive time. k Compensation is performed on telemetry observations guided by the system. ； in, For the compensated guidance telemetry observations.

6. The method for improving inertial guidance accuracy based on the least squares method according to claim 1, characterized in that, At each recursive time step, the binding value of the tool error is calculated using a determined tool error coefficient. Corrections are made to compensate for inertial guidance telemetry observations.

Images