Error modeling method based on recursive variance information of fiber-optic gyroscope

Abstract

The invention discloses an error modeling method based on recursive variance information of a fiber-optic gyroscope, and relates to the field of error identification of the fiber-optic gyroscope, the method comprises the following steps: acquiring N output data of the fiber-optic gyroscope within bundling time tau, and generating an original output sequence according to the output data; the output data comprises an angular rate; according to the original output sequence, based on an Allan variance estimation method, determining an Allan variance corresponding to the fiber-optic gyroscope; according to the output data and the Allan variance, constructing a random error representation model; and optimizing the output data by using the random error representation model. According to the method, the real-time performance and the accuracy of FOG random error analysis can be improved, and then different types of noise sources can be quickly and accurately identified.

Description

Technical Field

[0001] The present application relates to the field of fiber optic gyroscope error identification, and particularly to an error modeling method based on the recursive variance information of a fiber optic gyroscope. Background Art

[0002] A fiber optic gyroscope (FOG) is a high-precision rotational sensor, which is widely used in inertial navigation and guidance systems; the random errors output by the FOG include quantization noise (QN), angular random walk (ARW), bias instability (BI), angular rate random walk (RRW), rate ramp (RR), and other noises, which conform to the characteristics of power-law noise. Allan variance (AVAR) is a statistical tool for analyzing the stability of time series data and is used to evaluate the frequency stability of high-precision oscillators. By analyzing the data fluctuations on different time scales, Allan variance can effectively identify and quantify various noise sources and is widely used in fields such as inertial navigation systems and frequency measurements; therefore, Allan variance is used to determine the noise components of the FOG. In most cases, different noise terms appear in different collection time τ regions, so various random processes existing in the observed data can be easily identified.

[0003] For the variance analysis of the random errors of the FOG, it is generally carried out based on the angular rate output signal level and is determined according to the definition of Allan variance in IEEE Std 647 TM -2006. Among them, the traditional Allan variance method is essentially an offline analysis method, and a large amount of experimental data needs to be collected when calculating the variance of the long-correlation time random errors of the FOG.

[0004] Therefore, there is a problem of poor real-time performance. In order to improve the real-time performance and accuracy of the FOG random error analysis, and then quickly and accurately identify different types of noise sources and optimize the performance of the FOG, there is an urgent need to provide a new FOG random error analysis method or system. Summary of the Invention

[0005] The purpose of the present application is to provide an error modeling method based on the recursive variance information of a fiber optic gyroscope, which can improve the real-time performance and accuracy of the FOG random error analysis, and then quickly and accurately identify different types of noise sources.

[0006] To achieve the above purpose, the present application provides the following solutions:

[0007] The present application provides an error modeling method based on the recursive variance information of a fiber optic gyroscope, and the error modeling method based on the recursive variance information of a fiber optic gyroscope includes:

[0008] Obtain N output data of the fiber optic gyroscope within the integration time τ, and generate an original output sequence based on the output data; the output data includes: angular rate;

[0009] Based on the original output sequence and the Allan variance estimation method, determine the Allan variance corresponding to the fiber optic gyroscope;

[0010] Construct a random error characterization model according to the output data and the Allan variance;

[0011] Optimize the output data using the random error characterization model.

[0012] Optionally, the step of determining the Allan variance corresponding to the fiber optic gyroscope based on the original output sequence and the Allan variance estimation method specifically includes:

[0013] Judge whether the integration time τ is greater than τ0N / 2; where τ0 is the sampling time;

[0014] If it is greater, perform mirror mapping on the data at both ends of the original output sequence to obtain an extended output sequence; determine the total variance according to the extended output sequence and the Allan variance estimation method;

[0015] If it is not greater, determine the corresponding Allan variance based on the Allan variance estimation method.

[0016] Optionally, the step of, if it is greater, performing mirror mapping on the data at both ends of the original output sequence to obtain an extended output sequence specifically includes:

[0017] Use the formula to determine the mirror mapping principle;

[0018] where is the mirror mapping value of the x-th data Ω x in the original output sequence, is the mirror mapping value of the y-th data Ω y in the original output sequence, is the mirror mapping value of the (N + 1 - z)-th data Ω N+1-z in the original output sequence.

[0019] Optionally, the length of the extended output sequence is 3N - 2.

[0020] Optionally, the step of determining the total variance according to the extended output sequence and the Allan variance estimation method specifically includes:

[0021] Use the formula to determine the total variance;

[0022] where is the total variance, is the number of clustering times of the extended output sequence, and is the mean of the angular rates within the i-th and (i + 1)-th clustering times in the extended output sequence, is the extended output sequence, is the number of data within each clustering time in the extended output sequence, τ is the clustering time, and τ0 is the sampling time, represents the floor operation, and j is the serial number of the angular velocity output by the fiber optic gyro within different clustering times.

[0023] Optionally, if it is not greater than, based on the Allan variance estimation method, the corresponding Allan variance is determined, specifically including:

[0024] Using the formula to determine the Allan variance;

[0025] where k is the number of clustering times in the original output sequence, is the Allan variance corresponding to the k-th clustering time of the original output sequence excluding the target sequence, is the Allan variance corresponding to the (k - 1)-th clustering time of the original output sequence excluding the target sequence, is the square of the angular rate difference, and are the means of the angular rates within the k-th and (k + 1)-th clustering times of the original output sequence excluding the target sequence.

[0026] Optionally, constructing a random error characterization model according to the output data and Allan variance specifically includes:

[0027] Constructing a double-logarithmic curve of the Allan standard deviation based on the Allan variance;

[0028] Determining the ARW variance according to the double-logarithmic curve;

[0029] Based on the discrimination index, determining the optimal order of the random error characterization model according to the ARW variance;

[0030] Constructing a random error characterization model according to the optimal order.

[0031] Optionally, based on the discrimination index, determining the optimal order of the random error characterization model according to the ARW variance specifically includes:

[0032] Using the formula to determine the discrimination index η;

[0033] where is the variance of the random error characterization model error, is the ARW variance.

[0034] Optionally, the random error characterization model specifically includes: an ARMA model, an AR model, or an MA model.

[0035] According to the specific embodiments provided by the present application, the present application has the following technical effects:

[0036] The present application provides an error modeling method based on the recursive variance information of a fiber optic gyroscope. By constructing a random error characterization model according to the output data and the Allan variance, and using the random error characterization model to optimize the output data, the method of recursive fusion variance can not only improve the problem of poor confidence in the estimation of the long correlation time error variance, but also greatly shorten the calculation time of the variance of the FOG output sequence. Based on the random error characterization model, the present application can calculate the random error of the fiber optic gyroscope online. On the premise of not losing the calculation accuracy of the high-frequency noise variance information, the calculation efficiency of the variance is improved by the method of recursive fusion of the Allan variance. Description of the Drawings

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the following described drawings are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0038] Figure 1 is a schematic flowchart of an error modeling method based on the recursive variance information of a fiber optic gyroscope in an embodiment of the present application;

[0039] Figure 2 is a schematic flowchart of the recursive fusion variance calculation process;

[0040] Figure 3 is a schematic diagram of the comparison of the double logarithmic curves of the Allan standard deviation;

[0041] Figure 4 is a schematic diagram of the filtering results of different filtering methods on the FOG;

[0042] Figure 5 is a schematic diagram of the Allan variance corresponding to the filtering results of different filtering methods on the FOG;

[0043] Figure 6 is a schematic diagram of the power spectral density of the FOG output sequence after different filtering methods. Detailed Embodiments

[0044] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0045] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0046] In an exemplary embodiment, as Figure 1 shown, an error modeling method based on the recursive variance information of a fiber optic gyroscope is provided. This method includes the following S101 to S104. Wherein:

[0047] S101, obtain N output data of the fiber optic gyroscope within the integration time τ, and generate an original output sequence according to the output data; the output data includes: angular rate;

[0048] S102, based on the original output sequence and the Allan variance estimation method, determine the Allan variance corresponding to the fiber optic gyroscope;

[0049] S102 specifically includes:

[0050] S21, determine whether the integration time τ is greater than τ0N / 2; where τ0 is the sampling time;

[0051] S22 If it is greater, perform mirror mapping on the data at both ends of the original output sequence to obtain an extended output sequence; determine the total variance according to the extended output sequence and the Allan variance estimation method;

[0052] S22 specifically includes:

[0053] Perform mirror mapping on the data at both ends of the original output sequence to obtain an extended output sequence;

[0054] Use the formula to determine the mirror mapping principle;

[0055] Wherein, is the mirror mapping value of the xth data Ω x in the original output sequence, is the mirror mapping value of the yth data Ω y in the original output sequence, is the mirror mapping value of the N + 1 - zth data Ω N+1-z in the original output sequence.

[0056] The extended output sequence is:

[0057] using the formula to determine the total variance;

[0058] wherein, is the total variance, is the number of clustering times of the extended output sequence, and are the mean angular rates within the i-th and (i + 1)-th clustering times of the extended output sequence, is the extended output sequence, is the number of data within each clustering time of the extended output sequence, τ is the clustering time, τ0 is the sampling time, represents the floor operation, and j is the serial number of the angular velocity output by the fiber optic gyro within different clustering times.

[0059] As a specific embodiment, since the sample size is expanded, when estimating the variance of the FOG angular rate under the same clustering time, the calculation amount of the total variance is (3 - 2 / N) times that of the Allan variance calculation amount, and the real-time performance of the total variance calculation is worse. When the sample size is fixed, the Allan variance method can maintain a relatively high estimation confidence level for the variance of short-correlation-time errors. Therefore, it is considered to use the total variance estimation model to replace the Allan variance estimation values of several groups of sequences where the clustering time τ is close to τ0N / 2.

[0060] The calculation method of Allan variance can not only improve the problem of poor estimation confidence level of the long-correlation-time error variance, but also greatly shorten the calculation time of the variance of the FOG output sequence. The flowchart of the recursive fusion variance calculation process is as Figure 2 shown.

[0061] S23, if it is not greater than, then based on the Allan variance estimation method, determine the corresponding Allan variance.

[0062] The calculation process of the Allan variance estimation method is as follows:

[0063] wherein, τ = mτ0, in the formula, σ 2 (τ) is the Allan variance corresponding to different clustering times τ, Ω j is the sampling value of the FOG angular rate output at time t j , N is the total amount of FOG output data (angular rate), k is the number of clustering time intervals, and m is the number of FOG angular rates collected within each clustering time interval, is the mean value of the FOG angular rate within each integration time, and τ0 is the sampling time. Denotes the floor operation.

[0064] There is the following quantitative relationship between the Allan variance and the power spectral density of the fiber optic gyro random noise: In the formula, S Ω (f) is the power spectral density function of the signal, f is the spectral variable of the noise, π is the pi. In the time domain, various error source characteristic parameters of the fiber optic gyro can be obtained from the FOG angular rate. In practical engineering, usually the double-logarithmic curve of the Allan standard deviation σ(τ)-τ is analyzed. Due to the certain cross-coupling of each error term, it is almost impossible to accurately give the system comprehensive error model. Generally, it is assumed that all existing random errors are statistically independent, then there is: Among them, the ARW variance C arw is the angle random walk coefficient. In the double-logarithmic plot of σ(τ)-τ, the curve slope of the interval corresponding to the angle random walk noise is -1 / 2. The BI variance Among them, B is the bias instability coefficient, f0 is the cut-off frequency. In the double-logarithmic plot of σ(τ)-τ, the curve slope of the interval corresponding to the bias instability noise is 0. The RRW variance Among them, K is the rate random walk coefficient. In the double-logarithmic plot of σ(τ)-τ, the curve slope of the interval corresponding to the rate random walk noise is 1 / 2. Therefore, A n is the coefficient of the Allan variance polynomial.

[0065] Rewrite the formula into the following form:

[0066]

[0067] Furthermore, we get:

[0068]

[0069] The above formula is the recursive calculation form of the Allan variance, which can realize the online calculation of the Allan variance of the FOG output data and can greatly improve the deficiency of the poor real-time performance of the traditional Allan variance calculation.

[0070] And solve the problem that as k increases, the weight of the square of the corresponding angular rate difference decreases, resulting in insufficient information utilization in the case of a small sample size, through the method of determining the total variance.

[0071] Among them, k is the number of integration times in the original output sequence. Remove the Allan variance corresponding to the k-th beam time in the target sequence from the original output sequence. Remove the Allan variance corresponding to the (k - 1)-th beam time in the target sequence from the original output sequence. is the square of the angular rate difference. and is the mean value of the angular rates within the k-th and (k + 1)-th beam times in the target sequence removed from the original output sequence.

[0072] S103. Construct a random error characterization model according to the output data and the Allan variance.

[0073] S103 specifically includes:

[0074] S31. Construct a double logarithmic curve of the Allan standard deviation according to the Allan variance and the total variance corresponding to the target sequence.

[0075] S32. Determine the ARW variance according to the double logarithmic curve.

[0076] S33. Determine the optimal order of the random error characterization model based on the discrimination index according to the ARW variance.

[0077] S34. Construct a random error characterization model according to the optimal order.

[0078] As Figure 3 shown, the recursive fusion Allan variance method provided by the present application improves the calculation efficiency of the variance on the premise of not losing the calculation accuracy of the high-frequency noise variance information.

[0079] As a specific embodiment, the error of the fiber optic gyro is suppressed by the Kalman filtering method based on the ARMA (autoregressive moving average) model.

[0080] The ARMA model is a composite form of the AR (autoregressive) model and the MA (moving average) model. It can generally be used alone or in combination according to actual needs. At the same time, these three models can also be transformed into each other. The general form of the ARMA model is as follows

[0081] A(B -1 )x(t) = C(B -1 )ε(t):

[0082] In the formula, x(t) is the random signal time series, and the parameter parameter a i , c i are the coefficients of the ARMA model, p and q are the orders of the ARMA model, B is the delay operator, for example B - ix(t) = x(t - i), where ε(t) is a white noise sequence.

[0083] The expression of the AR model is:

[0084] A(B -1 )x(t) = ε(t);

[0085] The AR model has the characteristic of discrete superposition of time - related terms and white noise terms. Therefore, the AR model has become a commonly used model for suppressing the random walk error of the FOG angle. The determination of the order of the AR model is the key to affecting the modeling accuracy. Currently, the commonly used method for determining the order of the AR model is based on the AIC criterion or the BIC criterion. Taking the AIC criterion as an example, its measurement index can be given by the following formula

[0086]

[0087] where f is the number of parameters of the optimal model, N is the number of training samples, is the fitting residual variance (MSE) of the AR model.

[0088] The static output sequence of the FOG contains both colored noise with time - correlation and white noise (ARW error) with independence. On the premise of only considering suppressing the ARW error of the FOG, according to the fitting rule of the AR model, the AR model can approximate the time - related terms in the FOG output sequence with infinite precision, but a reasonable order of the AR model should be set. Otherwise, over - fitting or under - fitting will occur. To avoid over - fitting, most current studies will give a range of orders in advance before determining the optimal order of the AR model, and then use the AIC criterion to judge within this range, and give the number of parameters corresponding to the minimum AIC measurement index as the optimal order of the AR model. However, analyzing the judgment principle of the AIC criterion, it can be seen that such methods consider both the goodness of fit of the model and the model complexity, and finally give a balanced comprehensive index. The optimal model order obtained according to this index is not the optimal model order in the true sense, and most of the model orders given in advance are in the low - order range within 5 orders. Therefore, the above two factors are likely to lead to the occurrence of under - fitting of the AR model.

[0089] From the above analysis, since the AR model estimates parameters based on the measurement data of the FOG, the fitting residuals of the AR model contain both AR model errors and the ARW error of the FOG. Here, the model error can be approximately understood as the white noise term ε(t). Assuming that the model error ε(t) is independent of the ARW error of the FOG, according to the variance summation formula, further we can get:

[0090]

[0091] Among them, is the variance of the AR model error. According to the above formula, the following discrimination index η can be defined:

[0092]

[0093] It is easy to analyze that when the value of the index η is closer to 1, it indicates that the accuracy of the AR model is higher. At this time, perform a tangent matching with a slope of -1 / 2 on the double-logarithmic curve of the Allan variance, and estimate the intercept of this straight line and the vertical axis of the double-logarithmic curve of the Allan variance to obtain the ARW variance

[0094] Through the above analysis, it can be seen that the FOG random error modeling method proposed in this application can avoid the occurrence of overfitting or underfitting of the AR model in principle. Therefore, it is not necessary to artificially limit the order range of the AR model in advance, and thus can more accurately find the optimal order of the AR model, effectively improving the fitting accuracy of the AR model, which can also provide more accurate prior information for the subsequent ARW error suppression work based on adaptive Kalman filtering.

[0095] Based on this application, a fiber optic gyro random error suppression experiment was carried out. TVAKF(Proposed method), CKF, VSHKF, and TVAKF(AIC) are different filtering methods based on the traditional AIC criterion model respectively. The filtering results and the corresponding double-logarithmic curves of the Allan variance are as Figure 4 and Figure 5 shown, and the power spectral density is as Figure 6 shown. It can be seen from Figure 6 that compared with the original data and other filtering methods, the power spectral density curve of the gyro data filtered by the TVAKF(Proposed method) corresponding to this application changes from flat to uneven, which indicates that this application can almost completely suppress the influence of white noise. It further illustrates the effectiveness of this application.

[0096] S104. Optimize the output data using the random error characterization model.

[0097] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of relevant data need to comply with relevant regulations.

[0098] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0099] The databases involved in the embodiments provided in this application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in this application can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., without limitation.

[0100] In this application, all actions of obtaining signals, information, or data are carried out on the premise of complying with the corresponding data protection regulations and policies of the country where it is located and obtaining authorization from the owner of the corresponding device.

[0101] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

[0102] In this article, specific examples are used to illustrate the principles and implementation manners of the present application. The descriptions of the above embodiments are only for helping to understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. An error modeling method based on the recursive variance information of a fiber optic gyroscope, characterized in that, The error modeling method based on the recursive variance information of the fiber optic gyroscope includes: Obtain N output data of the fiber optic gyroscope within the aggregation time τ, and generate an original output sequence according to the output data; the output data includes: angular rate. Based on the Allan variance estimation method, determine the Allan variance corresponding to the fiber optic gyroscope according to the original output sequence. Construct a random error characterization model according to the output data and the Allan variance. Optimize the output data using the random error characterization model.

2. The error modeling method based on the recursive variance information of the fiber optic gyroscope according to claim 1, characterized in that, The step of determining the Allan variance corresponding to the fiber optic gyroscope based on the Allan variance estimation method according to the original output sequence specifically includes: Judge whether the aggregation time τ is greater than τ0N / 2; where τ0 is the sampling time. If it is greater, perform mirror mapping on the data at both ends of the original output sequence to obtain an extended output sequence; determine the total variance according to the extended output sequence and the Allan variance estimation method. If it is not greater, determine the corresponding Allan variance based on the Allan variance estimation method.

3. The error modeling method based on the recursive variance information of the fiber optic gyro according to claim 2, characterized in that The step of, if it is greater, performing mirror mapping on the data at both ends of the original output sequence to obtain an extended output sequence specifically includes: Use the formula to determine the mirror mapping principle; Among them, is the mirror mapping value of the x-th data Ω in the original output sequence x , is the mirror mapping value of the y-th data Ω in the original output sequence y , is the mirror mapping value of the (N + 1 - z)-th data Ω in the original output sequence N+1-z .

4. The error modeling method based on the recursive variance information of the fiber optic gyroscope according to claim 3, characterized in that, The length of the extended output sequence is 3N - 2.

5. The error modeling method based on the recursive variance information of the fiber optic gyro according to claim 4, characterized in that, The step of determining the total variance according to the extended output sequence and the Allan variance estimation method specifically includes: Use the formula to determine the total variance; Among them, is the total variance, is the number of clustering times of the extended output sequence, and are the mean angular rates within the i-th and (i + 1)-th clustering times in the extended output sequence, is the extended output sequence, is the number of data within each clustering time in the extended output sequence, τ is the clustering time, τ0 is the sampling time, represents the floor operation, and j is the serial number of the angular velocity output by the fiber optic gyro within different clustering times.

6. The error modeling method based on the recursive variance information of the fiber optic gyro according to claim 2, characterized in that The step of, if it is not greater, determining the corresponding Allan variance based on the Allan variance estimation method specifically includes: Use the formula to determine the Allan variance; where k is the number of beam times in the original output sequence, is the Allan variance corresponding to the k-th beam time of the target sequence removed from the original output sequence, is the Allan variance corresponding to the (k - 1)-th beam time of the target sequence removed from the original output sequence, is the square of the angular rate difference, and is the mean of the angular rates within the k-th and (k + 1)-th beam times of the target sequence removed from the original output sequence.

7. The error modeling method based on the recursive variance information of the fiber optic gyro according to claim 1, wherein The step of constructing a random error characterization model according to the output data and the Allan variance specifically includes: Construct a double logarithmic curve of the Allan standard deviation according to the Allan variance. Determine the ARW variance according to the double logarithmic curve. Based on the discrimination index, determine the optimal order of the random error characterization model according to the ARW variance. Construct a random error characterization model according to the optimal order.

8. The error modeling method based on the recursive variance information of the fiber optic gyro according to claim 7, characterized in that The step of determining the optimal order of the random error characterization model based on the discrimination index according to the ARW variance specifically includes: Using the formula to determine the discrimination index η; wherein, is the variance of the random error representing the model error, is the ARW variance.

9. The error modeling method based on the recursive variance information of the fiber optic gyroscope according to claim 1, characterized in that, The random error characterization model specifically includes: ARMA model, AR model or MA model.

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