Fiber-optic gyroscope temperature error segmented compensation method based on adaptive smoothing filter

Abstract

The application discloses a fiber-optic gyroscope temperature error segmented compensation method based on adaptive smoothing filtering, and relates to the field of fiber-optic gyroscopes. The method comprises the following steps: obtaining a fiber-optic gyroscope temperature to be compensated; performing smoothing filtering processing on the fiber-optic gyroscope temperature to be compensated to obtain a filtered fiber-optic gyroscope temperature; calculating a temperature change rate based on the filtered fiber-optic gyroscope temperature; obtaining a filtered temperature change rate by using an adaptive window filtering method based on the temperature change rate; obtaining an optimal feature matrix set based on the filtered fiber-optic gyroscope temperature and the filtered temperature change rate; inputting the optimal feature matrix set into a full-temperature-stage fiber-optic temperature error model to obtain a fiber-optic gyroscope temperature error, and compensating the fiber-optic gyroscope temperature to be compensated according to the fiber-optic gyroscope temperature error. The application can improve the full-temperature-stage fiber-optic gyroscope temperature error compensation precision.

Description

Technical Field

[0001] This application relates to the field of fiber optic gyroscopes, and in particular to a method for piecewise compensation of temperature error in fiber optic gyroscopes based on adaptive smoothing filtering. Background Technology

[0002] The internal optical system of a fiber optic gyroscope is quite complex, containing numerous temperature-sensitive core optical components such as polarization-maintaining fibers, optical couplers, and integrated optical modulators. Under wide temperature operating conditions, the physical properties of these components drift significantly due to changes in temperature gradients. In particular, the fiber optic loop, as a core sensitive component, exhibits strong temperature-dependent fluctuations in its refractive index due to thermo-optic effects, leading to unintended changes in the phase of light propagating in the fiber and ultimately resulting in non-reciprocal phase errors that severely limit measurement accuracy. Therefore, conducting multi-physics coupling analysis of the temperature characteristics of fiber optic gyroscopes and constructing a temperature compensation model with high fitting accuracy and strong generalization ability is of indispensable academic research significance and engineering practical value for improving the measurement accuracy, stability, and reliability of fiber optic gyroscopes under complex thermal environments, overcoming bottlenecks in high-end inertial sensing technology, and promoting their in-depth application in the field of precision inertial measurement.

[0003] In the engineering applications of fiber optic gyroscopes, the mainstream technical solutions for addressing the impact of temperature drift on output accuracy fall into two main categories: hardware compensation and software compensation. Hardware compensation technology primarily achieves this through improving the fiber winding process and constructing a temperature control system. The former includes various processes such as four-pole symmetrical winding, six-pole symmetrical winding, eight-pole symmetrical winding, and sixteen-pole symmetrical winding. Its core principle is to reduce the impact of temperature gradients on the phase consistency of the fiber ring through geometric symmetry design. However, this method faces engineering challenges such as complex winding processes, difficulty in controlling yield rates, and high manufacturing costs. The latter relies on high-precision temperature control modules to maintain the constant temperature of the fiber optic gyroscope's sensitive elements. However, this approach faces practical challenges such as increased power consumption, size limitations, and poor adaptability to high and low temperature environments.

[0004] Software compensation techniques focus on establishing a mapping model between the zero-bias error of a fiber optic gyroscope and temperature parameters, using data-driven methods to predict and compensate for temperature drift. With the continuous development of computational intelligence technology, AI-based modeling methods have gradually become a research hotspot. Existing temperature drift model identification methods, such as least-squares parameter fitting, BP neural network nonlinear modeling, and fuzzy logic system identification, while achieving temperature error fitting compensation to some extent, generally suffer from insufficient nonlinear feature characterization, limited model generalization performance, and high computational complexity, making it difficult to meet the stringent real-time and reliability requirements of high-precision inertial navigation systems.

[0005] Extreme Learning Machine (ELM) is a novel single-hidden-layer feedforward neural network algorithm. Its core advantage lies in its ability to rapidly calculate output weights by randomly initializing input weights and hidden layer biases, combined with least-squares analytical solutions, fundamentally overcoming the time bottleneck of traditional neural network iterative training. This algorithm combines excellent generalization performance with high computational efficiency; however, its accuracy in compensating for temperature errors in fiber optic gyroscopes still needs improvement. Summary of the Invention

[0006] The purpose of this application is to provide a segmented compensation method for temperature error of fiber optic gyroscopes based on adaptive smoothing filtering, which can improve the accuracy of temperature error compensation of fiber optic gyroscopes throughout the entire temperature range.

[0007] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a segmented compensation method for fiber optic gyroscope temperature error based on adaptive smoothing filtering, comprising: obtaining the temperature of the fiber optic gyroscope to be compensated; performing smoothing filtering on the temperature of the fiber optic gyroscope to be compensated to obtain the filtered temperature of the fiber optic gyroscope; calculating the temperature change rate based on the filtered temperature of the fiber optic gyroscope; obtaining the filtered temperature change rate based on the temperature change rate using an adaptive window filtering method; obtaining an optimal feature matrix set based on the filtered temperature of the fiber optic gyroscope and the filtered temperature change rate; inputting the optimal feature matrix set into a full-temperature stage fiber optic temperature error model to obtain the fiber optic gyroscope temperature error, and compensating for the temperature of the fiber optic gyroscope to be compensated according to the fiber optic gyroscope temperature error; wherein the full-temperature stage fiber optic temperature error model is constructed based on an extreme learning machine model.

[0008] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a segmented compensation method for fiber optic gyroscope temperature error based on adaptive smoothing filtering. By smoothing the temperature of the fiber optic gyroscope to be compensated, high-frequency noise is removed, resulting in a more realistic and stable temperature signal (i.e., the filtered fiber optic gyroscope temperature). Then, an adaptive window filtering method is employed. In regions of rapid signal change, a larger window is used to filter out noise, effectively suppressing strong noise. In regions of gradual signal change, a smaller window is used to preserve the true signal, effectively retaining details of temperature abrupt changes. This achieves dynamic adjustment of the temperature change rate, resulting in a more realistic and stable rate (i.e., the filtered temperature change rate). This ensures the accuracy of the input data for the subsequent full-temperature stage fiber optic temperature error model, improving the accuracy of the fiber optic gyroscope temperature error output by the model, thereby enhancing the overall accuracy of fiber optic gyroscope temperature error compensation. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating a segmented compensation method for temperature error of a fiber optic gyroscope based on adaptive smoothing filtering, provided in one embodiment of this application.

[0011] Figure 2 This is a detailed flowchart illustrating step S4 provided in an embodiment of this application.

[0012] Figure 3 A schematic diagram illustrating the process of constructing a full-temperature stage optical fiber temperature error model according to an embodiment of this application.

[0013] Figure 4 A schematic diagram showing the relationship between the output of a fiber optic gyroscope and temperature, provided for another embodiment of this application.

[0014] Figure 5 A schematic diagram showing the relationship between the output and temperature of a fiber optic gyroscope over time, provided for another embodiment of this application.

[0015] Figure 6 This is a schematic diagram showing the change of temperature term over time before processing by a fixed-window smoothing filter algorithm provided in another embodiment of this application.

[0016] Figure 7 A schematic diagram showing the change of temperature term over time after processing by a fixed-window smoothing filter algorithm provided in another embodiment of this application.

[0017] Figure 8 This is a schematic diagram illustrating the temperature change rate over time before adaptive window smoothing filtering processing, provided in another embodiment of this application.

[0018] Figure 9 This is a schematic diagram showing the temperature change rate over time after adaptive window smoothing filtering, provided in another embodiment of this application.

[0019] Figure 10 This is a schematic diagram showing the comparison of the rate of temperature change over time before and after adaptive window smoothing filtering, provided in another embodiment of this application.

[0020] Figure 11 This is a schematic diagram illustrating the window size change during filtering, provided in another embodiment of this application.

[0021] Figure 12This is a schematic diagram comparing the performance indicators of different compensation methods for the training set provided in another embodiment of this application.

[0022] Figure 13 A schematic diagram comparing the indices of different compensation methods for the first set of verification sets provided in another embodiment of this application.

[0023] Figure 14 This is a schematic diagram comparing the indices of different compensation methods for a second set of verification sets provided in another embodiment of this application. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, this application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] In one exemplary embodiment, such as Figure 1 As shown, a segmented compensation method for temperature error of fiber optic gyroscope based on adaptive smoothing filtering is provided. This method is executed by a computer device, specifically by a computer device such as a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is described using a server as an example, including the following steps S1 to S6.

[0027] Step S1: Obtain the temperature of the fiber optic gyroscope to be compensated.

[0028] Specifically, the current temperature (i.e., the temperature of the fiber optic gyroscope to be compensated) is collected by a temperature sensor. This directly reflects the influence of ambient temperature on the refractive index of the fiber optic ring and is the fundamental factor causing temperature errors in the fiber optic gyroscope. It is also a mandatory input option for all models. However, in the actual temperature signal acquisition process, due to the influence of various factors such as electromagnetic interference, thermal noise, and mechanical vibration in the environment, the signal output by the temperature sensor often contains a large amount of high-frequency noise and random fluctuation components. The presence of this noise leads to the instability of the temperature signal. If it is directly used as an input parameter in the temperature error compensation model, the model will find it difficult to accurately capture the true impact of temperature changes on the fiber optic gyroscope, thereby reducing the effectiveness of error compensation. If the temperature change rate term (in degrees Celsius per second, °C / s) is calculated using a temperature term with a large amount of noise, the noise will overwhelm the true temperature change rate term.

[0029] Step S2: Perform a smoothing filter on the temperature of the fiber optic gyroscope to be compensated to obtain the filtered temperature of the fiber optic gyroscope.

[0030] Specifically, the temperature term (°C) undergoes an n-second smoothing filter to remove high-frequency noise, obtaining a more realistic and stable temperature signal. This ensures accurate calculation of the temperature change rate and improves the reliability and effectiveness of subsequent analysis, judgment, and compensation algorithms. The value of n can be chosen based on the specific situation; for model verification, n=5 was selected. The formula for calculating the temperature of the filtered fiber optic gyroscope is as follows.

[0031] .

[0032] .

[0033] in, for Temperature of the fiber optic gyroscope after time-lapse filtering; This represents the number of sampling points; for The fiber optic gyroscope temperature needs to be compensated at all times. The number of seconds for smoothing filtering; The sampling frequency.

[0034] Step S3: Calculate the temperature change rate based on the filtered fiber optic gyroscope temperature.

[0035] Specifically, the rate of temperature change reflects the dynamic characteristics of the heat conduction process. The rate of temperature change affects the uniformity of temperature distribution inside the fiber optic ring, thus generating thermal stress and phase errors, especially in scenarios with rapid temperature changes. The temperature term, after being processed by n-second smoothing filtering, is used to calculate the rate of temperature change (in degrees Celsius per second, °C / s) using a gradient function and sampling frequency. Gradient calculations enhance the amplitude of high-frequency signals. Even if the noise amplitude is small, gradient calculations can significantly affect the accuracy of the rate of change. The calculated rate of change is then filtered again, further employing adaptive window smoothing filtering. The window size is adjusted based on the standard deviation of local noise. A larger window is used to filter noise in areas of rapid signal change, while a smaller window is used to preserve the true signal in areas of gradual signal change. The smaller and larger windows are usually preset to fixed values ​​to limit the range of window adjustment and avoid poor filtering effects or computational efficiency issues caused by windows that are too small or too large. The choice of smaller and larger windows depends on the sampling frequency and noise level. Windows are usually set to odd numbers to more reliably preserve the signal's time alignment and variation characteristics, avoiding noise amplification or detail distortion caused by window asymmetry.

[0036] Specifically, the rate of temperature change is calculated using a gradient function and a sampling frequency, and the calculation formula is as follows.

[0037] .

[0038] .

[0039] in, for The rate of temperature change over time; for Temperature of the fiber optic gyroscope after time-lapse filtering; The sampling interval is denoted as .

[0040] Step S4: Based on the temperature change rate, an adaptive window filtering method is used to obtain the filtered temperature change rate.

[0041] Furthermore, such as Figure 2 As shown, step S4 specifically includes steps S41-S48.

[0042] Step S41: Initialize parameters; parameters include: sampling frequency, filtering time, and smoothing factor.

[0043] Step S42: Construct a trend window based on the sampling frequency and filtering time.

[0044] Furthermore, the formula for calculating the trend window is as follows.

[0045] .

[0046] in, For trend windows; The sampling frequency; This is the filtering time.

[0047] Specifically, the minimum value of the trend window and the maximum value of the trend window Set based on sampling frequency Calculate the trend window for filtering time. Instead of directly setting a fixed window, this ensures the filter window is within a reasonable range and that the window size is odd. The minimum value of the trend window corresponds to the shortest filtering time (e.g., ...). =1 second), used to preserve details of temperature abrupt changes, with a large window corresponding to the longest filtering time (e.g., 1 second), used to preserve details of temperature abrupt changes, and the largest window corresponds to the longest filtering time (e.g., ... =10 seconds), used to suppress strong noise; simultaneously setting the trend window. Low-frequency trend terms of temperature change are extracted by averaging through smoothing filtering, and high-frequency noise is separated. Should be greater than less than Avoid oversmoothing or trend distortion (e.g.) =5 seconds).

[0048] Step S43: Use a trend window to smooth the temperature change rate to obtain the low-frequency trend temperature change rate and the high-frequency noise temperature change rate.

[0049] Specifically, through the trend window Smoothing filters extract the temperature change rate of low-frequency trends. The original temperature change rate Subtract trend item Effectively separates the temperature change rate of high-frequency noise. The separated noise components provide a direct basis for window adjustment. The stronger the noise (the larger the standard deviation), the more necessary it is to smooth the window with a large window; the weaker the noise, the more suitable it is to preserve details with a small window.

[0050] Step S44: Calculate the local noise standard deviation based on the low-frequency trend of the temperature change rate and the temperature change rate.

[0051] Furthermore, the formula for calculating the standard deviation of local noise is as follows.

[0052] .

[0053] in, for The standard deviation of local noise at any given time; This is the minimum value of the trend window; for The rate of temperature change at any given moment; for The rate of temperature change at low frequency over time; This represents the mean local noise level within the window.

[0054] Step S45: Calculate the global noise standard deviation based on the temperature change rate of high-frequency noise.

[0055] Step S46: Normalize the local noise standard deviation using the global noise standard deviation to obtain the normalized local noise standard deviation.

[0056] Furthermore, the formula for calculating the normalized local noise is as follows.

[0057] .

[0058] ; in, for Standard deviation of local noise after time-normalization; for The standard deviation of local noise at any given time; The global noise standard deviation; It is a function of standard deviation; for The rate of temperature change of high-frequency noise at any given time.

[0059] Specifically, by comparing the local noise standard deviation with the global noise standard deviation, a dimensionless normalized noise value is obtained, which facilitates unified noise assessment and comparison under different signal intensities. To ensure the stability of the noise estimation, the window is set to the smallest window centered on the current point at the beginning of each loop. Calculate the standard deviation of local noise within the window. , This is used to quantify the noise fluctuation level in the current local area; the larger the value, the "coarser" the signal.

[0060] Step S47: Calculate the adaptive smoothing filter window based on the normalized local noise standard deviation and smoothing factor.

[0061] Furthermore, the formula for calculating the adaptive smoothing filter window is as follows.

[0062] .

[0063] in, For adaptive smoothing filtering window; This is the minimum value of the trend window; This represents the maximum value of the trend window; It is a smoothing factor; This represents the normalized standard deviation of local noise.

[0064] Specifically, when (When the noise level is extremely low) ;when (When the noise is extremely high) And add window constraints. ; This is a smoothing factor that controls the sensitivity of window adjustment. The larger the value, the smoother the curve and the more stable the window changes. Typical values ​​are k=1~3 for rapid temperature change scenarios (sensitive window response) and k=5~10 for stable scenarios (suppressing window jitter). In this example, k=3 is used.

[0065] Step S48: Determine whether the adaptive smoothing filter window is odd; if so, filter the temperature change rate based on the adaptive smoothing filter window to obtain the filtered temperature change rate; if not, increase the adaptive smoothing filter window by one, and filter the temperature change rate based on the increased adaptive smoothing filter window to obtain the filtered temperature change rate.

[0066] Specifically, to ensure that the adaptive smoothing filter window is odd in number (to guarantee the central symmetry of the filter window), if Take even numbers If the number is odd, it remains unchanged.

[0067] Furthermore, the formula for calculating the filtered rate of temperature change is as follows.

[0068] .

[0069] in, for The rate of temperature change after filtering at any given time; for Time-adaptive smoothing filter window; for The rate of temperature change at any given time.

[0070] Step S5: Based on the filtered fiber optic gyroscope temperature and the filtered temperature change rate, obtain the optimal feature matrix set.

[0071] Furthermore, step S5 specifically includes steps S51 to S55.

[0072] Step S51: Calculate the cross-coupling term based on the filtered fiber optic gyroscope temperature and the filtered temperature change rate.

[0073] Specifically, the temperature term (°C) × temperature change rate (unit: degrees Celsius per second, °C / s) characterizes the key features of the thermal dynamic coupling effect. Its physical essence is the modulation effect of temperature level on thermal stress. This cross-coupling term can significantly improve the model's compensation accuracy for complex conditions such as rapid temperature changes and extreme temperatures, making it particularly suitable for high-end inertial navigation scenarios with stringent environmental adaptability requirements. After n-second smoothing filtering, the cross-coupling term is calculated by multiplying the filtered fiber optic gyroscope temperature by the filtered temperature change rate. The calculation formula for the cross-coupling term is as follows.

[0074] .

[0075] in, For cross-coupling terms; for for Temperature of the fiber optic gyroscope after time-lapse filtering; for The rate of temperature change after filtering at any given time.

[0076] Step S52: Based on the filtered fiber optic gyroscope temperature, generate a multi-hysteresis filtered fiber optic gyroscope temperature.

[0077] Specifically, the lag temperature term (unit: degrees Celsius, °C) is the temperature value in the previous n seconds. , , ..., The parameters can be adjusted according to the situation (k=5 is set during model verification). These are the key input parameters for characterizing the thermal hysteresis characteristics of the system. Their core function is to capture the time delay and inertia of the fiber optic ring temperature response, and to solve the problem of the correlation between the current error and the historical temperature caused by the slow heat conduction process. The filtered fiber optic gyroscope temperature is obtained by calculating the filtered fiber optic gyroscope temperature with multiple hysteresis.

[0078] Step S53: Based on the filtered fiber optic gyroscope temperature, generate higher-order terms of the filtered fiber optic gyroscope temperature.

[0079] Specifically, the higher-order terms of the fiber optic gyroscope temperature are key parameters characterizing the wide-temperature-range nonlinearity in fiber optic gyroscope temperature error modeling. By approximating the higher-order nonlinearity of the thermo-optic effect through polynomial expansion, and using the temperature term after n-second smoothing filtering to calculate the first m powers of the current temperature term (m is greater than 1; m=7 is set for model verification), this is used as the model input. Therefore, the higher-order temperature terms are: There are a total of m-1 items.

[0080] Step S54: Arbitrarily combine the filtered fiber optic gyroscope temperature, the filtered temperature change rate, the cross-coupling term, the filtered fiber optic gyroscope temperature with multiple hysteresis, and the higher-order terms of the filtered fiber optic gyroscope temperature with multiple hysteresis to obtain multiple feature matrix subsets, and the multiple feature matrix subsets form a feature matrix set.

[0081] Specifically, the filtered fiber optic gyroscope temperature, the filtered temperature change rate, the cross-coupling term, the k-term lagged filtered fiber optic gyroscope temperature, and the m-1 term of the higher-order filtered fiber optic gyroscope temperature, totaling (m+k+2) terms, constitute the feature matrix set of the ELM segmented prediction model.

[0082] Step S55: Based on the optimal feature matrix set of the samples, the feature matrix set is filtered to obtain the optimal feature matrix set; the optimal feature matrix set of the samples is obtained by filtering the sample feature matrix set using the full-temperature stage fiber optic temperature error model.

[0083] Furthermore, the full-temperature stage fiber temperature error model includes: the fiber temperature error model for the heating stage and the fiber temperature error stage model for the cooling stage; the sample optimal feature matrix set includes: the sample optimal feature matrix set for the heating stage and the sample optimal feature matrix set for the cooling stage; the optimal feature matrix set includes: the optimal feature matrix set for the heating stage and the optimal feature matrix set for the cooling stage.

[0084] Furthermore, step S55 specifically includes steps S551 to S555.

[0085] Step S551: Construct a sample feature matrix set; the sample feature matrix set includes multiple sample subsets and the actual fiber optic gyroscope temperature error corresponding to each sample subset; the sample subset is obtained by arbitrarily combining the fiber optic gyroscope temperature after sample filtering, the temperature change rate after sample filtering, the sample cross-coupling term, the fiber optic gyroscope temperature after multiple sample hysteresis, and the higher-order terms of the fiber optic gyroscope temperature after multiple sample filtering.

[0086] Step S552: Input multiple sample subsets into the fiber optic temperature error model during the heating stage, obtain the root mean square error corresponding to each sample subset, and select the sample subset with the smallest root mean square error as the optimal feature matrix set for the sample heating stage.

[0087] Step S553: ​​Input multiple sample subsets into the fiber optic temperature error model for the cooling stage, obtain the root mean square error corresponding to each sample subset, and select the sample subset with the smallest root mean square error as the optimal feature matrix set for the sample cooling stage.

[0088] Specifically, the formula for calculating the root mean square error (RMSE) is as follows.

[0089] .

[0090] in, This is the root mean square error; The number of samples in multiple sample subsets; This represents the actual temperature error of a fiber optic gyroscope. The predicted values ​​of fiber optic gyroscope temperature error are obtained by inputting multiple sample subsets into the fiber optic temperature error model during the cooling stage.

[0091] Step S554: Based on the optimal feature matrix set of the sample heating stage, filter the feature matrix set to obtain the optimal feature matrix set of the heating stage.

[0092] Step S555: Based on the optimal feature matrix set of the sample cooling stage, the feature matrix set is filtered to obtain the optimal feature matrix set of the cooling stage.

[0093] Specifically, the model traverses all non-empty subsets from the (m+k+2) parameter permutations in the input sample feature matrix set, with a total of 2^n combinations. m+k+2-1. For each non-empty subset, the average root mean square error (RMSE) after prediction by the fiber temperature error model in the heating stage and the fiber temperature error model in the cooling stage is used as the criterion for screening the feature matrix set of the model input samples. The minimum RMSE is taken as the optimal feature matrix set S1 for the heating stage and the optimal feature matrix set S2 for the cooling stage of the fiber temperature error model in the heating stage and the fiber temperature error model in the cooling stage, respectively.

[0094] Step S6: Input the optimal feature matrix set into the full-temperature stage fiber optic temperature error model to obtain the fiber optic gyroscope temperature error, and compensate for the temperature of the fiber optic gyroscope to be compensated based on the fiber optic gyroscope temperature error; the full-temperature stage fiber optic temperature error model is constructed based on the extreme learning machine model.

[0095] Further, step S6 specifically includes: determining whether the filtered temperature change rate is greater than or equal to zero; if so, inputting the optimal feature matrix set of the heating stage into the fiber optic temperature error model of the heating stage to obtain the fiber optic gyroscope temperature error; if not, inputting the optimal feature matrix set of the cooling stage into the fiber optic temperature error model of the heating stage to obtain the fiber optic gyroscope temperature error.

[0096] The process of constructing the full-temperature stage fiber temperature error model is as follows: Figure 3 As shown, the collected data is processed using steps S1-S5 above to construct a sample feature matrix set M. The ELM model is then trained based on the sample feature matrix set. Specifically, this includes: determining whether the temperature change rate after sample filtering is greater than or equal to zero; if so, using multiple sample subsets as input and the actual fiber optic gyroscope temperature error corresponding to each sample subset as output, the ELM model is trained using the least squares method to obtain the fiber optic temperature error model for the heating stage; if not, using multiple sample subsets as input and the actual fiber optic gyroscope temperature error corresponding to each sample subset as output, the ELM model is trained using the least squares method to obtain the fiber optic temperature error model for the cooling stage.

[0097] The beneficial effects of the fiber optic gyroscope temperature error segmentation compensation method based on adaptive smoothing filtering proposed in this application are mainly reflected in the following four aspects.

[0098] 1. By smoothing and filtering the temperature of the fiber optic gyroscope to be compensated, high-frequency noise is removed, resulting in a more realistic and stable temperature signal (i.e., the filtered fiber optic gyroscope temperature). Then, an adaptive window filtering method is used. In areas of rapid signal change, a larger window is used to filter out noise, effectively suppressing strong noise. In areas of gradual signal change, a smaller window is used to retain the real signal, effectively preserving the details of temperature abrupt changes. This achieves dynamic adjustment of the temperature change rate, resulting in a more realistic and stable rate (i.e., the filtered temperature change rate). This ensures the accuracy of the input data for the subsequent full-temperature stage fiber optic temperature error model, improving the accuracy of the fiber optic gyroscope temperature error output by the model, thereby improving the accuracy of the full-temperature stage fiber optic gyroscope temperature error compensation.

[0099] 2. An innovative approach using the ELM model for temperature error compensation in fiber optic gyroscopes. This deep learning method offers faster learning and prediction speeds compared to methods like BP neural network nonlinear modeling and fuzzy logic system identification, making it highly suitable for real-time temperature compensation of fiber optic gyroscopes. The process involves a two-stage division of the gyroscope's heating and cooling phases for model training. Based on the rate of temperature change after adaptive window smoothing filtering, the program automatically divides the process into heating and cooling phases, training ELM models for each phase separately.

[0100] 3. Modeling and compensating for the temperature error of the fiber optic gyroscope by dividing the ELM model into two stages, heating and cooling, is based on the temperature error mechanism of the fiber optic gyroscope and can effectively simplify the model complexity and improve the compensation effect.

[0101] 4. Innovatively, a method is proposed to filter the feature matrix set based on the optimal feature matrix set during the sample cooling stage, thereby obtaining the optimal feature matrix set during the cooling stage. This makes the model input data more accurate, thus improving the accuracy of the output compensation temperature.

[0102] Based on the fiber optic gyroscope temperature error segmentation compensation method based on adaptive smoothing filtering proposed in this application, specific embodiments are provided for illustration.

[0103] 1. Obtain learning samples.

[0104] This embodiment takes a fiber optic gyroscope of a certain type of inertial assembly as the research object. The gyroscope assembly is mounted on a horizontal turntable with a temperature control box. To eliminate the influence of the gyroscope's scaling factor on its temperature drift, the input angular velocity of the gyroscope must be ensured to be zero. Therefore, placing the gyroscope's input reference axis in a horizontal plane and making the angle between the reference axis and the eastward direction zero satisfies the condition of zero input angular velocity of the fiber optic gyroscope. The experiment employed a thermal cycling method. After the gyroscope was started, the temperature control chamber was adjusted to continuously raise and lower the temperature. Every second, a set of temperature (T) and gyroscope drift data (D) was output. The experiment measured temperatures from -10°C to 50°C. Temperature zero drift during temperature range changes was measured by collecting three sets of gyroscope output data during the heating and cooling processes, with the first set serving as the test set. Figure 4 and Figure 5 As shown, the second and third groups serve as the validation set.

[0105] 2. Perform a smoothing filter on the temperature of the fiber optic gyroscope to be compensated to obtain the filtered temperature of the fiber optic gyroscope.

[0106] The temperature signal, after 5 seconds of smoothing and filtering, is used to obtain the filtered fiber optic gyroscope temperature, which is then magnified and displayed for comparison. Figures 6-7 As shown.

[0107] 3. Calculate the rate of temperature change and apply adaptive window smoothing filter (i.e., adaptive window filtering method).

[0108] The filtered fiber optic gyroscope temperature is used to calculate the rate of temperature change using a gradient function and sampling frequency. The calculated rate of change is then filtered again, followed by adaptive window smoothing filtering to obtain the filtered rate of temperature change. The window size is adjusted by calculating the local standard deviation. A larger window is used to filter out noise in areas of rapid signal change, while a smaller window is used to preserve the true signal in areas of gradual signal change.

[0109] like Figures 8-10 As shown in the temperature change analysis graph of the test set, before applying adaptive window smoothing filtering to the temperature change rate term obtained from gradient function and sampling frequency calculations, the temperature change rate term fluctuates significantly, which does not conform to the actual temperature change pattern. This is because gradient calculation amplifies the amplitude of high-frequency signals. Even if the noise amplitude is small, gradient calculation can significantly affect the accuracy of the change rate. Therefore, it is necessary to filter the calculated change rate again. The window size changes throughout the process as follows: Figure 11 As shown.

[0110] 4. Calculate the temperature of the fiber optic gyroscope after multi-hysteresis filtering, the cross-coupling term, and the higher-order term of the temperature of the fiber optic gyroscope after multi-hysteresis filtering, and construct the feature matrix set.

[0111] Five hysteresis-lagging fiber optic gyroscope temperatures were calculated using the filtered gyroscope temperature, corresponding to the temperature values ​​T(t-5), T(t-4), T(t-3), T(t-2), and T(t-1) five seconds before time t. The cross-coupling term was calculated by multiplying the filtered gyroscope temperature by the filtered temperature change rate. Six higher-order terms of the filtered gyroscope temperature were then used to calculate the filtered gyroscope temperature. The temperature of the filtered fiber optic gyroscope Filtered temperature change rate Cross-coupling terms Temperature of the fiber optic gyroscope after 5-term hysteresis filtering The higher-order terms of the temperature of the fiber optic gyroscope after filtering (6 terms) The features are combined to form a feature matrix set, consisting of 13 temperature-related feature values.

[0112] 5. Select the optimal input parameter set S. Iterate through all non-empty subsets of the (m+k+2) parameter combinations from the model input feature matrix set, with a total of 2^n combinations. 13 -1. For each non-empty subset, the average root mean square error (RMSE) of the fiber temperature error model in the heating stage and the fiber temperature error model in the cooling stage are used as the criterion for selecting the model input feature matrix set. The minimum RMSE is taken as the optimal feature matrix set S1 for the heating stage and the optimal feature matrix set S2 for the cooling stage of the fiber temperature error model in the heating stage and the fiber temperature error model in the cooling stage, respectively. After analysis, the filtered fiber optic gyroscope temperature, the filtered temperature change rate and the cross-coupling term are selected as the optimal input feature matrix sets S1 and S2.

[0113] 6. Using the selected optimal input feature matrix sets S1 and S2 as inputs to the full-temperature stage fiber optic temperature error model, the fiber optic gyroscope temperature compensation was analyzed using the training set, the first validation set, and the second validation set. The analysis results are as follows: Comparison of indices for different compensation methods in the training set is shown below. Figure 12 As shown in Table 1, the indices of different compensation methods in the first validation set are compared as follows: Figure 13 As shown in Table 2, the indices of different compensation methods in the second validation set are compared as follows: Figure 14 As shown in Table 3.

[0114] Tables 1-3 show that the polynomial regression model, piecewise polynomial model, ELM model, and piecewise ELM model (i.e., the full-temperature fiber optic temperature error model) can all compensate for the overall mean of the fiber optic gyroscope temperature error. Among them, the piecewise ELM model has the best compensation effect on both the root mean square error and the sum of squared errors. For example, in the first validation set, the root mean square error using the piecewise ELM model was reduced by 73.92% compared to before compensation, by 71.77% compared to the polynomial regression model, and by 71.31% compared to the non-piecewise ELM model; the sum of squared errors using the piecewise ELM model... The accuracy of temperature error compensation for fiber optic gyroscopes was reduced by 99.90% compared to before compensation, 92.03% compared to the multinomial regression model, and 91.77% compared to the piecewise ELM model. In the second validation set, the root mean square error was reduced by 74.24% compared to before compensation and by 72.19% compared to the multinomial regression model. Other performance improvements can also be calculated from Tables 1-3. Furthermore, because ELM modeling is performed in two stages—heating and cooling—the model structure is simpler than the piecewise ELM model, and the real-time performance is also faster and better than the piecewise ELM model. Therefore, it can be seen that this application can improve the accuracy of fiber optic gyroscope temperature error compensation across the entire temperature range through adaptive smoothing filtering.

[0115] Table 1. Comparison of validation metrics after ELM segmented compensation model on the training set.

[0116] Table 2 Comparison of validation group metrics after ELM segmented compensation model in the first validation set

[0117] Table 3 Comparison of validation group metrics after ELM piecewise compensation model on the second validation set

[0118] 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 used for analysis, data stored, data displayed, 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 the relevant data must comply with relevant regulations.

[0119] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. 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), magnetic 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 take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0120] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0121] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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, they should be considered to be within the scope of this specification.

[0122] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for piecewise compensation of temperature error in fiber optic gyroscopes based on adaptive smoothing filtering, characterized in that, The fiber optic gyroscope temperature error segmentation compensation method based on adaptive smoothing filtering includes: Obtain the temperature of the fiber optic gyroscope to be compensated; The temperature of the fiber optic gyroscope to be compensated is smoothed by filtering to obtain the filtered temperature of the fiber optic gyroscope. The temperature change rate is calculated based on the filtered fiber optic gyroscope temperature. Based on the temperature change rate, an adaptive window filtering method is used to obtain the filtered temperature change rate. Based on the filtered fiber optic gyroscope temperature and the filtered temperature change rate, the optimal feature matrix set is obtained. The optimal feature matrix set is input into the full-temperature stage fiber optic temperature error model to obtain the fiber optic gyroscope temperature error, and the temperature of the fiber optic gyroscope to be compensated is compensated according to the fiber optic gyroscope temperature error; the full-temperature stage fiber optic temperature error model is constructed based on the extreme learning machine model.

2. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 1, characterized in that, Based on the aforementioned temperature change rate, an adaptive window filtering method is used to obtain the filtered temperature change rate, specifically including: Initialization parameters; these parameters include: sampling frequency, filtering time, and smoothing factor; A trend window is constructed based on the sampling frequency and the filtering time; The temperature change rate is smoothed and filtered using the trend window to obtain the low-frequency trend temperature change rate and the high-frequency noise temperature change rate. Calculate the local noise standard deviation based on the temperature change rate of the low-frequency trend and the temperature change rate. Calculate the global noise standard deviation based on the temperature change rate of the high-frequency noise; The local noise standard deviation is normalized using the global noise standard deviation to obtain the normalized local noise standard deviation. Based on the normalized local noise standard deviation and smoothing factor, the adaptive smoothing filter window is calculated. Determine whether the adaptive smoothing filter window is odd; If so, the temperature change rate is filtered based on the adaptive smoothing filter window to obtain the filtered temperature change rate. If not, the adaptive smoothing filter window is increased by one, and the temperature change rate is filtered based on the increased adaptive smoothing filter window to obtain the filtered temperature change rate.

3. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 2, characterized in that, The formula for calculating the trend window is: ； in, For trend windows; The sampling frequency; This is the filtering time.

4. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 2, characterized in that, The formula for calculating the standard deviation of local noise is: ； in, for The standard deviation of local noise at any given time; This is the minimum value of the trend window; for The rate of temperature change at any given moment; for The rate of temperature change at low frequency over time; This represents the mean local noise level within the window.

5. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 2, characterized in that, The formula for calculating the normalized local noise standard deviation is as follows: ； ； in, for Standard deviation of local noise after time-normalization; for The standard deviation of local noise at any given time; The global noise standard deviation; It is a function of standard deviation; for The rate of temperature change of high-frequency noise at any given time.

6. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 2, characterized in that, The formula for calculating the adaptive smoothing filter window is: ； in, For adaptive smoothing filtering window; This is the minimum value of the trend window; This represents the maximum value of the trend window; It is a smoothing factor; This represents the normalized standard deviation of local noise.

7. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 2, characterized in that, The formula for calculating the filtered temperature change rate is: ； in, for The rate of temperature change after filtering at any given time; for Time-adaptive smoothing filter window; for The rate of temperature change at any given time.

8. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 1, characterized in that, Based on the filtered fiber optic gyroscope temperature and the filtered temperature change rate, an optimal feature matrix set is obtained, specifically including: Based on the filtered fiber optic gyroscope temperature and the filtered temperature change rate, the cross-coupling term is calculated. Based on the filtered fiber optic gyroscope temperature, a multi-hysteresis filtered fiber optic gyroscope temperature is generated. Based on the filtered fiber optic gyroscope temperature, a number of higher-order terms of the filtered fiber optic gyroscope temperature are generated. Arbitrarily combine the filtered fiber optic gyroscope temperature, the filtered temperature change rate, the cross-coupling term, the filtered fiber optic gyroscope temperature with multiple hysteresis, and the higher-order term of the filtered fiber optic gyroscope temperature with multiple hysteresis to obtain multiple feature matrix subsets, and the multiple feature matrix subsets form a feature matrix set. The optimal feature matrix set is obtained by filtering the feature matrix set based on the optimal feature matrix set of the samples; the optimal feature matrix set of the samples is obtained by filtering the sample feature matrix set using a full-temperature stage fiber optic temperature error model.

9. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 8, characterized in that, The full-temperature stage fiber optic temperature error model includes: a heating stage fiber optic temperature error model and a cooling stage fiber optic temperature error stage model; the sample optimal feature matrix set includes: a sample optimal feature matrix set for the heating stage and a sample optimal feature matrix set for the cooling stage; the optimal feature matrix set includes: a heating stage optimal feature matrix set and a cooling stage optimal feature matrix set. The optimal feature matrix set is obtained by filtering the feature matrix set based on the optimal feature matrix set of the samples, specifically including: Construct a sample feature matrix set; the sample feature matrix set includes multiple sample subsets and the actual fiber optic gyroscope temperature error corresponding to each sample subset; the sample subset is obtained by any combination of the fiber optic gyroscope temperature after sample filtering, the temperature change rate after sample filtering, the sample cross-coupling term, the fiber optic gyroscope temperature after multiple sample hysteresis, and the higher-order terms of the fiber optic gyroscope temperature after multiple sample filtering. Multiple sample subsets are input into the fiber temperature error model of the heating stage to obtain the root mean square error corresponding to each sample subset, and the sample subset with the smallest root mean square error is selected as the optimal feature matrix set of the sample heating stage. Multiple sample subsets are input into the fiber optic temperature error model for the cooling stage to obtain the root mean square error corresponding to each sample subset, and the sample subset with the smallest root mean square error is selected as the optimal feature matrix set for the cooling stage. The optimal feature matrix set for the heating stage is obtained by filtering the feature matrix set based on the optimal feature matrix set for the sample heating stage. The optimal feature matrix set for the cooling stage is obtained by filtering the feature matrix set based on the optimal feature matrix set for the sample cooling stage.

10. The method for piecewise compensation of fiber optic gyroscope temperature error based on adaptive smoothing filtering according to claim 9, characterized in that, The optimal feature matrix set is input into the full-temperature stage fiber optic temperature error model to obtain the fiber optic gyroscope temperature error, specifically including: Determine whether the filtered rate of temperature change is greater than or equal to zero; If so, the optimal feature matrix set of the heating stage is input into the fiber optic temperature error model of the heating stage to obtain the fiber optic gyroscope temperature error. If not, the optimal feature matrix set of the cooling stage is input into the fiber optic temperature error model of the cooling stage to obtain the fiber optic gyroscope temperature error.

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