Error parameter estimation method and system of sensor

Abstract

The invention provides a sensor error parameter estimation method and system, and the method comprises the steps: collecting the measurement data of a sensor through a six-position method, and the sensor comprises a gyroscope and / or an accelerometer; carrying out sensor error modeling, and carrying out deterministic error parameter fitting on the sensor by using a least square method; performing error compensation according to the deterministic error parameter to obtain a random error of the sensor; taking the random error as a measurement value of a Kalman filtering algorithm, and modeling the random error by adopting a Gaussian-Markov model to serve as a state value of the Kalman filtering algorithm; designing a random error matrix and a driving noise covariance matrix; and based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix, performing time updating and measurement updating of a Kalman filtering algorithm, and correcting the random error of the sensor. In the real-time measurement, the estimation of the deterministic error parameter and the random error parameter can overcome the error measurement caused by the instrument, and more accurate measurement data can be obtained.

Description

Technical Field

[0001] This application relates to the field of inertial measurement unit (IMU) sensor technology, and more specifically, to a method and system for estimating the error parameters of a sensor. Background Technology

[0002] With the continuous development of the petroleum industry and the increasing difficulty of oil and gas exploration and development, domestic and international competition is becoming increasingly fierce. The role of carrier attitude measurement in the petroleum industry is becoming increasingly prominent. This means that the requirements for the real-time performance, accuracy, and continuous, dynamic measurement of inertial measurement sensors are also becoming increasingly stringent. Inertial measurement units (IMUs) are a major component of navigation systems and are now widely used in various systems. An IMU is a sensor assembly integrating accelerometers and gyroscopes, which can be produced at lower cost and higher volume. Accelerometers measure gravitational acceleration on their sensitive axes, and triaxial accelerometers are used to confirm the current attitude and position. In addition, gyroscopes measure angular rates on their sensitive axes, and the output of the gyroscopes is used to maintain orientation in space.

[0003] These two types of inertial sensors contain two main types of errors: deterministic errors, such as scaling factor, bias, and misalignment (installation error); and random errors, such as bias instability and scaling factor instability.

[0004] As the production cost of sensors decreases, their performance gradually declines. To improve the performance of inertial measurement units (IMUs), error compensation algorithms have attracted attention, and various algorithms have been designed. Therefore, to improve the performance of inertial sensors, calibration algorithms and error compensation models have been researched and developed to ensure real-time correction and more accurate sensor correction data. This is currently one of the research hotspots and challenges in this field. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the purpose of this application is to provide a method and system for estimating the error parameters of a sensor.

[0006] A first aspect of this application provides a method for estimating error parameters of a sensor, comprising: The measurement data of the sensor is acquired using a six-position method, and the sensor includes a gyroscope and / or an accelerometer; Based on the measurement data, error modeling is performed on the sensor, and the deterministic error parameters of the sensor are fitted using the least squares method. Error compensation is performed based on the deterministic error parameters to obtain the random error of the sensor; The random error is used as the measurement value of the Kalman filter algorithm. A Gauss-Markov model is used to model the random error and serve as the state value of the Kalman filter algorithm. Based on the Gauss-Markov model, the random error matrix and the driving noise covariance matrix are designed. Based on the measured values, the state values, the random error matrix, and the driving noise covariance matrix, a Kalman filter algorithm is used for time updates and measurement updates to correct the random errors of the sensor.

[0007] Optionally, when the sensor is an accelerometer, the step of performing error modeling on the sensor based on the measurement data and fitting the deterministic error parameters of the sensor using the least squares method includes: Establish error models for the three single-axis accelerometers: x, y, and z. ; in, Indicates the accelerometer output. Indicates actual acceleration. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. This indicates accelerometer noise, where d represents the x, y, or z axis. Based on the error models of the three single-axis accelerometers, and considering installation errors, a set of error equations for the triaxial accelerometers is established: ; Where M xy M xz M yx M yz M zx M zy This indicates installation error. The subscript ab indicates the coupled projection of the b-axis onto the a-axis, where a represents the x, y, and z axes, and b represents the x, y, and z axes. Based on the above set of triaxial accelerometer error equations, the least squares method is used to obtain the accelerometer fitting formula and all deterministic error parameters of the accelerometer.

[0008] Optionally, when the sensor is a gyroscope, the step of performing error modeling on the sensor based on the measurement data and fitting the deterministic error parameters of the sensor using the least squares method includes: Establish error models for the three single-axis gyroscopes: x, y, and z. ; in, Indicates the gyroscope output. Represents the actual angular velocity. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. This indicates gyroscope noise, where d represents x, y, or z; Based on the error models of three single-axis gyroscopes, and considering installation errors, the following equations for the three-axis gyroscope error model are established: ; Based on the above set of equations for the three-axis gyroscope error model, the least squares method is used to obtain the gyroscope fitting formula and all deterministic error parameters of the gyroscope.

[0009] Optionally, based on the measurement data when the sensor includes a gyroscope and an accelerometer, error modeling of the sensor is performed, and deterministic error parameter fitting of the sensor is done using the least squares method, including: Establish error models for the three single-axis gyroscopes: x, y, and z. ; in, Indicates the gyroscope output. Represents the actual angular velocity. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. The coefficient represents the correlation between gravitational acceleration g and g. This indicates gyroscope noise, where d represents x, y, or z; Based on the error models of three single-axis gyroscopes, and considering installation errors, the following equations for the three-axis gyroscope error model are established: ; in, , , This is the value after accelerometer error compensation, i.e., the actual acceleration; Based on the above set of equations for the three-axis gyroscope error model, the least squares method is used to obtain the gyroscope fitting formula and all deterministic error parameters of the gyroscope.

[0010] Optionally, the step of performing error compensation based on the deterministic error parameters to obtain the random error of the sensor includes: Based on the deterministic error parameters, the corrected measurement value of the sensor is obtained through the inverse equation of the sensor's error model. Based on the corrected measurement values ​​from the sensor, the residual error of the sensor, i.e., the random error, is obtained.

[0011] Optionally, the step of using the random error as a measurement value of the Kalman filter algorithm, modeling the random error using a Gauss-Markov model, and using it as the state value of the Kalman filter algorithm; and designing the random error matrix and the driving noise covariance matrix based on the state value, includes: The random error is used as a measurement in the Kalman filtering algorithm, and the random error includes bias instability; The bias instability is modeled using a Gauss-Markov model, and the modeled bias instability is defined as the state value of the Kalman filter. Based on the characteristics of the Gauss-Markov model, two covariance matrices are designed as follows: The bias instability covariance matrix describes the fluctuation range of the bias instability itself and reflects the uncertainty of the state value. The driving noise covariance matrix describes the noise characteristics of changes in driving bias instability, corresponding to the process noise covariance in Kalman filtering, and provides a basis for state prediction.

[0012] Optionally, the step of performing time and measurement updates using a Kalman filter algorithm based on the measured value, the state value, the random error matrix, and the driving noise covariance matrix to correct the random error of the sensor includes: The time update is as follows: State prediction: ; This represents the state value at the previous moment. This represents the predicted state value at the current moment. The elements of the state transition matrix A are the decay factors used in modeling bias instability. The driving noise corresponds to the driving noise covariance matrix; Error covariance prediction: ; This represents the error covariance at the previous time step. The uncertainty in the current state estimate is influenced by the random error matrix; Q represents the process noise, determined by the driving noise covariance matrix. The measurement is updated as follows: Calculate the Kalman gain: C is the measurement matrix, and R is the noise covariance matrix. Weights of predicted and measured values; Measurement equation update: ; This is the corrected current state, i.e., the corrected bias instability; Update the error covariance matrix: .

[0013] A second aspect of this application provides a sensor error parameter estimation system, comprising: Data module: The six-position method is used to acquire measurement data from the sensors, which include a gyroscope and an accelerometer; Deterministic error module: Based on the measurement data, the sensor performs error modeling and uses the least squares method to fit the deterministic error parameters of the sensor; Error compensation module: Performs error compensation based on the deterministic error parameters to obtain the random error of the sensor; Setting module: The random error is used as the measurement value of the Kalman filter algorithm. A Gauss-Markov model is used to model the random error as the state value of the Kalman filter algorithm. Based on the Gauss-Markov model, the random error matrix and the driving noise covariance matrix are designed. Random error module: Based on the measured value, the state value, the random error matrix, and the driving noise covariance matrix, it performs time updates and measurement updates using the Kalman filter algorithm to correct the random error of the sensor.

[0014] In a third aspect, this application provides a terminal including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it can be used to perform the method described above, or to run the system described above.

[0015] In a fourth aspect, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can be used to perform the method described thereon or to run the system described thereon.

[0016] The proposed method for estimating error parameters of gyroscopes and accelerometers first collects measurement data as samples to construct error parameter models for both the gyroscope and accelerometer. The deterministic error parameters of each gyroscope and accelerometer are then fitted using the least squares method. Finally, Kalman filtering combined with a Gauss-Markov model is used to estimate the random error parameters of each gyroscope and accelerometer. In real-time measurement scenarios, the estimated deterministic and random error parameters are used to compensate for instrument errors, thereby obtaining more accurate measurement data and improving the accuracy of applications such as attitude measurement.

[0017] Other technical effects resulting from the additional features will be further illustrated in the corresponding embodiments. Attached Figure Description

[0018] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating a sensor error parameter estimation method according to an exemplary embodiment; Figure 2 This is a schematic diagram illustrating sensor error types according to an exemplary embodiment; Figure 3 This is a schematic diagram illustrating different errors according to an exemplary embodiment; Figure 4 This is a structural diagram of a sensor error parameter estimation system according to an exemplary embodiment. Detailed Implementation

[0019] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application, and these all fall within the protection scope of the present application. Parts not described in detail in the following embodiments can be implemented using existing technology.

[0020] Inertial sensors primarily exhibit two types of error sources: deterministic errors, including scale factor deviation, zero-bias error, and inter-axis installation misalignment; and random errors, mainly manifested as zero-bias instability and scale factor instability. With the continuous reduction in sensor manufacturing costs, their overall performance indicators show a downward trend. Based on these issues, this application provides a sensor error parameter estimation method to address the aforementioned problems.

[0021] Reference Figure 1 As shown in one embodiment of this application, a method for estimating the error parameters of a sensor includes: Step 1: Acquire measurement data from the sensors using a six-position method. The sensors include a gyroscope and / or an accelerometer. Specifically, the error can be estimated based on the measurement data of the gyroscope or accelerometer separately; or the error of the gyroscope can be estimated based on the combined measurement data of the gyroscope and accelerometer.

[0022] Step 2: Based on the measurement data, perform error modeling on the sensor and use the least squares method to fit the deterministic error parameters of the sensor; Step 3: Perform error compensation based on the deterministic error parameters to obtain the random error of the sensor; Step 4: Use the random error as the measurement value of the Kalman filter algorithm, and model the random error using a Gauss-Markov model as the state value of the Kalman filter algorithm; based on the Gauss-Markov model, design the random error matrix and the driving noise covariance matrix. Step 5: Based on the measured values, state values, random error matrix, and driving noise covariance matrix, perform time updates and measurement updates using the Kalman filter algorithm to correct the random errors of the sensor.

[0023] Specifically, such as Figure 2 and Figure 3 As shown, deterministic error parameters include bias error, scaling factor error, and installation error. Random errors include bias instability. For the G-related error within deterministic errors and the scaling factor instability within random errors, their impact on overall measurement accuracy is minimal (their numerical magnitude is much lower than other major errors). To simplify the calculation process and balance accuracy and efficiency, they are temporarily ignored in the error parameter estimation of this application. The focus is on accurately solving and compensating for error terms that have a more significant impact on the measurement results.

[0024] In the embodiments described above, the estimation of deterministic error parameters and random error parameters in real-time measurement can overcome the measurement errors caused by the instrument itself, thereby obtaining more accurate measurement data.

[0025] To obtain sensor measurement data, a six-position method is used. The six-position method is a technique in inertial measurement that involves static data acquisition by placing the inertial measurement unit (IMU) in six specific spatial orientations (i.e., with the three coordinate axes facing up and down). In some specific embodiments of this application, step 1, acquiring measurement data from the gyroscope and accelerometer using the six-position method, can be performed using the following steps: First, an inertial measurement unit integrating an accelerometer and / or gyroscope is installed on the calibration frame.

[0026] Then, accelerometer and / or gyroscope measurements are collected alternately at six positions along each axis, moving up and down. Specifically: When the X-axis is upward, collect and record gyroscope data. and accelerometer data ; When the X-axis is downward, collect and record gyroscope data. and accelerometer data ; When the Y-axis is upward, collect and record gyroscope data. and accelerometer data ; When the Y-axis is downward, collect and record gyroscope data. and accelerometer data ; When the Z-axis is upward, collect and record gyroscope data. and accelerometer data ; When the Z-axis is downward, collect and record gyroscope data. and accelerometer data .

[0027] It should be noted that the 6-position method is the minimum number of positions required to solve the error. In other embodiments of this application, the multi-position method can also be used to obtain the sensor's measurement data.

[0028] In the embodiments described above, the collected data comes from static testing, relying on the Earth's gravitational field and rotational angular velocity as stable references. The data acquisition process is simple, low-cost, and covers operating conditions in both positive and negative directions of the three axes. This collected data is mainly used for the calibration of the inertial measurement unit (IMU), providing original evidence for solving key error parameters such as the zero bias and scaling factor of the accelerometer and gyroscope, and helping to distinguish and quantify these factors affecting measurement accuracy.

[0029] The aforementioned scaling factor and bias error can be calculated from the acquired data through basic processing in some embodiments. Specifically, the scaling factor error and bias error of the accelerometer are calculated as follows: ; ; Where g represents the acceleration due to gravity, and Av represents the average value. This indicates the current orientation of the corresponding accelerometer.

[0030] Calculate the scaling factor error and bias error of the gyroscope: ; ; in, This indicates the current orientation of the corresponding gyroscope. It represents the angular velocity of Earth's rotation.

[0031] The scaling factor and bias error calculated directly in the above embodiments can significantly reduce their interference with the measurement results in the early stages. However, the above process cannot obtain the installation error. Therefore, in order to obtain all deterministic errors of the accelerometer (including installation error), in some specific embodiments of this application, in step 2, the sensor error is modeled based on the measurement data, and the deterministic error parameters of the sensor are fitted using the least squares method. Depending on the sensor, this can be implemented in the following ways.

[0032] Specifically, when the sensor is used for acceleration timing, step 2 involves the following steps: S2011, Establish the error model for a single-axis accelerometer: ; in, This indicates the accelerometer output, i.e., the accelerometer data mentioned above. , , Indicates actual acceleration. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. This indicates sensor noise.

[0033] Similarly, the error models for the y-axis and z-axis can be expressed as follows: ; ; The error model structures for each axis are identical, with only subscripts distinguishing different axes.

[0034] S2012, Establish the triaxial accelerometer error equation set: ; Where M xy M xz M yx M yz M zx M zy This indicates the installation error. Where M... xy M xz M yx M yz M zx M zy The symbol represents the installation error. The subscript ab indicates the coupled projection of the b-axis onto the a-axis. The a-axis represents the x, y, and z axes, and the b-axis represents the x, y, and z axes.

[0035] S2013, based on the above triaxial accelerometer error equations, the least squares method is used to obtain the accelerometer fitting formula: ; in This represents the matrix of all deterministic error parameters of the accelerometer. The matrix representing accelerometer data. Represents the reference input matrix; Specifically, ; ; ; Specifically, when the sensor is used for acceleration timing, step 2 involves the following steps: S2021, the error model for a single-axis gyroscope is established as follows: ; in, This indicates the gyroscope output, i.e., the gyroscope data mentioned above. , , Represents the actual angular velocity. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. The coefficient represents the correlation between gravitational acceleration g and g. This indicates sensor noise.

[0036] Similarly, the gyroscope error models for the y-axis and z-axis can be expressed as follows: ; ; The error model structures for each axis are identical, with only subscripts distinguishing different axes.

[0037] S2022, the error model equations for the three gyroscopes are established as follows: ; Where M xy M xz M yx M yz M zx M zy This indicates installation error.

[0038] S2023, based on the above-mentioned three-axis gyroscope error model equations, uses the least squares method. ; in This represents the matrix of all deterministic error parameters of the gyroscope. This represents a matrix composed of gyroscope data. This represents the reference input matrix.

[0039] Specifically, ; ; ; in W h This represents the horizontal component of the gyroscope. W p The numbers 1-6 represent the vertical component of the gyroscope, and the numbers 1-6 represent the six positions in the six-position method.

[0040] It is worth noting that, however, this The correlation coefficient representing gravitational acceleration g is very small and can be ignored. Therefore, in some other specific embodiments, when the sensor is an accelerometer and a gyroscope, step 2 can also adopt the following steps: S2031, the error model for a single-axis gyroscope is established as follows: ; in, This indicates the gyroscope output, i.e., the gyroscope data mentioned above. , , Represents the actual angular velocity. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. This indicates sensor noise.

[0041] Similarly, the gyroscope error models for the y-axis and z-axis can be expressed as follows: ; ; The error model structures for each axis are identical, with only subscripts distinguishing different axes.

[0042] S2032, the error model equations for the three gyroscopes are established as follows: ; Where M xy M xz M yx M yz M zx M zy This indicates installation error.

[0043] S2033, based on the above-mentioned three-axis gyroscope error model equations, uses the least squares method. ; in This represents the matrix of all deterministic error parameters of the gyroscope. This represents a matrix composed of gyroscope data. This represents the reference input matrix. The forms of the matrices here are consistent with those in S2013.

[0044] Specifically, the process of determining the solution to the deterministic errors of the accelerometer and gyroscope mentioned above is derived through the following process: From equation S202, neglecting random errors, we obtain the following equation: ; From the least squares equation, we know that it is of the form of The approximate analytical solution of the equation is ; Therefore, the solutions for the deterministic errors of the accelerometer and gyroscope in S205 and S206 can be derived respectively.

[0045] The embodiments described above establish error models for single-axis and three-axis gyroscopes and accelerometers, incorporating error terms such as scaling factor error, bias error, installation error, scaling factor instability, bias instability, sensor noise, and the correlation coefficient of the gyroscope's gravitational acceleration into the models. The least squares method is then used to fit the error parameters, enabling a systematic and comprehensive quantification of various errors in both types of sensors. This approach can accurately extract deterministic error parameters, providing a reliable basis for subsequent error compensation, effectively improving the accuracy of sensor measurement data, and laying the foundation for precise applications based on this data (such as carrier spatial attitude measurement).

[0046] After obtaining the deterministic error parameters through the above process, error compensation is performed. In some specific embodiments of this application, step 3, performing error compensation based on the deterministic error parameters to obtain the random error of the sensor, includes the following steps: S301, based on deterministic error parameters, obtains the corrected accelerometer or gyroscope measurement value through the inverse equation of the error model of a single-axis accelerometer or gyroscope: ; ; The corrected acceleration measurement value output by the accelerometer after deterministic error compensation; This represents the original measurement value from the accelerometer; The corrected acceleration measurement value output by the gyroscope after deterministic error compensation; This represents the original measurement value of the gyroscope; S302, based on the corrected accelerometer or gyroscope measurements, obtains the residual acceleration error, i.e., the random error. The residual error of the gyroscope, i.e., the random error, is obtained. .

[0047] Of course, the random errors for the other two axes are obtained in the same way as described above.

[0048] In the above embodiment, S301 uses deterministic error parameters and inverse equations to correct the original measurement values ​​of the accelerometer and gyroscope, removing the influence of deterministic errors such as scaling factor and bias, and obtaining measurement results that are closer to the true values; S302 calculates the residual error (random error) based on the corrected values, preparing for subsequent processing of random errors using Kalman filtering and other methods.

[0049] To correct for random errors, in some specific embodiments of this application, step 4 involves using the random error as a measurement value of the Kalman filter algorithm, modeling the random error using a Gauss-Markov model, and using it as the state value of the Kalman filter algorithm. Based on the Gauss-Markov model, the random error matrix and the driving noise covariance matrix are designed, which can be achieved through the following steps: S401 uses random error as the measurement value of the Kalman filter algorithm. Random errors include bias instability; S402 uses a Gauss-Markov model to model bias instability. Define it as the state value of the Kalman filter. x k .

[0050] S403, and based on the characteristics of the S-Markov model, two covariance matrices are designed: The bias instability covariance matrix describes the range of fluctuations in the bias instability itself and reflects the state values. x k Uncertainty: ; The driving noise covariance matrix describes the noise characteristics of changes in driving bias instability, corresponding to the process noise covariance Q in Kalman filtering, and provides a basis for state prediction. ; in, dt Indicates the sampling period. Tc Represents the sensor time constant. This indicates the driving noise.

[0051] The embodiments described above utilize the physical characteristics of model adaptation bias instability to allow the state values ​​of Kalman filtering to accurately describe error changes, thus solving the problem that traditional methods struggle to dynamically capture error patterns. By deriving the bias instability covariance and the driving noise covariance, key parameters such as process noise Q are provided for Kalman filtering, enabling the filtering to quantify the "error fluctuation range" and "prediction uncertainty," thereby solving the problem of limited accuracy in error compensation due to unknown uncertainties.

[0052] Based on the parameters designed in S401-S403 above, random errors are further corrected. In some specific embodiments of this application, a Kalman filter algorithm is used for time updates and measurement updates based on the measured values, state values, random error matrix, and driving noise covariance matrix to correct the random errors of the sensor, specifically as follows: The time has been updated to: State prediction: ; This indicates the state at the previous moment. The state transition matrix A represents the predicted state at the current moment, and its elements are: , To drive noise, and correspond; Error covariance prediction: ; This represents the error covariance at the previous time step. To predict the uncertainty of the current state estimate, Q represents the process noise, which is determined by the driving noise covariance matrix; Measurement updated to: Calculate the Kalman gain: C is the measurement matrix, and R is the noise covariance matrix. Weights of predicted and measured values; Measurement equation update: ; This is the corrected current state, i.e., the corrected bias instability; Update the error covariance matrix: .

[0053] The embodiments described above in this application, by means of time updates (state and error covariance prediction) and measurement updates (Kalman gain calculation, state and covariance matrix correction), achieve real-time estimation and dynamic correction of bias instability, effectively suppress random error interference, improve the stability and accuracy of sensor measurement data, and provide reliable support for applications such as attitude measurement based on this data.

[0054] In some specific embodiments of this application, the inertial measurement unit has three accelerometers and three gyroscopes for measuring linear acceleration and angular rates about the x, y, and z axes. Therefore, a Kalman filter is used to estimate the bias instability of the six sensors. For this purpose, the state vector... It contains six states, representing the bias instabilities of the x-gyroscope, y-gyroscope, z-gyroscope, x-accelerometer, y-accelerometer, and z-accelerometer, respectively. Because the random errors output by the error compensation model correspond to the measurement information in the Kalman filter, and the six axis errors of the gyroscopes and accelerometers are independent, the measurement value of each axis is directly mapped from the error state of the corresponding axis, without inter-axis coupling. Therefore, using the identity matrix as the measurement matrix ensures a one-to-one correspondence between the measurement value and the error state of each axis, accurately transmitting the error information of each axis, adapting to multi-axis independent error processing scenarios, and guaranteeing the accuracy of the Kalman filter's estimation of the random errors of each axis.

[0055] Specifically, ; The left side of the equation represents the actual measured value, and the rightmost side represents random noise. B represents the deviation instability of the gyroscope and accelerometer. The output of the error compensation model is used as the measurement value in the Kalman filter algorithm; therefore, the identity matrix is ​​chosen as the measurement matrix. The above equation can then be written as: , Indicates the measured value. For the measurement matrix, This is due to bias instability. It is random noise.

[0056] The random noise from the gyroscope and accelerometer is used to determine the measurement noise covariance matrix R. Similarly, the unstable 3σ values ​​of the gyroscope and accelerometer biases are used to construct the initial values ​​for the error covariance matrix P.

[0057] Specifically, assuming k=0, initialize Representations of estimation error, uncertainty in state estimation, and error covariance: ; ; in, Represents the true state. This represents the estimated state; the maximum value of the true state is bias-unstable. Therefore, if the initial state is zero, according to the above formula, the maximum error can be bias-unstable. Therefore, the error covariance P k The initial values ​​of the diagonal elements become The bias of the gyroscope and accelerometer is unstable. The time difference is multiples. There is no correlation between the state and the error. Therefore, P... k The off-diagonal elements of R and Q are equal to zero.

[0058] ; ; ; P0 is the state estimation error covariance matrix, the initial iteration value. R is the measurement noise covariance matrix. Q is the process noise covariance matrix.

[0059] The embodiments described above in this application, by clarifying the specific form of the Kalman filter measurement equation, using the error compensation model output as the measured value and selecting the identity matrix as the measurement matrix, clearly establish the mapping relationship between the measured value and the state value. Simultaneously, based on random noise density, the 3σ value of bias instability, and other factors, the specific forms of the measurement noise covariance matrix R, the initial error covariance matrix P0, and the process noise covariance matrix Q are determined, and the off-diagonal elements are explicitly set to zero. This provides precise parameter basis for the initialization and iterative calculation of the Kalman filter, ensuring the accuracy and reliability of the estimation of gyroscope and accelerometer bias instability, and laying the foundation for the effective handling of random errors. Here, 3σ represents three times the standard deviation, representing a 99.7% confidence level. Using it to initialize the covariance matrix is ​​to provide a better estimate of uncertain errors and also to give the Kalman filter iteration a more reliable starting point.

[0060] Based on the same technical concept, other embodiments of this application also provide a sensor-based error parameter estimation system 100, such as... Figure 4 As shown, the system includes: Data module 110: Acquires measurement data from sensors using a six-position method, including gyroscopes and / or accelerometers; Deterministic error module 120: Based on measurement data, it models the error of the sensor and uses the least squares method to fit the deterministic error parameters of the sensor; Error compensation module 130: Performs error compensation based on deterministic error parameters to obtain the random error of the sensor; Setting module 140: Using random error as the measurement value of the Kalman filter algorithm, the random error is modeled using a Gauss-Markov model and used as the state value of the Kalman filter algorithm; designing the random error matrix and the driving noise covariance matrix; Random error module 150: Based on the measured value, state value, random error matrix and driving noise covariance matrix, it performs time update and measurement update using Kalman filtering algorithm to correct the random error of the sensor.

[0061] The specific implementation techniques of each module / unit in the above examples of this application can be referred to the steps of the sensor-based error parameter estimation and error compensation method in the above embodiments, which will not be repeated here.

[0062] The preferred features in the above embodiments can be used individually in any embodiment, or in any combination thereof, provided they do not conflict with each other. Furthermore, parts not described in detail in the embodiments can be implemented using existing technologies.

[0063] Based on the same technical concept, other embodiments of this application also provide a terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it can be used to execute the error parameter estimation method of the sensor, or to run the error parameter estimation system of the sensor.

[0064] Based on the same technical concept, other embodiments of this application also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, can be used to perform the error parameter estimation method of the sensor, or to run the error parameter estimation system of the sensor.

[0065] Optionally, the memory is used to store programs; the memory may include volatile memory, such as random-access memory (RAM), such as static random-access memory (SRAM), double data rate synchronous dynamic random-access memory (DDR SDRAM), etc.; the memory may also include non-volatile memory, such as flash memory. The memory is used to store computer programs (such as application programs and functional modules that implement the above methods), computer instructions, etc., and the aforementioned computer programs and computer instructions can be partitioned and stored in one or more memories. Furthermore, the aforementioned computer programs, computer instructions, data, etc., can be accessed by the processor.

[0066] The aforementioned computer programs, computer instructions, etc., can be stored in partitions within one or more memory locations. Furthermore, the aforementioned computer programs, computer instructions, data, etc., can be accessed by a processor.

[0067] A processor is used to execute a computer program stored in memory to implement the various steps of the methods involved in the above embodiments. For details, please refer to the relevant descriptions in the preceding method embodiments.

[0068] The processor and memory can be separate structures or integrated structures. When the processor and memory are separate structures, they can be coupled together via a bus.

[0069] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0070] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0071] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0072] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0073] The foregoing has described some specific embodiments of this application. It should be understood that this application is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the substantive content of this application. The above-described preferred features can be used in any combination without conflict.

Claims

1. A method for estimating error parameters of a sensor, characterized in that, include: The measurement data of the sensor is acquired using a six-position method, and the sensor includes a gyroscope and / or an accelerometer; Based on the measurement data, error modeling is performed on the sensor, and the deterministic error parameters of the sensor are fitted using the least squares method. Error compensation is performed based on the deterministic error parameters to obtain the random error of the sensor; The random error is used as the measurement value of the Kalman filter algorithm. A Gauss-Markov model is used to model the random error and serve as the state value of the Kalman filter algorithm. Based on the Gauss-Markov model, the random error matrix and the driving noise covariance matrix are designed. Based on the measured values, the state values, the random error matrix, and the driving noise covariance matrix, a Kalman filter algorithm is used for time updates and measurement updates to correct the random errors of the sensor.

2. The error parameter estimation method for a sensor according to claim 1, characterized in that, When the sensor is an accelerometer, the step of modeling the sensor's error based on the measurement data and fitting the sensor's deterministic error parameters using the least squares method includes: Establish error models for the three single-axis accelerometers: x, y, and z. ； in, Indicates the accelerometer output. Indicates actual acceleration. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. This indicates accelerometer noise, where d represents the x, y, or z axis. Based on the error models of the three single-axis accelerometers, and considering installation errors, a set of error equations for the triaxial accelerometers is established: ； Where M xy M xz M yx M yz M zx M zy This indicates installation error. The subscript ab indicates the coupled projection of the b-axis onto the a-axis, where a represents the x, y, and z axes, and b represents the x, y, and z axes. Based on the above set of triaxial accelerometer error equations, the least squares method is used to obtain the accelerometer fitting formula and all deterministic error parameters of the accelerometer.

3. The error parameter estimation method for a sensor according to claim 1, characterized in that, When the sensor is a gyroscope, the step of modeling the sensor's error based on the measurement data and fitting the sensor's deterministic error parameters using the least squares method includes: Establish error models for the three single-axis gyroscopes: x, y, and z. ； in, Indicates the gyroscope output. Represents the actual angular velocity. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. This indicates gyroscope noise, where d represents x, y, or z; Based on the error models of three single-axis gyroscopes, and considering installation errors, the following equations for the three-axis gyroscope error model are established: ； Based on the above set of equations for the three-axis gyroscope error model, the least squares method is used to obtain the gyroscope fitting formula and all deterministic error parameters of the gyroscope.

4. The error parameter estimation method for a sensor according to claim 1, characterized in that, The step of modeling the sensor's error based on the measurement data, when the sensor includes a gyroscope and an accelerometer, and fitting the sensor's deterministic error parameters using the least squares method, includes: Establish error models for the three single-axis gyroscopes: x, y, and z. ； in, Indicates the gyroscope output. Represents the actual angular velocity. This indicates the scaling factor error. This indicates the bias error. This indicates instability of the scaling factor. This indicates bias instability. The coefficient represents the correlation between gravitational acceleration g and g. This indicates gyroscope noise, where d represents x, y, or z; Based on the error models of three single-axis gyroscopes, and considering installation errors, the following equations for the three-axis gyroscope error model are established: ； in, , , This is the value after accelerometer error compensation, i.e., the actual acceleration; Based on the above set of equations for the three-axis gyroscope error model, the least squares method is used to obtain the gyroscope fitting formula and all deterministic error parameters of the gyroscope.

5. The error parameter estimation method for a sensor according to claim 1, characterized in that, The step of performing error compensation based on the deterministic error parameters to obtain the random error of the sensor includes: Based on the deterministic error parameters, the corrected measurement value of the sensor is obtained through the inverse equation of the sensor's error model. Based on the corrected measurement values ​​from the sensor, the residual error of the sensor, i.e., the random error, is obtained.

6. The error parameter estimation method for a sensor according to claim 1, characterized in that, The random error is used as the measurement value of the Kalman filter algorithm, and the random error is modeled using a Gauss-Markov model as the state value of the Kalman filter algorithm. Based on the aforementioned state values, design the random error matrix and the driving noise covariance matrix, including: The random error is used as a measurement in the Kalman filtering algorithm, and the random error includes bias instability; The bias instability is modeled using a Gauss-Markov model, and the modeled bias instability is defined as the state value of the Kalman filter. Based on the characteristics of the Gauss-Markov model, two covariance matrices are designed as follows: The bias instability covariance matrix describes the fluctuation range of the bias instability itself and reflects the uncertainty of the state value. The driving noise covariance matrix describes the noise characteristics of changes in driving bias instability, corresponding to the process noise covariance in Kalman filtering, and provides a basis for state prediction.

7. The error parameter estimation method for a sensor according to claim 6, characterized in that, The step of performing time and measurement updates using a Kalman filter algorithm based on the measured values, the state values, the random error matrix, and the driving noise covariance matrix to correct the random error of the sensor includes: The time update is as follows: State prediction: ; This represents the state value at the previous moment. This represents the predicted state value at the current moment. The elements of the state transition matrix A are the decay factors used in modeling bias instability. The driving noise corresponds to the driving noise covariance matrix; Error covariance prediction: ; This represents the error covariance at the previous time step. The uncertainty in the current state estimate is influenced by the random error matrix; Q represents the process noise, determined by the driving noise covariance matrix. The measurement is updated as follows: Calculate the Kalman gain: C is the measurement matrix, and R is the noise covariance matrix. Weights of predicted and measured values; Measurement equation update: ; This is the corrected current state, i.e., the corrected bias instability; Update the error covariance matrix: .

8. An error parameter estimation system for a sensor, characterized in that, include: Data module: The six-position method is used to acquire measurement data from the sensors, which include a gyroscope and an accelerometer; Deterministic error module: Based on the measurement data, the sensor performs error modeling and uses the least squares method to fit the deterministic error parameters of the sensor; Error compensation module: Performs error compensation based on the deterministic error parameters to obtain the random error of the sensor; Setting module: The random error is used as the measurement value of the Kalman filter algorithm. A Gauss-Markov model is used to model the random error as the state value of the Kalman filter algorithm. Based on the Gauss-Markov model, the random error matrix and the driving noise covariance matrix are designed. Random error module: Based on the measured value, the state value, the random error matrix, and the driving noise covariance matrix, it performs time updates and measurement updates using the Kalman filter algorithm to correct the random error of the sensor.

9. A terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it can be used to perform the method of any one of claims 1-7, or to run the system of claim 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program can be used to perform the method of any one of claims 1-7, or to run the system of claim 8.

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