A method and system for error parameter estimation of a sensor

Abstract

The application provides a sensor error parameter estimation method and system, comprising: collecting measurement data of a sensor by using a six-position method, the sensor comprising a gyroscope and / or an accelerometer; modeling a sensor error, performing sensor deterministic error parameter fitting 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, modeling the random error by using a Gaussian-Markov model to take the random error as a state value of the Kalman filtering algorithm; designing a random error matrix and a driving noise covariance matrix; performing time updating and measurement updating of the Kalman filtering algorithm based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix to correct the random error of the sensor. In real-time measurement, estimation of the deterministic error parameter and the random error parameter can overcome error measurement caused by the instrument itself, and more accurate measurement data can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of inertial measurement unit (IMU) sensor, in particular, to a sensor error parameter estimation method and system. BACKGROUND

[0002] With the continuous development of the oil industry and the increasing difficulty of oil and gas exploration and development, the competition at home and abroad is becoming more and more fierce. The position of carrier space attitude measurement in the field of oil industry is also becoming more and more prominent. This means that the real-time, accuracy and continuous, dynamic measurement requirements of inertial measurement sensors are also becoming higher and higher. Inertial measurement unit is the main component of navigation system, which is widely used in various systems today. Inertial measurement unit is a sensor component integrating accelerometer and gyroscope, which can be produced at lower cost and higher yield. Accelerometer measures the gravitational acceleration on its sensitive axis, and three-axis accelerometer is used to confirm the current attitude and position. In addition, the gyroscope measures the angular rate on its sensitive axis, and the output of the gyroscope is used to maintain the direction in space.

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

[0004] With the reduction of sensor production cost, the performance of these sensors gradually decreases. In order to improve the performance of inertial measurement unit, error compensation algorithm is concerned, and various algorithms are designed. Therefore, in order to improve the performance of inertial sensor, calibration algorithm and error compensation model are researched and developed to ensure that real-time correction, more accurate sensor correction data are obtained, which is one of the research hotspots and difficulties in this direction. SUMMARY

[0005] In view of the defects / one of the prior art, the purpose of the present application is to provide a sensor error parameter estimation method and system.

[0006] The first aspect of the present application provides a sensor error parameter estimation method, comprising:

[0007] Collecting measurement data of the sensor by using six-position method, the sensor comprising a gyroscope and / or an accelerometer;

[0008] Based on the measurement data, the sensor is modeled, and the least square method is used to fit the deterministic error parameters of the sensor;

[0009] According to the deterministic error parameters, error compensation is performed to obtain the random error of the sensor;

[0010] The random error is taken as a measurement value of a Kalman filtering algorithm, the random error is modeled by using a Gaussian-Markov model as a state value of the Kalman filtering algorithm, and a random error matrix and a driving noise covariance matrix are designed based on the Gaussian-Markov model;

[0011] Based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix, time update and measurement update of the Kalman filtering algorithm are performed to correct the random error of the sensor.

[0012] Optionally, when the sensor is an accelerometer, the error modeling of the sensor based on the measurement data includes using a least square method to perform fitting of deterministic error parameters of the sensor.

[0013] An error model of three single-axis accelerometers x, y and z is established.

[0014] ;

[0015] wherein, represents an accelerometer output, represents an actual acceleration, represents a scale factor error, represents a bias error, represents scale factor instability, represents bias instability, represents an accelerometer noise, and d represents an x, y or z axis.

[0016] Based on the error model of the three single-axis accelerometers, an error equation set of three-axis accelerometers is established in combination with installation errors.

[0017] ;

[0018] wherein M xy , M xz , M yx , M yz , M zx , M zy represents an installation error, and a subscript ab represents a coupling projection of a b axis on an a axis, a represents an x, y or z axis, and b represents an x, y or z axis.

[0019] Based on the above error equation set of three-axis accelerometers, a least square method is used to obtain an accelerometer fitting formula and all deterministic error parameters of the accelerometer.

[0020] Optionally, when the sensor is a gyroscope, the error modeling of the sensor based on the measurement data includes using a least square method to perform fitting of deterministic error parameters of the sensor.

[0021] The error model of three single-axis gyroscopes is established:

[0022] ;

[0023] wherein, gyroscope output, actual angular rate, scale factor error, bias error, scale factor instability, bias instability, gyroscope noise, d represents x, y or z;

[0024] Based on the error model of three single-axis gyroscopes, the error model equation set of three-axis gyroscopes is established in combination with installation errors:

[0025] ;

[0026] Based on the above three-axis gyroscope error model equation set, a gyroscope fitting formula is obtained by using the least square method, and all the deterministic error parameters of the gyroscope are obtained.

[0027] Optionally, when the sensor includes a gyroscope and an accelerometer, the measurement data is used to model errors of the sensor, and the least square method is used to fit the deterministic error parameters of the sensor, including:

[0028] The error model of three single-axis gyroscopes is established:

[0029] ;

[0030] wherein, gyroscope output, actual angular rate, scale factor error, bias error, scale factor instability, bias instability, gravity acceleration g related coefficient, gyroscope noise, d represents x, y or z;

[0031] Based on the error model of three single-axis gyroscopes, the error model equation set of three-axis gyroscopes is established in combination with installation errors:

[0032] ;

[0033] wherein, , 、 is a value compensated by the accelerometer error, i.e., an actual acceleration;

[0034] Based on the above three-axis gyroscope error model equation set, a least square method is used to obtain a gyroscope fitting formula to obtain all the deterministic error parameters of the gyroscope.

[0035] Optionally, the error compensation according to the deterministic error parameters to obtain the random error of the sensor includes:

[0036] Based on the deterministic error parameters, the inverse equation of the error model of the sensor is used to obtain the corrected measurement value of the sensor;

[0037] Based on the corrected measurement value of the sensor, the residual error, i.e., the random error, of the sensor is obtained.

[0038] Optionally, the random error is taken as a measurement value of a Kalman filtering algorithm, a Gaussian-Markov model is used to model the random error as a state value of the Kalman filtering algorithm; and a random error matrix and a driving noise covariance matrix are designed based on the state value, including:

[0039] The random error is taken as a measurement value of a Kalman filtering algorithm, and the random error includes a bias instability;

[0040] The Gaussian-Markov model is used to model the bias instability, and the modeled bias instability is defined as a state value of the Kalman filtering;

[0041] Based on the characteristics of the Gaussian-Markov model, two covariance matrices are designed, which are:

[0042] A bias instability covariance matrix, which describes the fluctuation range of the bias instability itself and reflects the uncertainty of the state value;

[0043] A driving noise covariance matrix, which describes the noise characteristics of driving the bias instability to change and corresponds to the process noise covariance in the Kalman filtering, and provides a basis for state prediction.

[0044] Optionally, based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix, time update and measurement update of the Kalman filtering algorithm are performed to correct the random error of the sensor, including:

[0045] The time update is:

[0046] State prediction: ; represents a state value at a previous time, represents the predicted state value at the current time, the elements of the state transition matrix A are the decay factors in modeling the bias instability, a driving noise, corresponding to the driving noise covariance matrix;

[0047] error covariance prediction: ; represents the error covariance at the previous time, represents the uncertainty of the state estimation at the current time, affected by the random error matrix; Q is the process noise, determined by the driving noise covariance matrix;

[0048] the measurement update is:

[0049] calculate the Kalman gain: ; C is the measurement matrix, and R is the noise covariance matrix, the weight of the predicted value and the measured value;

[0050] measurement equation update: ; is the corrected current state, i.e., the corrected bias instability;

[0051] update the error covariance matrix: .

[0052] In a second aspect of the present application, an error parameter estimation system of a sensor is provided, comprising:

[0053] a data module: six-position method is used to collect measurement data of the sensor, the sensor including a gyroscope and an accelerometer;

[0054] a deterministic error module: based on the measurement data, error modeling is performed on the sensor, and least squares method is used to fit the deterministic error parameters of the sensor;

[0055] an error compensation module: error compensation is performed according to the deterministic error parameters, and the random error of the sensor is obtained;

[0056] a setting module: the random error is taken as a measurement value of a Kalman filtering algorithm, a Gaussian-Markov model is used to model the random error as a state value of the Kalman filtering algorithm; based on the Gaussian-Markov model, a random error matrix and a driving noise covariance matrix are designed;

[0057] a random error module: based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix, time update and measurement update of the Kalman filtering algorithm are performed, and the random error of the sensor is corrected.

[0058] In a third aspect, the present application provides a terminal comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor is capable of executing the program to implement the method, or run the system.

[0059] In a fourth aspect, the present application provides a computer readable storage medium, which stores a computer program, wherein the program is capable of being executed by a processor to implement the method, or run the system.

[0060] The method for estimating error parameters of a gyroscope and an accelerometer provided by the present application first collects measurement data as samples, and then constructs error parameter models of the gyroscope and the accelerometer respectively. The least square method is used to fit the deterministic error parameters of the gyroscope and the accelerometer respectively, and then the Kalman filtering is combined with the Gauss-Markov model to estimate the random error parameters of the gyroscope and the accelerometer respectively. In a real-time measurement scenario, the deterministic and random error parameters estimated are used to compensate for the errors of the instruments, so as to obtain more accurate measurement data and improve the accuracy of applications such as attitude measurement.

[0061] Other technical effects brought by the additional features will be further described in the corresponding embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0062] Other features, objects, and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments with reference to the attached drawings:

[0063] Figure 1 A flow chart of a method for estimating error parameters of a sensor according to an exemplary embodiment is shown;

[0064] Figure 2 A sensor error type diagram according to an exemplary embodiment is shown;

[0065] Figure 3 A diagram of different errors according to an exemplary embodiment is shown;

[0066] Figure 4 A structure diagram of a system for estimating error parameters of a sensor according to an exemplary embodiment is shown. DETAILED DESCRIPTION

[0067] The present application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. 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 belong to the protection scope of the present application. The parts not described in detail in the following embodiments can be implemented by using the prior art.

[0068] There are mainly two types of error sources for inertial sensors: one is deterministic error, including scale factor bias, zero bias error and inter-axis installation misalignment; the other is random error, mainly manifested as zero bias instability and scale factor instability. With the continuous reduction of sensor manufacturing cost, the comprehensive performance index shows a downward trend. Based on the above problems, the error parameter estimation method of the sensor is provided to solve the above problems.

[0069] Referring to Figure 1 In an embodiment of the present application, an error parameter estimation method of a sensor includes:

[0070] Step 1, using six-position method to collect measurement data of the sensor, the sensor including a gyroscope and / or an accelerometer;

[0071] Specifically, the error of the gyroscope or the accelerometer can be estimated according to the measurement data of the gyroscope or the accelerometer respectively; or the error of the gyroscope can be estimated according to the combined measurement data of the gyroscope and the accelerometer.

[0072] Step 2, based on the measurement data, error modeling is performed on the sensor, and least square method is used for fitting the deterministic error parameters of the sensor;

[0073] Step 3, error compensation is performed according to the deterministic error parameters, and the random error of the sensor is obtained;

[0074] Step 4, the random error is taken as a measurement value of Kalman filtering algorithm, a Gaussian-Markov model is used for modeling the random error as a state value of the Kalman filtering algorithm; based on the Gaussian-Markov model, a random error matrix and a driving noise covariance matrix are designed;

[0075] Step 5, based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix, time update and measurement update of the Kalman filtering algorithm are performed, and the random error of the sensor is corrected.

[0076] Specifically, as shown in Figure 2 and Figure 3 The deterministic error parameters include bias error, scale factor error and installation error. The random error includes bias instability. For the G-related error in the deterministic error and the scale factor instability in the random error, their influence on the overall measurement accuracy is very small (the numerical magnitude is much lower than other main errors), in order to simplify the calculation process, balance the accuracy and efficiency, they are ignored in the error parameter estimation of the present application, and the error items which have more significant influence on the measurement results are focused on for accurate solution and compensation.

[0077] The above embodiments of the present application can overcome the error measurement caused by the instrument itself in real-time measurement, so as to obtain more accurate measurement data.

[0078] In order to obtain the measurement data of the sensor, the six-position method is used for measurement. The six-position method is a static data acquisition method in the field of inertial measurement, in which an inertial measurement unit (IMU) is placed in six specific spatial positions (i.e., three coordinate axes are respectively upward and downward). In some embodiments of the present application, in step 1, the measurement data of the gyroscope and the accelerometer are collected by using the six-position method, and the following steps can be used:

[0079] First, the inertial measurement unit integrated with the accelerometer and / or the gyroscope is installed on the calibration frame.

[0080] Then, the accelerometer and / or the gyroscope measurement data in six positions are collected alternately in each axis. Specifically:

[0081] When the X-axis is upward, collect and record the gyroscope data and the accelerometer data .

[0082] When the X-axis is downward, collect and record the gyroscope data and the accelerometer data .

[0083] When the Y-axis is upward, collect and record the gyroscope data and the accelerometer data .

[0084] When the Y-axis is downward, collect and record the gyroscope data and the accelerometer data .

[0085] When the Z-axis is upward, collect and record the gyroscope data and the accelerometer data .

[0086] When the Z-axis is downward, collect and record the gyroscope data and the accelerometer data .

[0087] It should be noted that the six-position method is the minimum number of positions for solving errors, and in other embodiments of the present application, the multi-position method can also be used to obtain the measurement data of the sensor.

[0088] In the above embodiments of the present application, the collected data comes from static test, relies on the earth's gravitational field and the angular velocity of rotation as a stable reference, the collection process is simple, low cost, and covers the working conditions of three-axis positive and negative directions. These collected data are mainly used for calibration of inertial measurement unit (IMU), which can provide original basis for solving key error parameters such as zero bias and scale factor of accelerometer and gyroscope, and help to distinguish and quantify these factors affecting measurement accuracy.

[0089] The above-mentioned scale factor and bias error can be calculated by basic processing of the collected data in some embodiments. Specifically, the scale factor error and bias error of the accelerometer are calculated as follows:

[0090] ;

[0091] ;

[0092] wherein g represents the gravitational acceleration, Av represents the average value, represents the current orientation of the corresponding accelerometer.

[0093] The scale factor error and bias error of the gyroscope are calculated as follows:

[0094] ;

[0095] ;

[0096] wherein, represents the current orientation of the corresponding gyroscope, represents the angular velocity of the earth's rotation.

[0097] The scale factor and bias error calculated by basic processing in the above embodiments can greatly reduce the interference with the measurement results in the early stage. However, the above process cannot obtain installation error. Therefore, in order to obtain all the deterministic errors of the accelerometer (including installation error), in some specific embodiments of the present application, in step 2, the sensor is error modeled based on the measurement data, and the least square method is used to fit the deterministic error parameters of the sensor. For different sensors, the following methods can be used to realize them respectively.

[0098] Specifically, when the sensor is an accelerometer, step 2 adopts the following steps:

[0099] S2011, an error model of single-axis accelerometer is established:

[0100] ;

[0101] wherein, represents the output of the accelerometer, i.e. the above-mentioned accelerometer data 、 , represents the actual acceleration, represents the scale factor error, represents the bias error, represents the scale factor instability, represents the bias instability, represents the sensor noise.

[0102] Similarly, the error models for the y-axis and z-axis can be represented as:

[0103] ;

[0104] ;

[0105] The error model structures for each axis are the same, with only the subscript distinguishing the different axes.

[0106] S2012, establish a three-axis accelerometer error equation set:

[0107] ;

[0108] where M xy , M xz , M yx , M yz , M zx , M zy represent the installation error. Where M xy , M xz , M yx , M yz , M zx , M zy represent the installation error, and the subscript ab represents the coupling projection of the b-axis on the a-axis, and the a-axis represents the x, y, z axis, and the b-axis represents the x, y, z axis.

[0109] S2013, based on the above three-axis accelerometer error equation set, using the least squares method, the accelerometer fitting formula is obtained:

[0110] ;

[0111] where represents the accelerometer all deterministic error parameter matrix, represents the matrix composed of accelerometer data, represents the reference input matrix;

[0112] Specifically, ;

[0113] ;

[0114] ;

[0115] In particular, when the sensor is an accelerometer, step 2 adopts the following steps:

[0116] S2021, the error model of single-axis gyroscope is established as:

[0117] ;

[0118] wherein, represents the gyroscope output, i.e. the gyroscope data mentioned above 、 , represents the actual angular rate, represents the proportional factor error, represents the bias error, represents the proportional factor instability, represents the bias instability, represents the gravity acceleration g related coefficient, represents the sensor noise.

[0119] Similarly, the gyroscope error models of y-axis and z-axis can be respectively expressed as:

[0120] ;

[0121] ;

[0122] The error model structures of each axis are the same, and only the subscripts distinguish different axial directions.

[0123] S2022, the error model equation set of three gyroscopes is established as:

[0124] ;

[0125] wherein M xy , M xz , M yx , M yz , M zx , M zy represent the installation errors.

[0126] S2023, based on the above three-axis gyroscope error model equation set, the least square method is adopted,

[0127] ;

[0128] wherein represents the matrix of all deterministic error parameters of the gyroscope, represents the matrix composed of gyroscope data, This represents the reference input matrix.

[0129] Specifically,

[0130] ;

[0131] ;

[0132] ;

[0133] 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.

[0134] 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:

[0135] S2031, the error model for a single-axis gyroscope is established as follows:

[0136] ;

[0137] 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.

[0138] Similarly, the gyroscope error models for the y-axis and z-axis can be expressed as follows:

[0139] ;

[0140] ;

[0141] The error model structures for each axis are identical, with only subscripts distinguishing different axes.

[0142] S2032, the error model equations for the three gyroscopes are established as follows:

[0143] ;

[0144] wherein M xy , M xz , M yx , M yz , M zx , M zy represents installation error.

[0145] S2033, based on the above three-axis gyroscope error model equation set, using the least square method,

[0146] ;

[0147] wherein represents the gyroscope all deterministic error parameter matrix, represents the gyroscope data matrix, represents the reference input matrix. The form of each matrix here is consistent with that in S2013.

[0148] Specifically, the determination process of the solution of the above accelerometer and gyroscope deterministic error is derived by the following process:

[0149] From S202 formula, ignoring random error, the following formula is obtained,

[0150] ;

[0151] From the least square equation, the approximate analytical solution of the equation like is

[0152] ;

[0153] Therefore, the solutions of the accelerometer and gyroscope deterministic error in S205 and S206 can be derived respectively.

[0154] The above embodiments of the present application establish single-axis and three-axis gyroscope and accelerometer error models, and the proportional factor error, bias error, installation error, proportional factor instability, bias instability, sensor noise and gyroscope gravity acceleration correlation coefficient and other error terms are included in the model. Then, the least square method is used to fit the error parameters, which can systematically and comprehensively quantify various errors of the two types of sensors. This way can accurately extract deterministic error parameters, provide reliable basis for subsequent error compensation, effectively improve the accuracy of sensor measurement data, and lay the foundation for precise applications based on these data (such as carrier space attitude measurement).

[0155] After obtaining the deterministic error parameters through the above process, error compensation is performed. In some specific embodiments of the present application, step 3, error compensation is performed according to the deterministic error parameters to obtain the random error of the sensor, including the following steps:

[0156] S301, based on the deterministic error parameters, through the inverse equation of the error model of the single-axis accelerometer or gyroscope, the corrected accelerometer or gyroscope measurement value is obtained:

[0157] ;

[0158] ;

[0159] the corrected acceleration measurement value of the accelerometer output after being compensated by the deterministic error; represents the original measurement value of the accelerometer; the corrected acceleration measurement value of the gyroscope output after being compensated by the deterministic error; represents the original measurement value of the gyroscope;

[0160] S302, based on the corrected accelerometer or gyroscope measurement value, the acceleration residual error, i.e. random error , the residual error of the gyroscope, i.e. random error .

[0161] Of course, the other two axes use the same method as above to obtain the random error.

[0162] The above embodiment, by S301, using the deterministic error parameters and the inverse equation, the original measurement value of the accelerometer and the gyroscope is corrected, the influence of the deterministic error such as the scale factor and the bias is removed, and the measurement result closer to the true value is obtained; S302, based on the corrected value, the residual error (random error) is calculated, which is prepared for subsequent processing of random error by Kalman filtering.

[0163] In order to correct the random error, in some specific embodiments of the application, step 4, the random error is taken as the measurement value of the Kalman filtering algorithm, the Gaussian-Markov model is used to model the random error as the state value of the Kalman filtering algorithm; based on the Gaussian-Markov model, the random error matrix and the driving noise covariance matrix are designed, which can use the following steps:

[0164] S401, taking the random error as the measurement value of the Kalman filtering algorithm , the random error includes bias instability;

[0165] S402, using the Gaussian-Markov model to model the bias instability, which is defined as the state value of the Kalman filtering x k .

[0166] S403, and based on the characteristics of the Gaussian-Markov model, two covariance matrices are designed:

[0167] bias instability covariance matrix, describing the fluctuation range of bias instability itself, reflecting the uncertainty of state value x k

[0168] ;

[0169] drive noise covariance matrix, describing the noise characteristics of driving bias instability change, corresponding to process noise covariance Q in Kalman filtering, providing basis for state prediction:

[0170] ;

[0171] wherein, dt denotes a sampling period, Tc denotes a sensor time constant, denotes drive noise.

[0172] The above embodiments of the present application utilize model adaptation of the physical characteristics of bias instability to make the state value of Kalman filtering accurately describe error change, solving the problem that traditional methods are difficult to dynamically capture error rules; by deriving bias instability covariance and drive noise covariance, key parameters such as process noise Q are provided for Kalman filtering, so that the filtering can quantify the "error fluctuation range" and "prediction uncertainty", solving the problem of precision limitation caused by unknown uncertainty in error compensation.

[0173] On the basis of the parameters designed in the above S401-S403, further repair random error. In some specific embodiments of the present application, based on the measurement value, the state value, the random error matrix and the drive noise covariance matrix, the time update and the measurement update of the Kalman filtering algorithm are performed, and the random error of the sensor is corrected, specifically:

[0174] Time update is:

[0175] State prediction: ; denotes the state at the last time, denotes the predicted state at the current time, the elements of the state transition matrix A are , drive noise, corresponding to ;

[0176] Error covariance prediction: ; denotes the error covariance at the last time, is the uncertainty of the state estimation at the current time, and Q is the process noise, which is determined by the drive noise covariance matrix;

[0177] ​The measurement update is:

[0178] The Kalman gain is calculated: ; C is the measurement matrix, and R is the noise covariance matrix, The weight of the predicted value and the measurement value;

[0179] The measurement equation update is: ; is the corrected current state, i.e., the corrected bias instability;

[0180] The error covariance matrix is updated: .

[0181] The above embodiments of the present application, with the help of time update (state and error covariance prediction), measurement update (Kalman gain calculation, state and covariance matrix correction), realize real-time estimation and dynamic correction of bias instability, effectively suppress random error interference, and improve the stability and accuracy of sensor measurement data, providing reliable support for attitude measurement and other applications based on the data.

[0182] In some specific embodiments of the present application, the inertial measurement unit has three accelerometers and three gyroscopes for measuring linear acceleration and angular rate around the x, y and z axes. Therefore, the bias instability of the six sensors is estimated using the Kalman filter. For this purpose, the state vector contains six states, which respectively represent the bias instability of the x gyroscope, the y gyroscope, the z gyroscope, the x accelerometer, the y accelerometer and the z accelerometer. Because the random error output by the error compensation model corresponds to the measurement information in the Kalman filter, and the six axis errors of the gyroscopes and accelerometers are independent of each other, the measurement value of each axis is directly mapped by the error state of the corresponding axis without inter-axis coupling. Therefore, using the unit matrix as the measurement matrix can make the measurement value of each axis correspond to the error state one by one, accurately transfer the error information of each axis, adapt to the processing scene of multiple independent axis errors, and ensure the accuracy of the Kalman filter in estimating the random error of each axis.

[0183] Specifically,

[0184] ;

[0185] wherein the left side of the equation is the actual measurement value, and the rightmost side is the random noise; B represents the bias instability of the gyroscopes and accelerometers, and the output of the error compensation model is used as the measurement value in the Kalman filter algorithm, so the unit matrix is selected as the measurement matrix. Then the above formula can be written as: , represents the measurement value, is the measurement matrix, is the bias instability, for the random noise.

[0186] The random noise of the gyroscopes and accelerometers is used to determine the measurement noise covariance matrix R. Likewise, the 3σ values of the gyroscope and accelerometer biases instability are used to constitute the initial values of the error covariance matrix P.

[0187] In particular, assuming k = 0, the initialization , the representation of the estimation error, the uncertainty of the state estimation and the error covariance is:

[0188] ;

[0189] ;

[0190] wherein represents the real state, represents the estimated state, the maximum value of the real state being the bias instability times. Therefore, if the initial state is equal to zero, according to the above formula, the maximum value of the error can be the bias instability times. Therefore, the initial value of the diagonal elements of the error covariance P k becomes times the gyroscope and accelerometer bias instability times. There is no correlation between the state and the error. Therefore, the non-diagonal elements of P k , R, Q are equal to zero.

[0191] ;

[0192] ;

[0193] ;

[0194] P0is the state estimation error covariance matrix, initial iteration value. R is the measurement noise covariance matrix. Q is the process noise covariance matrix.

[0195] In the above embodiments of the present application, by specifying the specific form of the Kalman filter measurement equation, taking the error compensation model output as the measurement value and selecting a unit matrix as the measurement matrix, the mapping relationship between the measurement value and the state value is clearly established. Meanwhile, based on the 3σ value of random noise density and bias instability, the specific form of the measurement noise covariance matrix R, the error covariance initial matrix P0 and the process noise covariance matrix Q is determined, and the non-diagonal elements are specified as zero, which provides accurate parameter basis for the initialization and iterative calculation of the Kalman filter, ensures the accuracy and reliability of the estimation of the bias instability of the gyroscope and the accelerometer, and lays a foundation for the effective processing of random errors. Wherein, 3σ represents 3 times of the standard deviation, representing 99.7% confidence, which is used to initialize the covariance matrix in order to have a better estimation of the uncertain error, and also provides a more reliable starting point for the Kalman filter iteration.

[0196] Based on the same technical concept, in other embodiments of the present application, a sensor-based error parameter estimation system 100 is also provided, as shown in Figure 4 The system comprises:

[0197] The data module 110 collects the measurement data of the sensor by using the six-position method, and the sensor comprises a gyroscope and / or an accelerometer.

[0198] The deterministic error module 120 models the error of the sensor based on the measurement data, and uses the least square method to fit the deterministic error parameters of the sensor.

[0199] The error compensation module 130 compensates the error according to the deterministic error parameters to obtain the random error of the sensor.

[0200] The setting module 140 takes the random error as the measurement value of the Kalman filter algorithm, models the random error by using the Gauss-Markov model as the state value of the Kalman filter algorithm, and designs the random error matrix and the driving noise covariance matrix.

[0201] The random error module 150 performs time update and measurement update of the Kalman filter algorithm based on the measurement value, the state value, the random error matrix and the driving noise covariance matrix, and corrects the random error of the sensor.

[0202] In the above examples of the present application, each module / unit can refer to the implementation technology of the corresponding steps of the sensor-based error parameter estimation and error compensation method in the above embodiments, which will not be described here.

[0203] In the above embodiments, each preferred feature can be used alone in any embodiment, and can also be used in combination on the premise of not conflicting. In addition, the parts not described in detail in the embodiments can be implemented by using the prior art.

[0204] Based on the same technical concept, in other embodiments of the present application, a terminal is also provided, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor is configured to execute the program to implement the error parameter estimation method of the sensor or to run the error parameter estimation system of the sensor.

[0205] Based on the same technical concept, in other embodiments of the present application, a computer readable storage medium is also provided, which stores a computer program, and the program is executable on a processor to implement the error parameter estimation method of the sensor or to run the error parameter estimation system of the sensor.

[0206] Optionally, the memory is configured to store the program; the memory can comprise a volatile memory (English: volatile memory), such as a random access memory (English: random-access memory, abbreviated as RAM), for example, a static random access memory (English: static random-access memory, abbreviated as SRAM), a double data rate synchronous dynamic random access memory (English: Double Data Rate Synchronous Dynamic Random Access Memory, abbreviated as DDR SDRAM), etc.; the memory can also comprise a non-volatile memory (English: non-volatile memory), such as a flash memory (English: flash memory). The memory is configured to store computer programs (such as application programs, functional modules, etc. for implementing the above method), computer instructions, etc. The above computer programs, computer instructions, etc. can be stored in one or more memories. And the above computer programs, computer instructions, data, etc. can be called by the processor.

[0207] The above computer programs, computer instructions, etc. can be stored in one or more memories. And the above computer programs, computer instructions, data, etc. can be called by the processor.

[0208] The processor is configured to execute the computer program stored in the memory to implement each step in the method related to the above embodiments. For details, please refer to the related description in the above method embodiments.

[0209] The processor and the memory can be an independent structure, or an integrated structure. When the processor and the memory are independent structures, the memory and the processor can be coupled and connected through a bus.

[0210] Those skilled in the art will appreciate that embodiments of the application can be readily used as software, hardware, or a combination of software and hardware. In one embodiment, the application can be implemented in software and can be stored on a computer readable medium, which can include random access memory (RAM), read only memory (ROM), magnetic disk or optical disk, or the like. The application can also be implemented as a combination of both software and hardware. In addition, the application can be implemented as a computer program product that can include a computer readable medium having stored computer program code thereon.

[0211] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0212] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0213] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0214] The above description is implemented by way of specific embodiments. It is to be understood that the application is not limited to these specific embodiments. Various modifications and changes can be made thereto without departing from the essence of the application. The scope of the application is defined by the appended claims.

Claims

1. A method of estimating an error parameter of a sensor, characterized by, include: S1. The measurement data of the sensor is acquired using a six-position method, wherein the sensor includes a gyroscope and / or an accelerometer; S2. Based on the measurement data, perform error modeling on the sensor and fit the deterministic error parameters of the sensor using the least squares method; the deterministic error parameters include bias error, scaling factor error, and installation error. When the sensor is a gyroscope, the deterministic error also includes G-correlation error. S3. Perform error compensation based on the deterministic error parameters to obtain the random error of the sensor, including: obtaining the corrected measurement value of the sensor based on the deterministic error parameters through the inverse equation of the sensor's error model; and obtaining the residual error of the sensor, i.e., the random error, based on the corrected measurement value of the sensor. S4. Using the random error as the measurement value of the Kalman filter algorithm, a Gauss-Markov model is used to model the random error, which is then used as the state value of the Kalman filter algorithm. Based on the Gauss-Markov model and the state value, the random error matrix and the driving noise covariance matrix are designed, 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 the driving bias instability change, which corresponds to the process noise covariance in Kalman filtering and provides a basis for state prediction. S5. Based on the measured value, the state value, the random error matrix, and the driving noise covariance matrix, perform time updates and measurement updates using a Kalman filter algorithm to correct the random error of the sensor, including: The time update is as follows: State prediction: denotes the state value at the previous time instant, denotes the predicted state value at the current time instant, the elements of the state transition matrix A are biasing instability modeling decay factors, is the driving noise, corresponding to the driving noise covariance matrix; Error covariance prediction: denotes the error covariance at the previous time instant, for predicting the uncertainty of the state estimate at the current time instant, influenced by the random error matrix; Q is the process noise, determined by the driving noise covariance matrix; The measurement is updated as follows: The Kalman gain is calculated as: ; C is the measurement matrix and R is the noise covariance matrix, represents the Kalman gain, which determines the weight assignment of the predicted value and the measured value; Measurement equation update: for the corrected current state, i.e. the corrected bias instability; Updating the error covariance matrix: (I- C) .

2. The method of claim 1, wherein 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. ； wherein, represents an accelerometer output, represents an actual acceleration, represents a scale factor error, represents a bias error, represents a scale factor instability, represents a bias instability, represents an accelerometer noise, d represents 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: ； wherein M xy , M xz , M yx , M yz , M zx , M zy represents an installation error, the subscript ab represents a coupling projection of the b-axis on the a-axis, a represents an x, y, z axis, and b represents an x, y, z axis; 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 method of claim 1, wherein 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. ； wherein, represents the gyroscope output, represents the actual angular rate, represents the scale factor error, represents the bias error, represents the scale factor instability, represents the bias instability, represents the gyroscope noise, 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: + ； wherein M xy , M xz , M yx , M yz , M zx , M zy represents an installation error, the subscript ab represents a coupling projection of the b-axis on the a-axis, a represents the x, y, z-axis, and b represents the x, y, z-axis; Based on the three-axis gyroscope error model equation set, the least square method is used to obtain the gyroscope fitting formula, and all the deterministic error parameters of the gyroscope are obtained.

4. The method of claim 1, wherein Based on the three-axis gyroscope error model equation set, the least square method is used to obtain the gyroscope fitting formula, and all the deterministic error parameters of the gyroscope are obtained. The error model of the x, y, and z single-axis gyroscopes is established: ； wherein represents a gyroscope output, represents an actual angular rate, represents a scale factor error, represents a bias error, represents a scale factor instability, represents a bias instability, represents a gravity acceleration g correlation coefficient, represents a gyroscope noise, d represents x, y, or z; Based on the three-axis gyroscope error model equation set, the least square method is used to obtain the gyroscope fitting formula, and all the deterministic error parameters of the gyroscope are obtained. ； ； wherein, , , is the value of the accelerometer after compensation of the error, i.e. the actual acceleration; wherein M xy , M xz , M yx , M yz , M zx , M zy denotes the mounting error, the index ab denotes the coupled projection of the b-axis on the a-axis, a denotes the x, y, z axis, b denotes the x, y, z axis; Based on the three-axis gyroscope error model equation set, the least square method is used to obtain the gyroscope fitting formula, and all the deterministic error parameters of the gyroscope are obtained.

5. A system for estimating error parameters of a sensor for implementing the method of estimating error parameters of a sensor according to any one of claims 1 to 4, characterized in that, The data module collects the measurement data of the sensor using the six-position method, and the sensor includes a gyroscope and an accelerometer. The deterministic error module models the error of the sensor based on the measurement data, and uses the least square method to fit the deterministic error parameters of the sensor. The error compensation module compensates the error based on the deterministic error parameters to obtain the random error of the sensor. The setting module sets the random error as the measurement value of the Kalman filtering algorithm, uses the Gaussian-Markov model to model the random error as the state value of the Kalman filtering algorithm, and designs the random error matrix and the driving noise covariance matrix based on the Gaussian-Markov model. The random error module performs time update and measurement update of the Kalman filtering algorithm based on the measurement value, the state value, the random error matrix, and the driving noise covariance matrix, and corrects the random error of the sensor. The processor executes the program to execute the method of any one of claims 1-4, or run the system of claim 5.

6. A terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The program is executed by the processor to execute the method of any one of claims 1-4, or run the system of claim 5.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that ​

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