A least square prediction correction Kalman filter high-precision signal conditioning method

Abstract

The application provides a high-precision signal conditioning method of least square prediction correction Kalman filtering, comprising the following steps: defining a nonlinear model and an ellipsoid set, analyzing process noise, measurement noise and an initialized state ellipsoid set, and constructing an extended set member filtering model; performing recursive calculation according to the extended set member filtering model to obtain an extended set member filtering method improved based on least square method, wherein the recursive calculation comprises time updating, prediction error and measurement updating; based on the extended set member filtering method improved based on least square method, designing a software filtering module in a current-voltage sensing system, constructing an ellipsoid set to cover a real state set of current and voltage, and obtaining accurate current-voltage sampling values. The application adopts least square method to construct a prediction error model on line, applies to ellipsoid set updating of extended set member Kalman filtering, solves the problem of ellipsoid set updating stagnation of the filtering algorithm when the model mutates and the working condition changes, and improves the effectiveness and accuracy of sampling data.

Description

Technical Field

[0001] This invention relates to the field of sensing technology, and in particular to a high-precision signal conditioning method using least squares prediction-corrected Kalman filtering. Background Technology

[0002] Among the various information detected by current and voltage signal sensors, the majority are non-electrical signals. Non-electrical signals refer to parameters other than electrical quantities, such as pressure, flow rate, size, offset, mass, force, instantaneous speed, rotational speed, temperature, pH, etc. Non-electrical signals cannot be directly measured using general electrical instruments and meters because these instruments require input signals as electrical signals and can only detect electrical quantities. Non-electrical signals must be converted into electrical signals with a certain correlation before accurate measurement. The component that performs this conversion technology is the current and voltage signal sensor. Therefore, a current and voltage signal sensor is a measuring device that can sense the required measured quantity and convert it into a definite and easily processed electrical signal (such as voltage, current, frequency, etc.) with a certain precision.

[0003] The current and voltage sensing system mainly includes a signal detection module, a hardware filtering module, an isolation amplification module, a sampling module, and a software filtering module. The software filtering module provides signal processing strategies to support the sampling accuracy of the sensing signal. For example, the existing Chinese patent application number CN201610120754.X—"Wireless Positioning of Gas Sources Based on Nonlinear Least Squares Method and Extended Set Membership Filtering"—specifically discloses the following steps: using gas concentration information detected by a wireless sensor network to pre-position the gas source using the least squares method; calculating the initial feasible set of the extended set membership filtering algorithm based on the pre-positioned location obtained by the least squares method; substituting the pre-positioned location and the initial feasible set into the extended set membership filtering algorithm, iterating cyclically to obtain the gas source positioning result. Although this patent uses the least squares method to pre-locate the gas source position and back-calculates the initial feasible set of the extended set member filter algorithm to ensure that the true position is included in the initial feasible set and to ensure the numerical stability of the algorithm, this patent only uses the least squares method to pre-locate the initial position at the beginning of the algorithm. That is, it only affects the initial ellipsoid size of the extended set member Kalman filter. Moreover, its algorithm is mainly applied to spatial positioning, and some parts of the algorithm are run offline. It needs to collect a large amount of detection data in advance. When the model changes abruptly or the working conditions change, the ellipsoid set update will stagnate, and the accuracy will be insufficient. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a high-precision signal conditioning method for least squares predictive correction Kalman filtering, which realizes online real-time accurate signal conditioning.

[0005] This invention is implemented as follows: A high-precision signal conditioning method using least squares prediction-corrected Kalman filtering includes the following steps:

[0006] Step S1: Define the nonlinear model and ellipsoid set, analyze process noise, measurement noise and initial state ellipsoid set, and construct the extended set member filtering model;

[0007] Step S2: Perform recursive calculations based on the extended set member filtering model to obtain an extended set member filtering method improved by least squares.

[0008] Step S3: Based on the extended set member filtering method improved by the least squares method, design a software filtering module in the current and voltage sensing system. By constructing an ellipsoidal set to cover the real state set of current and voltage, accurate current and voltage sample values ​​are obtained.

[0009] Furthermore, step S1 specifically includes:

[0010] Step S11: Define the nonlinear system model as follows:

[0011]

[0012] Where x is the state variable, y is the observation variable, w is the process noise, ν is the measurement noise, f(.) is the system state transition function, h(.) is the system measurement function, and k is the sampling time of the discrete system;

[0013] Step S12: Define the ellipsoid set as:

[0014] E(a,P,σ)={x∈R n :(xa) T P -1 (xa)≤σ 2};

[0015] Where a is the focus of the ellipsoid, P is the positive definite symmetric envelope matrix of the ellipsoid shape, σ is the radius of the ellipsoid, and R is the focal point of the ellipsoid. n Let n be the vector space of the set of real numbers;

[0016] Step S13: Map the process noise w and measurement noise ν to an ellipsoid set:

[0017]

[0018] Where Q is the process noise covariance matrix, R is the measurement noise covariance matrix, and σ v To measure the radius of the ellipsoid of the noise ν, σ w Let w be the radius of the ellipsoid of the process noise w;

[0019] Step S14: Taylor expansion of the nonlinear system:

[0020]

[0021] Where x(k) is the state variable, R represents the estimated value of the state variable. f (.) and R h (.) represents the higher-order linearization error, h(.) is the system measurement function, and F(k) and H(k) are the correlation Jacobian matrices of the state transition function and the measurement function, respectively. The specific calculation method is as follows:

[0022]

[0023] Mapping higher-order linear errors to an ellipsoid set:

[0024]

[0025] in, It is a higher-order linearization error of process noise and measurement noise. It is a higher-order linearized error ellipsoid set of process noise and measurement noise. It is the radius of the higher-order linearized error ellipsoid set of process noise and measurement noise;

[0026] Integrating higher-order linear errors and noise, a noise ellipsoid set is defined, i.e., an extended set-member filtering model:

[0027]

[0028] in, It is an ellipsoidal set that integrates higher-order linear errors and process noise. It is an ellipsoidal set that integrates higher-order linear errors and measurement noise. It is a noise variable that integrates higher-order linear error and measurement noise. It is a noise variable that integrates higher-order linear error and process noise;

[0029] Step S15: Define the initial state ellipsoid set E(0) and the initial observation ellipsoid set S(0) as follows:

[0030]

[0031] in, To estimate the variables for extended set membership filtering, The error covariance matrix is ​​used to integrate higher-order linear errors and measurement noise, where γ is the radius of the ellipsoid set integrating higher-order linear errors and measurement noise, and e r This represents the error value due to mismeasurement.

[0032] Furthermore, the recursive calculation in step S2 includes time update, prediction error, and measurement update. Step S2 specifically includes:

[0033] Step S21: Obtain the next-step prediction ellipsoid set from the state ellipsoid set of the previous time step, and perform time update:

[0034] Step S211: Calculate the predicted values ​​of the state variables:

[0035]

[0036] Step S212: Calculate the radius of the ellipsoid.

[0037] σ 2 (k|k-1)=σ(k-1);

[0038] Step S213: Calculate the shape matrix:

[0039]

[0040] The parameter p(k) is recursively calculated using the minimum trace method of the externally bounded ellipsoid:

[0041]

[0042] Where tr(.) is the sum of the diagonal elements of the square matrix, and is the trace of the matrix;

[0043] Step S22: Calculate the prediction error by fitting the rate of change of error using the recursive least squares method.

[0044] Step S221: Calculate the current error:

[0045]

[0046] Step S222, Rate of change of fitting error using recursive least squares method:

[0047]

[0048] Among them, P r (k) is the covariance matrix, and θ r (k)=[θ r1 (k)θ r2 (k)] T θ r1 (k) represents the current rate of change of error, θ r2 (k) represents the rate of change of the prediction error, i.e., θ r (k) indicates that θ is included. r1 (k), θ r2 (k) A vector of two variables, x r (k) = [1, m] T, where m is the number of sampling periods;

[0049] Step S223: Estimate the prediction error value using the rate of change of the prediction error and the current error.

[0050]

[0051] Where, θ base The minimum baseline value for the application prediction error is set, where m is the prediction step size and e(k) is the current error.

[0052] Step S23: Update the gain matrix, optimal estimate, ellipsoid shape matrix, and ellipsoid radius using the state ellipsoid set and the observation ellipsoid set to achieve measurement update:

[0053] Step S231: Update the observation ellipsoid set:

[0054]

[0055] Where γ is the set minimum ellipsoid radius;

[0056] Step S232: Update parameter λ(k) and optimize the upper bound of the ellipsoid:

[0057]

[0058] Where g(k) is the observation variable error covariance matrix G(k)=H(k)P(k|k-1)H T The maximum singular value of (k);

[0059] Step S233: Update the gain matrix:

[0060]

[0061] Step S234: Update the ellipsoid shape matrix:

[0062]

[0063] Step S235: Update the ellipsoid radius:

[0064]

[0065] Step S236: Calculate the optimal estimate:

[0066]

[0067] The above steps implement an extended set membership filtering strategy based on the least squares method, which effectively improves the convergence speed of the filtering algorithm.

[0068] Furthermore, the software filtering module specifically performs the following operations:

[0069] Step S31: Based on the current signal I output by the sampling module in the current and voltage sensing system... i and voltage signal U i The characteristic formula is used to derive the relational equation combining the discrete target signals at three consecutive time points;

[0070] The characteristic formula is:

[0071]

[0072] The relationship between the discrete target signals at three consecutive time points, derived from the aforementioned characteristic formula, is as follows:

[0073]

[0074] Where A1 and A2 are the amplitudes of the current and voltage signals, and T s f1 and f2 are the sampling time and the AC current and voltage frequencies, respectively. For current and voltage phase;

[0075] Step S32: Based on the above equations, establish the following state model and observation model:

[0076]

[0077] Where w is the error caused by model mismatch, and ν is the error caused by sampling noise;

[0078] Step S33: Initialize the state ellipsoid set and observation ellipsoid set And calculate the Jacobian matrices F and H;

[0079] Step S34: During online operation, recursive real-time filtering is achieved through three parts: time update, prediction error, and measurement update. The state ellipsoid set and observation ellipsoid set are updated using the iterative update method from steps 231 to 235, and the optimal estimates of current and voltage I are further calculated. r and U r :

[0080]

[0081] Furthermore, the current and voltage sensing system also includes a current sensing subsystem and a voltage sensing subsystem. The current sensing subsystem and the voltage sensing subsystem respectively process the signals they collect, and then input them into the software filtering module to construct an ellipsoidal set to cover the real state set of current and voltage, thereby obtaining accurate current and voltage sample values.

[0082] Furthermore, the current sensing subsystem includes a current detection module, a hardware filtering module, an isolation amplification module, and a sampling module. The hardware filtering module uses a second-order low-pass filter to effectively filter out high-frequency noise signals. The isolation amplification module uses electrical isolation, separated by an isolation barrier with extremely strong electromagnetic interference resistance. The sampling module specifically uses a 16-bit high-speed parallel interface for digital sampling. The current sensing subsystem specifically performs the following operations:

[0083] The primary current is converted to the secondary current in the current detection module to obtain the current I. s The current signal is converted into a voltage signal U1 by a resistor, then amplified to obtain U2, then filtered by a hardware filter module to obtain U3, then isolated and amplified to obtain U4, and finally sampled by a high-speed sampling module. The resulting digital signal is used to calculate the sampled current signal I based on the conditioning circuit structure. i The input is processed by a software filtering module for high-precision filtering.

[0084] Furthermore, the voltage sensing subsystem includes a voltage detection module, a hardware filtering module, an isolation amplification module, and a sampling module. The hardware filtering module uses a second-order low-pass filter to effectively filter out high-frequency noise signals. The isolation amplification module uses electrical isolation, separated by an isolation barrier with extremely strong electromagnetic interference resistance. The sampling module specifically uses a 16-bit high-speed parallel interface for digital sampling. The voltage sensing subsystem specifically performs the following operations:

[0085] The voltage amplitude is adjusted by the transformer in the voltage detection module to obtain U. s Then, U5 is calculated using a capacitor voltage divider structure, U6 is obtained after passing through a hardware filtering module, and U7 is obtained after passing through an isolation amplification module. U7 is then acquired by a high-speed sampling module, and the resulting digital signal is used to calculate the sampling voltage signal U based on the conditioning circuit structure. i The input is processed by a software filtering module for high-precision filtering.

[0086] The present invention has the following advantages:

[0087] 1. The least squares method is used to construct the prediction error model online and apply it to the ellipsoid set update of the extended set member Kalman filter. This invention does not require data collection in advance and is implemented online, which solves the problem of ellipsoid set update stagnation when the filtering algorithm changes due to model mutation and operating conditions.

[0088] 2. A least-squares extended set member Kalman filtering strategy suitable for high-precision current and voltage sensing systems is proposed to accelerate the coverage of the state set of the sensing signal by the ellipsoid set, thereby improving the effectiveness and accuracy of the sampled data. Attached Figure Description

[0089] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0090] Figure 1 This is a flowchart illustrating the execution process of the method of the present invention.

[0091] Figure 2 This is a schematic diagram illustrating the execution of the least-squares-based improved member Kalman filter algorithm in the current and voltage sensing system of this invention.

[0092] Figure 3 This is a schematic diagram of the current sensing system structure in an embodiment of the present invention.

[0093] Figure 4 This is a schematic diagram of the voltage sensing system structure in an embodiment of the present invention. Detailed Implementation

[0094] The overall design concept of the technical solution in this application embodiment is as follows: For the first time, the recursive least squares method is used to construct the prediction error model online, and the prediction error is substituted into the iterative calculation of the extended set member Kalman filter to accelerate the update speed of the middle ellipsoid set and improve the accuracy of the filtering algorithm. An extended set member Kalman filter strategy with least squares improvement suitable for high-precision current and voltage sensing systems is designed. By fitting the system prediction error model in real time, the measurement error of the sensing system is reduced. The prediction error is applied to the ellipsoid set update of the extended set member Kalman filter to improve the measurement accuracy of current and voltage.

[0095] Please refer to Figures 1 to 4 This invention provides a high-precision signal conditioning method using least squares prediction-corrected Kalman filtering, comprising the following steps:

[0096] Step S1: Define the nonlinear model and ellipsoid set, analyze process noise, measurement noise and initial state ellipsoid set, and construct the extended set member filtering model;

[0097] Step S2: Perform recursive calculations based on the extended set member filtering model to obtain an extended set member filtering method improved by least squares.

[0098] Step S3: Based on the extended set member filtering method improved by the least squares method, design a software filtering module in the current and voltage sensing system. By constructing an ellipsoidal set to cover the real state set of current and voltage, accurate current and voltage sample values ​​are obtained.

[0099] Preferably, step S1 specifically includes:

[0100] Step S11: Define the nonlinear system model as follows:

[0101]

[0102] Where x is the state variable, y is the observation variable, w is the process noise, ν is the measurement noise, f(.) is the system state transition function, h(.) is the system measurement function, and k is the sampling time of the discrete system;

[0103] Step S12: Define the ellipsoid set as:

[0104] E(a,P,σ)={x∈R n :(xa) T P -1 (xa)≤σ 2};

[0105] Where a is the focus of the ellipsoid, P is the positive definite symmetric envelope matrix of the ellipsoid shape, σ is the radius of the ellipsoid, and R is the focal point of the ellipsoid. n Let n be the vector space of the set of real numbers;

[0106] Step S13: Map the process noise w and measurement noise ν to an ellipsoid set:

[0107]

[0108] Where Q is the process noise covariance matrix, R is the measurement noise covariance matrix, and σ v To measure the radius of the ellipsoid of the noise ν, σ w Let w be the radius of the ellipsoid of the process noise w;

[0109] Step S14: Taylor expansion of the nonlinear system:

[0110]

[0111] Where x(k) is the state variable, R represents the estimated value of the state variable. f (.) and R h (.) represents the higher-order linearization error, h(.) is the system measurement function, and F(k) and H(k) are the correlation Jacobian matrices of the state transition function and the measurement function, respectively. The specific calculation method is as follows:

[0112]

[0113] Mapping higher-order linear errors to an ellipsoid set:

[0114]

[0115] in, It is a higher-order linearization error of process noise and measurement noise. It is a higher-order linearized error ellipsoid set of process noise and measurement noise. It is the radius of the higher-order linearized error ellipsoid set of process noise and measurement noise;

[0116] Integrating higher-order linear errors and noise, a noise ellipsoid set is defined, i.e., an extended set-member filtering model:

[0117]

[0118] in, It is an ellipsoidal set that integrates higher-order linear errors and process noise. It is an ellipsoidal set that integrates higher-order linear errors and measurement noise. It is a noise variable that integrates higher-order linear error and measurement noise. It is a noise variable that integrates higher-order linear error and process noise;

[0119] Step S15: Define the initial state ellipsoid set E(0) and the initial observation ellipsoid set S(0) as follows:

[0120]

[0121] in, To estimate the variables for extended set membership filtering, The error covariance matrix is ​​used to integrate higher-order linear errors and measurement noise, where γ is the radius of the ellipsoid set integrating higher-order linear errors and measurement noise, and e r This represents the error value due to mismeasurement.

[0122] Preferably, the recursive calculation in step S2 includes time update, prediction error, and measurement update, and step S2 specifically includes:

[0123] Step S21: Obtain the next-step prediction ellipsoid set from the state ellipsoid set of the previous time step, and perform time update:

[0124] Step S211: Calculate the predicted values ​​of the state variables:

[0125]

[0126] Step S212: Calculate the radius of the ellipsoid.

[0127] σ 2 (k|k-1)=σ(k-1);

[0128] Step S213: Calculate the shape matrix:

[0129]

[0130] The parameter p(k) is recursively calculated using the minimum trace method of the externally bounded ellipsoid:

[0131]

[0132] Where tr(.) is the sum of the diagonal elements of the square matrix, and is the trace of the matrix;

[0133] Step S22: Calculate the prediction error by fitting the rate of change of error using the recursive least squares method.

[0134] Step S221: Calculate the current error:

[0135]

[0136] Step S222, Rate of change of fitting error using recursive least squares method:

[0137]

[0138] Among them, P r (k) is the covariance matrix, and θ r (k)=[θ r1 (k)θ r2 (k)] T θ r1 (k) represents the current rate of change of error, θ r2 (k) represents the rate of change of the prediction error, i.e., θ r (k) indicates that θ is included. r1 (k), θ r2 (k) A vector of two variables, x r (k) = [1, m] T , where m is the number of sampling periods;

[0139] Step S223: Estimate the prediction error value using the rate of change of the prediction error and the current error.

[0140]

[0141] Where, θ base This is the minimum baseline value for the application prediction error, where m is the prediction step size and e(k) is the current error.

[0142] Step S23: Update the gain matrix, optimal estimate, ellipsoid shape matrix, and ellipsoid radius using the state ellipsoid set and the observation ellipsoid set to achieve measurement update:

[0143] Step S231: Update the observation ellipsoid set:

[0144]

[0145] Where γ is the set minimum ellipsoid radius;

[0146] Step S232: Update parameter λ(k) and optimize the upper bound of the ellipsoid:

[0147]

[0148] Where g(k) is the observation variable error covariance matrix G(k)=H(k)P(k|k-1)H T The maximum singular value of (k);

[0149] Step S233: Update the gain matrix:

[0150]

[0151] Step S234: Update the ellipsoid shape matrix:

[0152]

[0153] Step S235: Update the ellipsoid radius:

[0154]

[0155] Step S236: Calculate the optimal estimate:

[0156]

[0157] The above steps implement an extended set membership filtering strategy based on the least squares method, which effectively improves the convergence speed of the filtering algorithm.

[0158] Better, such as Figure 3 and Figure 4 As shown, the current and voltage sensing system further includes a current sensing subsystem and a voltage sensing subsystem. The current sensing subsystem and voltage sensing subsystem respectively process the signals they acquire, and then input them into the software filtering module. By constructing an ellipsoidal set covering the true state set of current and voltage, accurate current and voltage sample values ​​are obtained. That is, before executing the software filtering module designed in step 3, the current and voltage sample values ​​must first be obtained through the various hardware modules of the current sensing subsystem and voltage sensing subsystem. Then, these sample values ​​are input into the software filtering module designed in this invention for optimization and output of the optimal estimate (including current I). r and voltage U r ).

[0159] Specifically, such as Figure 3 As shown, the current sensing subsystem includes a current detection module, a hardware filtering module, an isolation amplification module, and a sampling module. The hardware filtering module uses a second-order low-pass filter to effectively filter out high-frequency noise signals. The isolation amplification module uses electrical isolation, separated by an isolation barrier with extremely strong anti-electromagnetic interference performance. The sampling module specifically uses a 16-bit high-speed parallel interface for digital sampling. The current sensing subsystem specifically performs the following operations:

[0160] The primary current is converted to the secondary current in the current detection module to obtain the current I. s :

[0161]

[0162] Among them, I p I s These are the primary current and the secondary current, respectively, and N1 and N2 are the number of turns of the primary and secondary windings, respectively.

[0163] The current signal is converted into a voltage signal U1 by a resistor:

[0164] U1 = I s R s ;

[0165] Amplify the measured voltage signal to obtain U2:

[0166]

[0167] U2 is filtered by a hardware filtering module to obtain U3. The specific cutoff frequency setting method is as follows:

[0168]

[0169] U3 is amplified by an isolation module to obtain U4. U4 is then sampled by a high-speed sampling module. The resulting digital signal is used to calculate the sampling current signal I based on the conditioning circuit structure. i The input is processed by a software filtering module for high-precision filtering.

[0170] like Figure 4 As shown, the voltage sensing subsystem includes a voltage detection module, a hardware filtering module, an isolation amplification module, and a sampling module. The hardware filtering module uses a second-order low-pass filter to effectively filter out high-frequency noise signals. The isolation amplification module uses electrical isolation, separated by an isolation barrier with extremely strong anti-electromagnetic interference performance. The sampling module specifically uses a 16-bit high-speed parallel interface for digital sampling. The voltage sensing subsystem specifically performs the following operations:

[0171] The voltage amplitude is adjusted by the transformer in the voltage detection module to obtain U. s :

[0172]

[0173] Among them, U p U s These are the AC voltages of the primary and secondary transformers, respectively; N1 and N2 are the number of turns of the primary and secondary coils, respectively.

[0174] U5 is calculated using a capacitor voltage divider structure. The specific output voltage calculation method is as follows:

[0175]

[0176] U5 is filtered by a hardware filtering module to obtain U6. The specific cutoff frequency setting method is as follows:

[0177]

[0178] U6 is amplified by an isolation module to obtain U7. U7 is then acquired by a high-speed sampling module. The resulting digital signal is used to calculate the sampling voltage signal U based on the conditioning circuit structure. i The input is processed by a software filtering module for high-precision filtering.

[0179] Preferably, the software filtering module specifically performs the following operations:

[0180] Step S31: Based on the current signal I output by the sampling module in the current and voltage sensing system... i and voltage signal U i The characteristic formula is used to derive the relational equation combining the discrete target signals at three consecutive time points;

[0181] The characteristic formula is:

[0182]

[0183] The relationship between the discrete target signals at three consecutive time points, derived from the aforementioned characteristic formula, is as follows:

[0184]

[0185] Where A1 and A2 are the amplitudes of the current and voltage signals, and T s f1 and f2 are the sampling time and the AC current and voltage frequencies, respectively. For current and voltage phase;

[0186] Step S32: Based on the above equations, establish the following state model and observation model:

[0187]

[0188] Where w is the error caused by model mismatch, and ν is the error caused by sampling noise;

[0189] Step S33: Initialize the state ellipsoid set and observation ellipsoid set And calculate the Jacobian matrices F and H;

[0190] Step S34: During online operation, recursive real-time filtering is achieved through three parts: time update, prediction error, and measurement update. The state ellipsoid set and observation ellipsoid set are updated using the iterative update method from steps 231 to 235, and the optimal estimates of current and voltage I are further calculated. r and U r :

[0191]

[0192] Since the two subsystems share a single processor, the voltage and current signals obtained from the high-speed sampling modules of each subsystem are placed in a matrix and calculated in the software filtering module. In the formula... It is a formula that has already been calculated by substituting specific state variables, and is consistent with step 236 and... Figure 2 of Correspondingly, among which The calculation method is an iterative update in steps 231 to 235.

[0193] The above-mentioned technical solution of the present invention has at least the following advantages: It proposes to construct a prediction error model online using the recursive least squares method, predict and estimate multi-step prediction errors, and substitute the prediction errors of real-time fitting into the measurement update stage of the extended set member Kalman filter, thereby reducing the number of ellipsoid set iteration updates, quickly covering the state set of the actual system, and accelerating the convergence speed of the filtering algorithm; Based on the current and voltage sensing system, it designs an improved extended set member Kalman filter method combined with the least squares method to achieve active suppression of noise interference, reduce the harmonic content of voltage and current signals, and improve the sampling accuracy of the overall system.

[0194] While specific embodiments of the present invention have been described above, those skilled in the art should understand that the specific embodiments described are merely illustrative and not intended to limit the scope of the present invention. Equivalent modifications and variations made by those skilled in the art in accordance with the spirit of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A high-precision signal conditioning method using least squares prediction-corrected Kalman filtering, characterized in that: Includes the following steps: Step S1: Define the nonlinear model and ellipsoid set, analyze process noise, measurement noise and initial state ellipsoid set, and construct the extended set member filtering model; Step S2: Perform recursive calculations based on the extended set member filtering model to obtain an extended set member filtering method improved by least squares. Step S3: Based on the extended set member filtering method improved by the least squares method, design a software filtering module in the current and voltage sensing system, and obtain accurate current and voltage sample values ​​by constructing an ellipsoidal set to cover the real state set of current and voltage. Step S1 specifically includes: Step S11: Define the nonlinear system model as follows: ； Where x is the state variable, y is the observation variable, w is the process noise, ν is the measurement noise, f(.) is the system state transition function, h(.) is the system measurement function, and k is the sampling time of the discrete system; Step S12: Define the ellipsoid set as: ； in, a The foci of the ellipsoid. P Let R be the positive definite symmetric envelope matrix of the ellipsoid shape, σ be the radius of the ellipsoid, and R be the positive definite symmetric envelope matrix of the ellipsoid shape. n Let n be the vector space of the set of real numbers; Step S13: Map the process noise w and measurement noise ν to an ellipsoid set: ； Where Q is the process noise covariance matrix, R is the measurement noise covariance matrix, and σ v To measure the radius of the ellipsoid of the noise ν, σ w Let w be the radius of the ellipsoid of the process noise w; Step S14: Taylor expansion of the nonlinear system: ； in, For state variables, R represents the estimated value of the state variable. f (.) and R h (.) represents the higher-order linearization error, and F(k) and H(k) are the correlation Jacobian matrices of the state transition function and the measurement function, respectively. The specific calculation method is as follows: ； Mapping higher-order linear errors to an ellipsoid set: ； in, , It is a higher-order linearization error of process noise and measurement noise. , It is a higher-order linearized error ellipsoid set of process noise and measurement noise. , It is the radius of the higher-order linearized error ellipsoid set of process noise and measurement noise; Integrating higher-order linear errors and noise, a noise ellipsoid set is defined, i.e., an extended set-member filtering model: ； in, It is an ellipsoidal set that integrates higher-order linear errors and process noise. It is an ellipsoidal set that integrates higher-order linear errors and measurement noise. It is a noise variable that integrates higher-order linear error and measurement noise. It is a noise variable that integrates higher-order linear error and process noise; Step S15: Define the initial state ellipsoid set E(0) and the initial observation ellipsoid set S(0) as follows: in, To estimate the variables for extended set membership filtering, To integrate the error covariance matrix of higher-order linear error and measurement noise, To integrate the ellipsoid set radius of higher-order linear errors and measurement noise, e r This represents the error value due to mismeasurement. The recursive calculation in step S2 includes time update, prediction error, and measurement update. Step S2 specifically includes: Step S21: Obtain the next-step prediction ellipsoid set from the state ellipsoid set of the previous time step, and perform time update: Step S211: Calculate the predicted values ​​of the state variables: ； Step S212: Calculate the radius of the ellipsoid. ； Step S213: Calculate the shape matrix: ； The parameter p(k) is recursively calculated using the minimum trace method of the externally bounded ellipsoid: ； Where tr(.) is the sum of the diagonal elements of the square matrix, and is the trace of the matrix; Step S22: Calculate the prediction error by fitting the rate of change of error using the recursive least squares method. Step S221: Calculate the current error: ； Step S222, Rate of change of fitting error using recursive least squares method: ； Among them, P r (k) is the covariance matrix, and θ r ( k )=[ θ r1 ( k ) θ r2 ( k )] T , θ r1 ( k ) represents the current rate of change of error. θ r2 ( k ) represents the rate of change of the prediction error, i.e. θ r (k) indicates that it contains θ r1 (k) θ r2 (k) A vector of two variables, x r (k)=[1,n] T , where n is the number of sampling periods; Step S223: Estimate the prediction error value using the rate of change of the prediction error and the current error. ； Where, θ base This is the minimum baseline value for the application prediction error, where m is the prediction step size. e ( k ) represents the current error; Step S23: Update the gain matrix, optimal estimate, ellipsoid shape matrix, and ellipsoid radius using the state ellipsoid set and the observation ellipsoid set to achieve measurement update: Step S231: Update the observation ellipsoid set: ； Step S232: Update parameter λ(k) and optimize the upper bound of the ellipsoid: ； Where g(k) is the covariance matrix of the observed variable error. G ( k )= H ( k ) P ( k | k -1) H T ( k The maximum singular value; Step S233: Update the gain matrix: ； Step S234: Update the ellipsoid shape matrix: ； Step S235: Update the ellipsoid radius: ； Step S236: Calculate the optimal estimate: ； The above steps implement an extended set membership filtering strategy based on the least squares method, which effectively improves the convergence speed of the filtering algorithm.

2. The method according to claim 1, characterized in that: The software filtering module specifically performs the following operations: Step S31: Based on the current signal output by the sampling module in the current and voltage sensing system. I i and voltage signal U i The characteristic formula is used to derive the relational equation combining the discrete target signals at three consecutive time points; The characteristic formula is: ； The relationship between the discrete target signals at three consecutive time points, derived from the aforementioned characteristic formula, is as follows: ； Where A1 and A2 are the amplitudes of the current and voltage signals, and T s f1 and f2 are the sampling time and the AC current and voltage frequencies, respectively. , For current and voltage phase; Step S32: Establish the following state model and observation model: ； Step S33: Initialize the state ellipsoid set and observation ellipsoid set And calculate the Jacobian matrices F and H; Step S34: During online operation, recursive real-time filtering is achieved through three parts: time update, prediction error, and measurement update. The state ellipsoid set and observation ellipsoid set are updated using the iterative update method from steps 231 to 235, and the optimal estimates of current and voltage are further calculated. I r and U r : 。 3. The method according to claim 1, characterized in that: The current and voltage sensing system further includes a current sensing subsystem and a voltage sensing subsystem. The signals collected by the current sensing subsystem and the voltage sensing subsystem are processed by the respective subsystems and then input into the software filtering module. By constructing an ellipsoidal set to cover the real state set of current and voltage, accurate current and voltage sample values ​​are obtained.

4. The method according to claim 3, characterized in that: The current sensing subsystem includes a current detection module, a hardware filtering module, an isolation amplification module, and a sampling module. The hardware filtering module uses a second-order low-pass filter to effectively filter out high-frequency noise signals. The isolation amplification module uses electrical isolation, separated by an isolation barrier with extremely strong electromagnetic interference resistance. The sampling module specifically uses a 16-bit high-speed parallel interface for digital sampling. The current sensing subsystem specifically performs the following operations: The primary current is converted to the secondary current in the current detection module to obtain the current. I s The current signal is converted into a voltage signal through a resistor. U 1. Then amplify the measured voltage signal to obtain U 2. Then, it is obtained through a hardware filtering module. U 3. Then, after passing through the isolation amplification module, it becomes... U 4. Data is collected via a high-speed sampling module. U 4. The obtained digital signal is used to calculate the sampling current signal based on the conditioning circuit structure. I i The input is processed by a software filtering module for high-precision filtering.

5. The method according to claim 3, characterized in that: The voltage sensing subsystem includes a voltage detection module, a hardware filtering module, an isolation amplification module, and a sampling module. The hardware filtering module uses a second-order low-pass filter to effectively filter out high-frequency noise signals. The isolation amplification module uses electrical isolation, separated by an isolation barrier with extremely strong electromagnetic interference resistance. The sampling module specifically uses a 16-bit high-speed parallel interface for digital sampling. The voltage sensing subsystem specifically performs the following operations: The voltage amplitude is adjusted by the transformer in the voltage detection module to obtain U. s Then, the capacitor voltage divider structure was used to calculate the result. U 5. After passing through the hardware filtering module, the result is obtained. U 6. Then, after passing through the isolation amplification module, it becomes... U 7. Data is collected via a high-speed sampling module. U 7. The obtained digital signal is used to calculate the sampling voltage signal based on the conditioning circuit structure. U i The input is processed by a software filtering module for high-precision filtering.

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