Current / frequency conversion circuit temperature compensation method based on multiple linear regression

Abstract

The invention belongs to the field of inertial navigation, discloses a current / frequency conversion circuit temperature compensation method based on multiple linear regression, and aims to solve the problem that a scale factor of a current / frequency conversion circuit presents a complex and irregular drift phenomenon and a heat hysteresis effect along with the change of an environment temperature on the basis of a multiple linear regression theory. The method comprises the following steps: establishing a temperature compensation model of comprehensive parameters such as environment temperature and variable temperature rate, dynamically screening temperature parameters which have obvious influence on temperature drift of a current / frequency conversion circuit scale factor through t statistical test and F hypothesis test in stepwise regression, iteratively optimizing the temperature compensation model of the current / frequency conversion circuit scale factor, and calculating the temperature drift of the current / frequency conversion circuit scale factor. According to the invention, high-precision temperature compensation of the current / frequency conversion circuit can be completed, and a temperature parameter having a significant contribution to the scale factor drift amount of the current / frequency conversion circuit can be adaptively selected. The method has high application value for improving the temperature stability of the current / frequency conversion circuit in the inertial navigation system.

Description

Technical Field

[0001] The present invention belongs to the field of inertial navigation, and relates to a compensation technology for a current / frequency conversion circuit, specifically to a temperature compensation method for a current / frequency conversion circuit based on multiple linear regression. Background Art

[0002] A current / frequency conversion circuit is an analog-to-digital hybrid circuit that linearly converts an analog current signal into a digital pulse frequency signal. Compared with a traditional analog-to-digital converter (ADC), the current / frequency conversion method has high conversion accuracy, fast conversion speed, and small cumulative error, and is commonly used in the current sampling link of a quartz flexure accelerometer in a high-precision inertial navigation system. The current / frequency conversion circuit is based on the charge balance principle and consists of an integration circuit, a digital logic control circuit, a constant current source circuit, a polarity switch, etc. Among them, the constant current source circuit provides a constant cancellation current for the integration circuit under the control of the digital logic circuit and the polarity switch. The output current accuracy of the constant current source circuit and the switching control time of the polarity switch directly affect the conversion accuracy of the current / frequency conversion circuit. However, the performance of the electronic components and the polarity switch in the constant current source circuit is affected by the ambient temperature, resulting in a temperature drift phenomenon in the output signal of the current / frequency conversion circuit, that is, under the condition of a constant input current, the output frequency of the circuit changes in real time with the ambient temperature.

[0003] The temperature drift problem of the current / frequency conversion circuit is specifically manifested as the characteristic that its scale factor changes irregularly with temperature. Common temperature compensation methods can be divided into hardware compensation and algorithm compensation: Hardware compensation is mainly achieved by adding a compensation circuit in the constant current source circuit, which has the characteristics of simple principle and fast response speed. The disadvantage is that it can only compensate for the low-order temperature drift coefficient term of the conversion circuit and cannot achieve high-precision compensation; Algorithm compensation mainly fits the temperature characteristic curve of the scale factor in a digital signal processor to achieve accurate estimation and compensation of the high-order temperature error term in the circuit scale factor. Commonly used fitting methods include polynomial fitting, multiple linear regression, neural network, etc. These methods are based on a deterministic temperature compensation model and usually require prior knowledge to pre-determine the compensation parameters that affect the current / frequency conversion circuit. When there is a deviation in the preset compensation parameters, it is difficult for the temperature compensation model to achieve accurate compensation of the scale factor of the current / frequency conversion circuit.

[0004] Aiming at the temperature drift problem of the current / frequency conversion circuit, the present invention comprehensively considers the temperature characteristics of electronic components and establishes a temperature compensation model that combines environmental temperature and temperature change rate and other parameters based on multiple linear regression and stepwise regression. The present invention has high application value for improving the temperature stability of the current / frequency conversion circuit in an inertial navigation system. Summary of the Invention

[0005] The object of the present invention is to provide a temperature compensation method for a current / frequency conversion circuit based on multiple linear regression. By using the theories of multiple linear regression and stepwise regression, parameters that have a significant impact on the temperature drift of the scale factor of the current / frequency conversion circuit are dynamically iteratively screened, and a temperature compensation model that combines parameters such as the ambient temperature and the temperature change rate is constructed to achieve high-precision compensation for the output frequency signal of the current / frequency conversion circuit, effectively improving the temperature stability of the current / frequency conversion circuit.

[0006] To solve the problem of temperature drift of the current / frequency conversion circuit, the present invention proposes the following solutions:

[0007] A temperature compensation method for a current / frequency conversion circuit based on multiple linear regression includes the following steps:

[0008] S1. Place the current / frequency conversion circuit in a high-precision temperature chamber environment, and set the temperature chamber to continuously heat up and cool down within the operating temperature range of the current / frequency conversion circuit.

[0009] S2. Supply power to the current / frequency conversion circuit through a voltage stabilizer. Under the condition of accessing a stable input current, collect the measured values of the scale factor of the current / frequency conversion circuit with respect to the real-time ambient temperature T n of the measurement where n = 1, 2,..., N represents the time sequence number at different temperatures, and a total of N groups of measurement values are collected.

[0010] S3. From the measured values of the scale factor of the current / frequency conversion circuit, calculate its drift amount with respect to temperature as:

[0011]

[0012] where is the mean value of the measurement values;

[0013] S4. Establish a candidate parameter set Λ and a selected parameter set Θ for the temperature compensation model of the scale factor of the current / frequency conversion circuit. The candidate parameter set Λ contains candidate parameters for the temperature compensation model related to temperature, including the ambient temperature, the temperature change rate, their higher-order terms, and cross terms. The number of elements is denoted as p, and the initial number of parameters in the candidate parameter set Λ is P. The selected parameter set Θ contains parameters that currently contribute to the compensation of the temperature drift amount of the scale factor of the current / frequency conversion circuit. The initial parameter is Θ = {1}, and the number of elements is denoted as q, and the initial value of q is 1.

[0014] S5. Construct a temperature compensation model for the drift amount of the scale factor of the current / frequency conversion circuit to be solved as

[0015] y = β P ·x P +…+β2·x2+β1·x1+β0+ε (2)

[0016] where y is the drift of the scale factor of the current / frequency conversion circuit with respect to temperature change, x1, x2, …, x P ∈Λ are candidate parameters related to temperature, β0, β1, β2, …, β P are the linear regression coefficients of the temperature compensation model, and ε is the temperature compensation residual; initialize the temperature compensation model of the scale factor of the current / frequency conversion circuit, that is, let β P =…=β2 = β1 = 0;

[0017] S6. Introduce the parameter x j ∈Λ, j = 1, ..., p in the candidate parameter set Λ into the temperature compensation model (2) in step S5 alone, that is, β j ≠0, assume that the drift y of the scale factor of the current / frequency conversion circuit is linearly related to the parameter x j Based on the least squares algorithm, with the condition of minimizing the temperature compensation residual ε, from the real-time ambient temperature T n measured in step S2 and the measured value of the scale factor drift calculate the estimated values of the combined linear regression coefficients of all q parameters in the selected parameter set Θ and the parameter x j introduced from the candidate parameter set Λ to jointly construct the temperature compensation model (2) in step S5, and obtain p linear regression equations as

[0018]

[0019] where j = 1, 2, …, p is the parameter index of the candidate parameter set Λ, is the estimated value of the linear regression coefficient of all parameters in the selected parameter set Θ, is the estimated value of the combined linear regression coefficient when the parameter x j in the candidate parameter set Λ is introduced into the temperature compensation model (3), is the predicted value of the drift of the scale factor of the current / frequency conversion circuit fitted after the parameter x j is introduced into the temperature compensation model (3);

[0020] S7. Calculate the t-test statistic t j of the candidate parameter x j in the p linear regression equations obtained in step S6 in turn;

[0021] S8. Retain the parameters that contribute most significantly to the predictive ability of the temperature compensation model (2), i.e., the parameters corresponding to the maximum value among the absolute values |t j | of p t-test statistics

[0022]

[0023] Delete the parameter from the candidate parameter set Λ, i.e., and add it to the selected parameter set Θ, i.e.,

[0024] S9. Update the linear regression equation in step S5 corresponding to the parameter to the current temperature compensation model as

[0025]

[0026] where is the linear regression coefficient of the parameter in the temperature compensation model (5), is the parameter currently added to the selected parameter set Θ, is the linear regression coefficient of the parameter in the selected parameter set Θ in the temperature compensation model (5), is the parameter in the selected parameter set Θ, is the predicted value of the scale factor drift of the current / voltage conversion circuit after adding the parameter to the selected parameter set Θ;

[0027] S10. Calculate the predicted value of the scale factor drift of the current / voltage conversion circuit in the temperature compensation model (5) in step S9 k Θ and the F-test statistic F j0 for all q + 1 parameters x

[0028] S11. Use the F-test statistic F j0 to verify the overall significance of the temperature compensation model (5) and measure the overall linearity between the predicted value of the scale factor drift in the temperature compensation model (5) and all the parameters in the selected parameter set Θ

[0029]

[0030] where H1 represents the hypothesis that the temperature compensation model (5) has a significant linear relationship, H0 represents the hypothesis that the temperature compensation model (5) does not have a linear relationship, and F αis the F hypothesis test threshold at the confidence level of 1-α;

[0031] S12. When the statistic F of the temperature compensation model (5) j0 satisfies the H1 hypothesis, proceed to step S13; conversely, when the H0 hypothesis is satisfied, the parameter is removed from the selected parameter set Θ, that is After that, return to the said step S6 and reselect the candidate parameters;

[0032] S13. Calculate the t-test statistic t of each parameter in the temperature compensation model (5) k , and judge the significance and contribution degree of each parameter x k Θ , k = 1,..., q + 1 to the temperature compensation model (5);

[0033] S14. Use the t-test statistic t of the q + 1 parameters x k Θ , k = 1,..., q + 1 in the temperature compensation model (5) of step S9 k , and test the contribution degree of each parameter to the predicted value of the scale factor drift of the current / frequency conversion circuit one by one, that is

[0034] |t k | > t α / 2 , k = 1,…, q + 1 (7) where t α / 2 is the t hypothesis test threshold at the confidence level of 1-α;

[0035] S15. When the t-test statistics t of all parameters x k Θ all satisfy the said relation (7), then jump to step S17; when there exists a parameter x k k Θ ∈Θ whose t-test statistic t k cannot satisfy the said relation (7), then it is removed from the selected parameter set Θ, that is Then continue step S16;

[0036] S16. Use the parameters x k Θ , k = 1,..., h in the selected parameter set Θ in step S15, where h is the number of parameters in the selected parameter set Θ that fail the t-test, and based on the least squares algorithm, with the condition of minimizing the temperature compensation residual ε constraint, recalculate and update the temperature compensation model from the ambient temperature T n and the measured value of the scale factor drift as​

[0037]

[0038] where h is the number of elements in the selected parameter set Θ of the parameters eliminated by the t-test in step S15 is the parameter in the selected parameter set Θ of the parameters eliminated by the t-test in step S15 represents the linear regression coefficient of the updated temperature compensation model (8) is the predicted value of the temperature compensation model (8) for the drift of the scale factor of the current / frequency conversion circuit

[0039] S17. Determine whether the candidate parameter set Λ is an empty set. If the candidate parameter set Λ is an empty set, output the temperature compensation model constructed in step S9 or step S16; otherwise, return to step S6 to reselect candidate parameters

[0040] Preferably, the scale factor of the current / frequency conversion circuit in step S2 is the frequency of the output pulse signal under the condition of unit input current. When positive current and negative current are input, the drift amounts of the positive scale factor and the negative scale factor of the current / frequency conversion circuit with the change of the ambient temperature are different, and temperature compensation is performed on the positive scale factor and the negative scale factor of the current / frequency conversion circuit respectively

[0041] Preferably, the ambient temperature T in step S4 n is measured by the temperature acquisition circuit of the current / frequency conversion circuit, and the measured value of the temperature change rate △T n is obtained by subtracting the ambient temperature T at the previous moment from the ambient temperature T at the nth moment n n-1

[0042] Preferably, the temperature compensation model (2) in step S5 is expressed in matrix form as

[0043] y = X T β + ε (9)

[0044] where X = [1, x1, …, x P T represents the candidate parameter vector, and β = [β0, β1, …, β P T represents the regression coefficient vector of the temperature compensation model

[0045] In step S3, N sets of measured sample values of the drift of the scale factor of the current / frequency conversion circuit are collected, and its column vector form is expressed as The measurement sample matrix composed of the corresponding candidate parameter vectors X is expressed as ​​​​

[0046]

[0047] Where P is the number of initial parameters in the candidate parameter set Λ, and N is the number of measured values collected. is the measured value of the i-th parameter at the j-th time, and is represented by denote the measurement residual vector of the scale factor drift of the current / frequency conversion circuit, then the relationship between the measured value of the scale factor drift of the current / frequency conversion circuit obtained by N measurements and the parameters is expressed as

[0048]

[0049] Define the loss function as

[0050]

[0051] Where is the measurement sample vector of the temperature drift of the scale factor of the current / frequency conversion circuit;

[0052] Under the minimization constraint of the temperature compensation residual The estimated values of the linear regression coefficients of the parameters in the temperature compensation model (9) are obtained by the least squares method as

[0053]

[0054] Substitute the estimated values of the linear regression coefficients into the temperature compensation model (9) to determine the temperature compensation model of the current / frequency conversion circuit based on multiple linear regression as

[0055]

[0056] Where is the predicted value of the scale factor drift of the current / frequency conversion circuit.

[0057] Preferably, the temperature compensation model (3) in step S6 is constructed by setting the parameter of the candidate parameter vector X in the matrix form (9) of the temperature compensation model to zero, where x m is the parameter that does not belong to the selected parameter set Θ in the candidate parameter vector X. When constructing the measurement sample matrix of the candidate parameter vector X, the row vector m of the measurement sample values corresponding to the parameter x is also set to the zero vector. Based on the least squares algorithm, with the minimization of the temperature compensation residual as the constraint condition, the obtained estimated value of the linear regression coefficient Substitute the non-zero elements into step S6 to obtain the temperature compensation model (3); construct the temperature compensation model (8) in step S16 by setting the parameters of the candidate parameter vector X in the matrix form (9) of the temperature compensation model to zero. When constructing the measurement sample matrix of the candidate parameter vector X, the row vector of the measurement sample values corresponding to the parameter x is also set to a zero vector. Based on the least squares algorithm, with the minimization of the temperature compensation residual as the constraint condition, the obtained estimated values of the linear regression coefficients are substituted into step S16 with non-zero elements to obtain the temperature compensation model (8). Set to zero, and when constructing the measurement sample matrix of the candidate parameter vector X the parameter x m the corresponding row vector of the measurement sample values is also set to a zero vector. Based on the least squares algorithm, with the minimization of the temperature compensation residual as the constraint condition, the obtained estimated values of the linear regression coefficients are substituted into step S16 with non-zero elements to obtain the temperature compensation model (8).

[0058] Preferably, in step S11, the overall significance of the temperature compensation model (5) is discriminated by the F-test statistic F j0 ; first, establish the null hypothesis H0 and the alternative hypothesis H1

[0059] The null hypothesis H0: all multiple linear regression coefficients are zero, that is, there is no linear relationship between the scale factor drift of the current / frequency conversion circuit temperature compensation model (5) currently constructed and the parameters in the selected parameter set Θ

[0060] The alternative hypothesis H1: at least one multiple linear regression coefficient is not zero, that is, there is a parameter in the selected parameter set Θ that has a significant linear relationship with the scale factor drift of the current / frequency conversion circuit temperature compensation model (5) currently constructed

[0061] Then, calculate the F-test statistic of the temperature compensation model (5) from the measured values and estimated values of the scale factor drift as

[0062]

[0063] where represents the drift of the scale factor of the current / frequency conversion circuit measured at the ambient temperature T n , is the predicted value of the drift of the scale factor of the current / frequency conversion circuit fitted after adding the parameter to the selected parameter set Θ represents the mean value of the measured scale factor drift , N is the number of measured values collected, and the number of elements of the parameters in the selected parameter set Θ is q + 1

[0064] Finally, make a hypothesis test decision. If F j0 > F α , where F αIf it is obtained by looking up a table, the original hypothesis H0 is rejected, and the temperature compensation model (5) is overall significant at the α level. There are parameters in the selected parameter set Θ that have a significant linear contribution to the scale factor drift of the current / frequency conversion circuit. Otherwise, it indicates that there is no linear relationship in the temperature compensation model (5).

[0065] Preferably, in the step S14, the significance of the q + 1 parameters in the temperature compensation model (5) that passes the F test is tested using the t test. The significance determines the contribution degree of each parameter to the prediction ability of the temperature compensation model (5); First, for the parameter x k Θ , k = 1,...,(q + 1), the original hypothesis and the alternative hypothesis are proposed for the corresponding multiple linear regression coefficients

[0066] The original hypothesis H0: The parameter x k Θ has no significant effect on the scale factor drift of the current / frequency conversion circuit;

[0067] The alternative hypothesis H1: The parameter x k Θ has a significant effect on the scale factor drift of the current / frequency conversion circuit;

[0068] Then calculate the t statistic as:

[0069]

[0070] where is the estimated value of the regression coefficient of the parameter x k Θ , is the standard error of the estimated regression coefficient , represents the kth diagonal element of the inverse matrix of the covariance matrix of the measurement sample matrix ;

[0071] Finally, make a t test decision. If |t k | > t α / 2 , where t α / 2 is obtained by looking up a table, the original hypothesis H0 is rejected, and the parameter x k Θ is retained in the selected parameter set Θ. Otherwise, the parameter x k Θ has an insignificant contribution in the temperature compensation model (5), and the parameter x k Θ needs to be deleted from the selected parameter set Θ.

[0072] Preferably, using the multiple determination coefficient R 2Measure the fitting degree of the temperature compensation model in step S17; the multiple determination coefficient R 2 is

[0073]

[0074] where is the predicted value of the drift amount of the scale factor of the current / frequency conversion circuit by the temperature compensation model output in step S17, represents the environmental temperature T n the drift amount of the scale factor of the current / frequency conversion circuit measured at, represents the measured value of the scale factor drift amount the mean value of, N is the number of measured value points collected; R 2 ranges from [0, 1], and the value of the multiple determination coefficient R 2 close to 1 indicates that the final temperature compensation model in step S17 has a good fitting effect on the drift amount of the scale factor of the current / frequency conversion circuit with temperature change.

[0075] Preferably, measure and record the real-time temperature of the current / frequency conversion circuit, calculate all the parameters in the selected parameter set Θ Using the temperature compensation model output in step S17, obtain the estimated value of the drift amount of the scale factor of the current / frequency conversion circuit, and subtract the estimated value from the measured value of the scale factor of the current / frequency conversion circuit to achieve high-precision compensation for the scale factor of the current / frequency conversion circuit.

[0076] Compared with the prior art, the advantages of the present invention are:

[0077] (1) The scale factor of the current / frequency conversion circuit is affected by a variety of temperature-sensitive electronic components, and its drift amount with temperature change shows complex characteristics and exhibits a thermal hysteresis effect. Parameters such as environmental temperature, temperature change rate, and their higher-order terms and cross terms are introduced into the temperature compensation model based on the theory of multiple linear regression, more comprehensively and accurately fitting the change law of the scale factor of the current / frequency conversion circuit;

[0078] (2) In the process of constructing the temperature compensation model based on multiple linear regression, the F-test is used to ensure the linearity of the scale factor compensation model of the current / frequency conversion circuit, and the t-test is used to retain the parameters that have a significant contribution to the temperature compensation model and eliminate the irrelevant parameters, taking into account both compensation accuracy and computational complexity, and establishing an accurate and efficient temperature compensation model;

[0079] (3) By setting a complete set of candidate parameters, during the process of constructing the temperature compensation model, the F-test and t-test of the stepwise regression theory are used for decision-making, and the parameters that significantly contribute to the drift of the scale factor of the current / frequency conversion circuit are adaptively selected, so as to quickly and accurately generate a scale factor temperature compensation model that matches the circuit, making the method highly versatile and capable of finely describing the specificity of the scale factor of different current / frequency conversion circuits changing with temperature. Brief Description of the Drawings

[0080] Figure 1 is a flowchart for establishing a temperature compensation model of a current / frequency conversion circuit provided by an embodiment of the present invention;

[0081] Figure 2 are temperature characteristic curves of the scale factor of a current / frequency conversion circuit before and after compensation at different temperature change rates provided by an embodiment of the present invention. Detailed Embodiments

[0082] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0083] As Figure 1 shown, a temperature compensation method for a current / frequency conversion circuit based on multiple linear regression includes:

[0084] S1. Place the current / frequency conversion circuit in a high-precision temperature chamber environment, and set the temperature chamber to continuously heat up and cool down at three different rates of 1 °C / minute, 2 °C / minute, and 4 °C / minute within the operating temperature range of -40 °C to 60 °C of the current / frequency conversion circuit;

[0085] S2. Supply power to the current / frequency conversion circuit through a voltage stabilizer. Under the condition of connecting a stable input current, collect the measured values of the scale factor of the current / frequency conversion circuit with the real-time ambient temperature T n of the measurement where n = 1, 2,..., N represents the time sequence number at different temperatures, and a total of N groups of measurement values are collected;

[0086] S3. From the measured values of the scale factor of the current / frequency conversion circuit, calculate its drift amount changing with temperature as:

[0087]

[0088] where is the mean value of the measurement values;

[0089] S4. Establish a set of candidate parameters Λ and a set of selected parameters Θ for the temperature compensation model of the current / frequency conversion circuit scale factor. The set of candidate parameters Λ contains candidate parameters of the temperature compensation model related to temperature, including ambient temperature, temperature change rate, higher-order terms and cross-terms of the two, and the number of elements is denoted as p. The initial number of parameters of the set of candidate parameters Λ is P. The set of selected parameters Θ contains parameters that currently contribute to the compensation of the temperature drift of the current / frequency conversion circuit scale factor. The initial parameter is Θ = {1}, and the number of elements is denoted as q, and the initial value of q is 1;

[0090] S5. Construct the temperature compensation model for the drift of the current / frequency conversion circuit scale factor to be solved as

[0091] y = β P ·x P +…+β2·x2 + β1·x1 + β0 + ε (18)

[0092] where y is the drift of the current / frequency conversion circuit scale factor with respect to temperature, x1, x2, …, x P ∈Λ are candidate parameters related to temperature, β0, β1, β2, …, β P are the linear regression coefficients of the temperature compensation model, and ε is the temperature compensation residual; Initialize the temperature compensation model of the current / frequency conversion circuit scale factor, that is, let β P =…=β2 = β1 = 0;

[0093] S6. Introduce the parameter x j ∈Λ, j = 1, …, p in the set of candidate parameters Λ into the temperature compensation model (2) in step S5 alone, that is, β j ≠0. Assume that the drift y of the current / frequency conversion circuit scale factor is linearly related to the parameter x j . Based on the least squares algorithm, with the condition of minimizing the temperature compensation residual ε, from the real-time ambient temperature T n measured in step S2 and the measured value of the scale factor drift , calculate all q parameters in the set of selected parameters Θ and the parameter x j introduced from the set of candidate parameters Λ to jointly construct the estimated value of the combined linear regression coefficient of the temperature compensation model (2) in step S5, and obtain p linear regression equations as

[0094]

[0095] where j = 1, 2, …, p is the parameter index of the set of candidate parameters Λ, is the estimated value of the linear regression coefficient of all parameters in the set of selected parameters Θ, For the parameter x in the candidate parameter set Λ j introduce the estimated value of the joint linear regression coefficient of the temperature compensation model (3), is the parameter x j the predicted value of the scale factor drift of the current / frequency conversion circuit fitted after introducing the temperature compensation model (3);

[0096] S7. Calculate the t-test statistic t of the candidate parameter x j in the p linear regression equations obtained in the above step S6 j ;

[0097] S8. Retain the parameter that makes the most significant contribution to the prediction ability of the temperature compensation model (2), that is, the parameter corresponding to the maximum value among the absolute values |t j | of the p t-test statistics

[0098]

[0099] Delete the parameter from the candidate parameter set Λ, that is and add it to the selected parameter set Θ, that is

[0100] S9. Update the linear regression equation in the above step S5 corresponding to the parameter to the current temperature compensation model as

[0101]

[0102] where is the linear regression coefficient of the parameter in the temperature compensation model (5), is the parameter currently added to the selected parameter set Θ, is the linear regression coefficient of the parameter in the selected parameter set Θ in the temperature compensation model (5), is the parameter in the selected parameter set Θ, is the predicted value of the scale factor drift of the current / frequency conversion circuit fitted after adding the parameter to the selected parameter set Θ;

[0103] S10. Calculate the predicted value of the scale factor drift of the current / frequency conversion circuit in the temperature compensation model (5) in the above step S9 k Θ and the F-test statistic F of all q + 1 parameters x j0 ∈ Θ, k = 1,..., q + 1

[0104] S11. Use the F-test statistic F j0 to verify the overall significance of the temperature compensation model (5) and measure the overall linearity between the predicted value of the scale factor drift in the temperature compensation model (5) and all the parameters in the selected parameter set Θ

[0105]

[0106] where H1 represents the hypothesis that the temperature compensation model (5) has a significant linear relationship, H0 represents the hypothesis that the temperature compensation model (5) does not have a linear relationship, and F 0.01 is the F hypothesis test threshold at the 99% confidence level;

[0107] S12. When the statistic F of the temperature compensation model (5) j0 satisfies the H1 hypothesis, proceed to step S13; conversely, when the H0 hypothesis is satisfied, then remove the parameter from the selected parameter set Θ, that is and then return to the said step S6 to reselect candidate parameters;

[0108] S13. Calculate the t-test statistic t of each parameter in the temperature compensation model (5) k to judge the significance and contribution degree of each parameter x k Θ , k = 1,..., q + 1 to the temperature compensation model (5);

[0109] S14. Use the t-test statistic t of the q + 1 parameters x k Θ , k = 1,..., q + 1 in the temperature compensation model (5) obtained in step S9 k to test the contribution degree of each parameter to the predicted value of the scale factor drift of the current / frequency conversion circuit one by one, that is

[0110] |t k | > t 0.005 Θ , k = 1,…, q + 1 (23)

[0111] where t 0.005 is the t hypothesis test threshold at the 99% confidence level;

[0112] S15. When the t-test statistic t of all the parameters x k Θ all satisfies the said relation (7), then jump to step S17; when there exists a parameter x k k Θ ∈Θ whose t-test statistic t k ​When the relational expression (7) cannot be satisfied, it is deleted from the selected parameter set Θ, that is Then continue with step S16;

[0113] S16. Use the parameter x in the selected parameter set Θ in step S15 k Θ , k = 1, ..., h, where h is the number of parameters in the selected parameter set Θ that fail the t-test and are deleted. Based on the least squares algorithm, with the condition of minimizing the temperature compensation residual ε, from the ambient temperature T n and the measured value of the scale factor drift Recalculate and update the temperature compensation model as

[0114]

[0115] where h is the number of elements in the selected parameter set Θ that excludes the parameters that fail the t-test in step S15 is the parameter in the selected parameter set Θ that excludes the parameters that fail the t-test in step S15 represents the linear regression coefficient of the updated temperature compensation model (8) is the predicted value of the scale factor drift of the current / frequency conversion circuit by the temperature compensation model (8);

[0116] S17. Determine whether the candidate parameter set Λ is an empty set. If the candidate parameter set Λ is an empty set, that is, p = 0, then output the temperature compensation model constructed in step S9 or step S16; otherwise, return to step S6 to reselect candidate parameters.

[0117] Preferably, the scale factor of the current / frequency conversion circuit in step S2 is the output pulse signal frequency under the condition of unit input current. When inputting +1 mA current and -1 mA current, the drift amounts of the positive scale factor and the negative scale factor of the current / frequency conversion circuit with the change of ambient temperature are different, and temperature compensation is performed on the positive scale factor and the negative scale factor of the current / frequency conversion circuit respectively.

[0118] Preferably, the ambient temperature T in step S4 n is measured by the temperature acquisition circuit of the current / frequency conversion circuit, and the measured value of the temperature change rate △T n is obtained by subtracting the ambient temperature T n at the previous moment from the ambient temperature T n-1 at the nth moment.

[0119] Preferably, the temperature compensation model (2) in step S5 is expressed in matrix form as

[0120] y = X Tβ + ε (25)

[0121] where X = [1, x1, …, x P T represents the candidate parameter vector, and β = [β0, β1, …, β P T represents the regression coefficient vector of the temperature compensation model;

[0122] In the step S3, N sets of measured sample values of the scale factor drift of the current / frequency conversion circuit are collected, and its column vector form is expressed as The measurement sample matrix composed of the corresponding candidate parameter vectors X is then expressed as

[0123]

[0124] where P is the number of initial parameters in the candidate parameter set Λ, N is the number of measured values collected, is the measured value of the i-th parameter at the j-th time, and is denoted by represents the measurement residual vector of the scale factor drift of the current / frequency conversion circuit. Then, the relationship between the measured values of the scale factor drift of the current / frequency conversion circuit obtained by N measurements and the parameters is expressed as

[0125]

[0126] The loss function is defined as

[0127]

[0128] where is the measurement sample vector of the temperature drift of the scale factor of the current / frequency conversion circuit;

[0129] Under the minimization constraint condition of the temperature compensation residual The linear regression coefficient estimation values of the parameters in the temperature compensation model (9) are obtained by the least squares method as

[0130]

[0131] Substitute the linear regression coefficient estimation values into the temperature compensation model (9) to determine the temperature compensation model of the current / frequency conversion circuit based on multiple linear regression as

[0132]

[0133] where is the predicted value of the scale factor drift of the current / frequency conversion circuit.

[0134] ​​Preferably, the temperature compensation model (3) in step S6 is constructed by setting the parameters of the candidate parameter vector X in the matrix form (9) of the temperature compensation model to zero, where x is the parameter that does not belong to the selected parameter set Θ in the candidate parameter vector X. When constructing the measurement sample matrix m of the candidate parameter vector X, the row vector of the measurement sample values corresponding to the parameter x is also set to a zero vector. Based on the least squares algorithm, with the constraint of minimizing the temperature compensation residual, the non-zero elements of the estimated value of the linear regression coefficient m are substituted into step S6 to obtain the temperature compensation model (3); the temperature compensation model (8) in step S16 is constructed by setting the parameters of the candidate parameter vector X in the matrix form (9) of the temperature compensation model to zero. When constructing the measurement sample matrix of the candidate parameter vector X, the row vector of the measurement sample values corresponding to the parameter x is also set to a zero vector. Based on the least squares algorithm, with the constraint of minimizing the temperature compensation residual, the non-zero elements of the estimated value of the linear regression coefficient are substituted into step S16 to obtain the temperature compensation model (8). is also set to a zero vector. Based on the least squares algorithm, with the constraint of minimizing the temperature compensation residual, the non-zero elements of the estimated value of the linear regression coefficient m are substituted into step S16 to obtain the temperature compensation model (8). is also set to a zero vector. Based on the least squares algorithm, with the constraint of minimizing the temperature compensation residual, the non-zero elements of the estimated value of the linear regression coefficient are substituted into step S16 to obtain the temperature compensation model (8).

[0135] Preferably, in step S11, the overall significance of the temperature compensation model (5) is discriminated by the F-test statistic F j0 . First, the null hypothesis H0 and the alternative hypothesis H1 are established.

[0136] Null hypothesis H0: All multiple linear regression coefficients are zero, that is, there is no linear relationship between the scale factor drift of the current / frequency conversion circuit temperature compensation model (5) currently constructed and the parameters in the selected parameter set Θ.

[0137] Alternative hypothesis H1: At least one multiple linear regression coefficient is not zero, that is, there is a parameter in the selected parameter set Θ that has a significant linear relationship with the scale factor drift of the current / frequency conversion circuit temperature compensation model (5) currently constructed.

[0138] Then, the F-test statistic of the temperature compensation model (5) is calculated from the measured value and the estimated value of the scale factor drift as

[0139]

[0140] where represents the drift of the scale factor of the current / frequency conversion circuit measured at the ambient temperature T n , Add a parameter to the selected set of parameters Θ The predicted value of the scale factor drift of the subsequently fitted current / frequency conversion circuit, Denote the measured value of the scale factor drift is the mean value, N is the number of measured values collected, and the number of elements of the parameters in the selected set of parameters Θ is q + 1;

[0141] Finally, make a hypothesis testing decision. If F j0 > F 0.01 , where F 0.01 is obtained by looking up the table, then reject the original hypothesis H0. The temperature compensation model (5) is overall significant at the 99% level, and there are parameters in the selected set of parameters Θ that have a significant linear contribution to the scale factor drift of the current / frequency conversion circuit. Otherwise, it indicates that there is no linear relationship in the temperature compensation model (5).

[0142] Preferably, in the step S14, use a t-test to test the significance of the q + 1 parameters in the temperature compensation model (5) that pass the F-test. The significance level determines the contribution degree of each parameter to the prediction ability of the temperature compensation model (5); First, put forward the original hypothesis and the alternative hypothesis for the multiple linear regression coefficients corresponding to the parameter x k Θ , k = 1,...,(q + 1).

[0143] Original hypothesis H0: The parameter x k Θ has no significant effect on the scale factor drift of the current / frequency conversion circuit;

[0144] Alternative hypothesis H1: The parameter x k Θ has a significant effect on the scale factor drift of the current / frequency conversion circuit;

[0145] Then calculate the t-statistic as:

[0146]

[0147] where is the estimated value of the regression coefficient of the parameter x k Θ , is the standard error of the estimated value of the regression coefficient , represents the k-th diagonal element of the inverse matrix of the covariance matrix of the measurement sample matrix ;

[0148] Finally, make a t-test decision. If |t k | > t 0.005 , where t 0.005If it is obtained by looking up the table, the original hypothesis H0 is rejected, and the parameter x k Θ is retained in the selected parameter set Θ. Conversely, if the parameter x k Θ has a non-significant contribution in the temperature compensation model (5), then the parameter x k Θ needs to be deleted from the selected parameter set Θ.

[0149] Preferably, the multiple determination coefficient R 2 is used to measure the fitting degree of the temperature compensation model in the step S17; the multiple determination coefficient R 2 is

[0150]

[0151] where is the predicted value of the temperature compensation model output in the step S17 for the drift amount of the scale factor of the current / frequency conversion circuit, represents the environmental temperature T n the drift amount of the scale factor of the current / frequency conversion circuit measured at, y represents the measured value of the scale factor drift amount mean value, N is the number of measured values collected; the value range of R 2 is [0,1]. The closer the value of the multiple determination coefficient R 2 is to 1, the better the fitting effect of the final temperature compensation model in the step S17 on the drift amount of the scale factor of the current / frequency conversion circuit with temperature change.

[0152] Preferably, measure and record the real-time temperature of the current / frequency conversion circuit, calculate all the parameters in the selected parameter set Θ Using the temperature compensation model output in the step S17, obtain the estimated value of the drift amount of the scale factor of the current / frequency conversion circuit, and subtract the estimated value from the measured value of the scale factor of the current / frequency conversion circuit to achieve high-precision compensation for the scale factor of the current / frequency conversion circuit.

[0153] According to the above technical solution, a temperature compensation model of the current / frequency conversion circuit based on multiple linear regression is established, as Figure 1 shown in the flowchart of this method.

[0154] Using the temperature compensation model output in the step S17 to compensate for the scale factor temperature drift amount measured by the current / frequency conversion circuit in the working temperature range of -40°C to 60°C, as Figure 2As shown, where the first column and the second column respectively represent the three cooling processes and the three heating processes, and the first, second, and third rows respectively represent the temperature change rates of 1 °C / minute, 2 °C / minute, and 4 °C / minute. The solid line and the dashed line respectively represent the characteristic curves of the scale factor varying with the ambient temperature before and after temperature compensation. Compared with before temperature compensation, the characteristic curve of the scale factor varying with temperature after being compensated by the method provided by the present invention is flatter, and the compensated current / frequency conversion circuit has higher temperature stability.

[0155] After testing, the temperature compensation method based on multiple linear regression proposed by the present invention can effectively improve the temperature stability of the scale factor of the current / frequency conversion circuit, and the temperature coefficient of the scale factor after compensation is better than 0.2 ppm / °C.

[0156] The above description is only the preferred implementation manner of the present invention and is not intended to limit the present invention. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. Several improvements and refinements made without departing from the principle of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A temperature compensation method for a current / frequency conversion circuit based on multiple linear regression, characterized in that Including the following steps: S1. Place the current / frequency conversion circuit in a high-precision temperature chamber environment, and set the temperature chamber to continuously increase and decrease the temperature within the operating temperature range of the current / frequency conversion circuit; S2. Power the current / frequency conversion circuit through a voltage stabilizer. Under the condition of accessing a stable input current, collect the scale factor of the current / frequency conversion circuit with respect to the real-time ambient temperature T n measurement value where n = 1, 2, …, N represents the time sequence numbers at different temperatures, and a total of N groups of measurement values are collected; S3. Calculate the drift amount of the measured value of the scale factor of the current / frequency conversion circuit with respect to temperature change as follows: wherein is the mean value of the measured values; S4. Establish a candidate parameter set Λ and a selected parameter set Θ for the temperature compensation model of the scale factor of the current / frequency conversion circuit. The candidate parameter set Λ contains candidate parameters of the temperature compensation model related to temperature, including the ambient temperature, the temperature change rate, the higher-order terms and cross-terms of the two, and the number of elements is denoted as p. The initial number of parameters of the candidate parameter set Λ is P. The selected parameter set Θ contains the parameters that currently contribute to the compensation of the temperature drift of the scale factor of the current / frequency conversion circuit. The initial parameter is Θ = {1}, and the number of elements is denoted as q. The initial value of q is 1; S5. Construct the temperature compensation model for the drift of the scale factor of the current / frequency conversion circuit to be solved as y = β P ·x P +…+β2·x2+β1·x1+β0+ε (2) where y is the drift of the scale factor of the current / frequency conversion circuit with respect to temperature variation, x1, x2, …, x P ∈Λ are candidate parameters related to temperature, β0, β1, β2, …, β P are the linear regression coefficients of the temperature compensation model, and ε is the temperature compensation residual; initialize the temperature compensation model of the scale factor of the current / frequency conversion circuit, i.e., let β P = … = β2 = β1 = 0; S6. Introduce the parameter x in the candidate parameter set Λ j ∈Λ, j = 1, ..., p into the temperature compensation model (2) in the step S5 separately, that is, β j ≠0. Assume that the drift y of the scale factor of the current / frequency conversion circuit is linearly correlated with the parameter x j . Based on the least squares algorithm, with the condition of minimizing the temperature compensation residual ε constraint, from the real-time ambient temperature T n measured in the step S2 and the measured value of the scale factor drift calculate all q parameters in the selected parameter set Θ and the parameter x introduced from the candidate parameter set Λ j together to construct the estimated value of the joint linear regression coefficient of the temperature compensation model (2) in the step S5, and obtain p linear regression equations as where \(j = 1, 2, \ldots, p\) is the parameter index of the candidate parameter set \(\Lambda\), for all parameters in the selected parameter set \(\Theta\) the estimated value of the linear regression coefficient, for the parameter \(x\) in the candidate parameter set \(\Lambda\) j the estimated value of the combined linear regression coefficient introducing the temperature compensation model (3), is the parameter \(x\) j the predicted value of the scale factor drift of the current / frequency conversion circuit fitted after introducing the temperature compensation model (3); S7. Calculate the t-test statistic t of the candidate parameter x in the p linear regression equations obtained in the step S6 in sequence j ; j ; S8. Retain the parameters that contribute most significantly to the predictive ability of the temperature compensation model (2), that is, the parameters corresponding to the maximum value among the absolute values |t j | of p t-test statistics Delete the parameter from the candidate parameter set Λ, that is and add it to the selected parameter set Θ, that is S9. Update the linear regression equation in the step S5 corresponding to the parameter to the current temperature compensation model as wherein is a parameter corresponding to the linear regression coefficient in the temperature compensation model (5), is the parameter currently added to the selected parameter set Θ, is the linear regression coefficient of the parameter in the selected parameter set Θ in the temperature compensation model (5), is the parameter in the selected parameter set Θ, is to add a parameter to the selected parameter set Θ and is the predicted value of the scale factor drift of the current / frequency conversion circuit after fitting. S10. Calculate the predicted value of the scale factor drift of the current / frequency conversion circuit of the temperature compensation model (5) in step S9 and all q + 1 parameters x in the selected parameter set Θ k Θ ∈ Θ, k = 1, ..., q + 1 for the F-test statistic F j0 ; S11. Use the F-test statistic F j0 to verify the overall significance of the temperature compensation model (5) and measure the overall linearity between the predicted value of the scale factor drift in the temperature compensation model (5) and all parameters in the selected parameter set Θ ​ where H1 represents the assumption that the temperature compensation model (5) has a significant linear relationship, H0 represents the assumption that the temperature compensation model (5) does not have a linear relationship, and F α is the F hypothesis test threshold at a confidence level of 1-α; S12. When the statistic F of the temperature compensation model (5) j0 satisfies the H1 hypothesis, proceed to step S13; Conversely, when the H0 hypothesis is satisfied, the parameter is excluded from the selected parameter set Θ, that is, After that, return to the step S6 and reselect the candidate parameter; S13. Calculate the t-test statistic t of each parameter in the temperature compensation model (5). k , and judge the significance and contribution degree of each parameter x in the selected parameter set Θ k Θ , k = 1, ..., q + 1 to the temperature compensation model (5). S14. Use the t-test statistic t of q + 1 parameters x, k = 1, ..., q + 1 in the temperature compensation model (5) of step S9 k Θ to test one by one the contribution degree of the parameters to the predicted value of the scale factor drift of the current / frequency conversion circuit k , that is ​ |t k |>t α / 2 , k = 1, …, q + 1 (7) where t α / 2 is the t - hypothesis test threshold at a confidence level of 1 - α; S15. When all the parameters x k Θ 's t-test statistic t k all satisfy the said relation (7), then jump to step S17; when there exists a parameter x k Θ ∈Θ whose t-test statistic t k cannot satisfy the said relation (7), then delete it from the selected parameter set Θ, that is and then continue with step S16; S16. Use the parameter x in the selected parameter set Θ in the said step S15 k Θ , k = 1, ..., h, where h is the number of parameters in the selected parameter set Θ that fail the t-test. Based on the least squares algorithm, with the condition of minimizing the temperature compensation residual ε constraint, from the ambient temperature T n and the measured values of the scale factor drift recalculate and update the temperature compensation model as where h is the number of elements in the selected parameter set Θ of the parameters that fail the t-test in step S15, is the parameter in the selected parameter set Θ of the parameters that fail the t-test in step S15, represents the linear regression coefficient of the updated temperature compensation model (8), is the predicted value of the temperature compensation model (8) for the drift of the scale factor of the current / frequency conversion circuit; S17. Determine whether the candidate parameter set Λ is an empty set. If the candidate parameter set Λ is an empty set, that is, p = 0, then output the temperature compensation model constructed in step S9 or step S16; otherwise, return to step S6 to re-select candidate parameters.

2. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 1, characterized in that In step S2, the scale factor of the current / frequency conversion circuit is the frequency of the output pulse signal under the condition of unit input current. When positive current and negative current are input, the drift amounts of the positive scale factor and the negative scale factor of the current / frequency conversion circuit vary with the ambient temperature differently. Temperature compensation is performed on the positive scale factor and the negative scale factor of the current / frequency conversion circuit respectively.

3. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 1, wherein The ambient temperature T in step S4 n is measured by the temperature acquisition circuit of the current / frequency conversion circuit, and the temperature change rate △T n is obtained by subtracting the ambient temperature T n at the previous moment from the ambient temperature T n-1 at the nth moment.

4. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 1, wherein Express the temperature compensation model (2) in step S5 in matrix form as y = X T β + ε (9) where X = [1, x1, …, x P T represents the candidate parameter vector, and β = [β0, β1, …, β P T represents the regression coefficient vector of the temperature compensation model;​​ In step S3, N measurement sample values of the scale factor drift of the current / frequency conversion circuit are collected, and are represented in the form of a column vector as The measurement sample matrix composed of the corresponding candidate parameter vectors X is represented as where \(P\) is the number of initial parameters in the candidate parameter set \(\Lambda\), and \(N\) is the number of measured value points collected. is the measured value of the \(i\)-th parameter at the \(j\)-th time, and is represented by denotes the measurement residual vector of the scale factor drift of the current / frequency conversion circuit. Then, the relationship between the measured value of the scale factor drift of the current / frequency conversion circuit obtained from \(N\) measurements and the parameters is expressed as Define the loss function as wherein is a measurement sample vector of the temperature drift amount of the scale factor of the current / frequency conversion circuit; In the temperature compensation residual Under the minimization constraint condition, the least squares method is used to obtain the estimated values of the linear regression coefficients of the various parameters in the temperature compensation model (9) as Substitute the estimated value of the linear regression coefficient into the temperature compensation model (9) to determine the temperature compensation model of the current / frequency conversion circuit based on multiple linear regression as Among them is the predicted value of the scale factor drift of the current / frequency conversion circuit.

5. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 1, characterized in that In the step S11, the overall significance of the temperature compensation model (5) is discriminated by the F-test statistic F j0 First, the null hypothesis H0 and the alternative hypothesis H1 are established Null hypothesis H0: All multiple linear regression coefficients are zero, that is, there is no linear relationship between the scale factor drift amount of the currently constructed temperature compensation model (5) of the current / frequency conversion circuit and the parameters in the selected parameter set Θ; Alternative hypothesis H1: At least one multiple linear regression coefficient is not zero, that is, there are parameters in the selected parameter set Θ that have a significant linear relationship with the scale factor drift amount of the currently constructed temperature compensation model (5) of the current / frequency conversion circuit; Then calculate the F-test statistic of the temperature compensation model (5) from the measured value and the estimated value of the scale factor drift amount as wherein represents the drift of the current / frequency conversion circuit scale factor measured at the ambient temperature T n , the predicted value of the drift of the current / frequency conversion circuit scale factor fitted after adding a parameter to the selected parameter set Θ is the mean value of the measured values of the scale factor drift amount, N is the number of measured values collected, and the number of elements of the parameters in the selected parameter set Θ is q + 1; the predicted value of the drift of the current / frequency conversion circuit scale factor fitted after adding a parameter to the selected parameter set Θ represents the measured value of the scale factor drift amount ​ Finally, make a hypothesis testing decision. If F j0 > F α , where F α is obtained by looking up the table, then reject the original hypothesis H0. The temperature compensation model (5) is overall significant at the α level, and there are parameters in the selected parameter set Θ that have a significant linear contribution to the scale factor drift of the current / frequency conversion circuit. Otherwise, it indicates that there is no linear relationship in the temperature compensation model (5).

6. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 1, wherein, In the step S14, the significance of q + 1 parameters in the temperature compensation model (5) passing the F test is tested by using the t test. The significance level determines the contribution degree of each parameter to the prediction ability of the temperature compensation model (5); First, the null hypothesis and the alternative hypothesis are proposed for the multiple linear regression coefficients corresponding to the parameters x k Θ , k = 1, ..., (q + 1). The null hypothesis H0: parameter x k Θ has no significant effect on the drift of the scale factor of the current / frequency conversion circuit; Alternative hypothesis H1: Parameter x k Θ has a significant effect on the drift of the scale factor of the current / frequency conversion circuit; Then calculate the t statistic as: where is the estimated value of the regression coefficient of parameter x k Θ , and is the standard error of the estimated value of the regression coefficient , and represents the k-th diagonal element of the inverse matrix of the covariance matrix of the measurement sample matrix ; Finally, make a t-test decision. If |t k | > t α / 2 , where t α / 2 is obtained by looking up the table, then reject the original hypothesis H0, and retain the parameter x k Θ in the selected parameter set Θ. Conversely, if the contribution degree of the parameter x k Θ in the temperature compensation model (5) is not significant, then the parameter x k Θ needs to be deleted from the selected parameter set Θ.

7. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 1, characterized in that Using the multiple determination coefficient R 2 to measure the fitting degree of the temperature compensation model in the step S17; the multiple determination coefficient R 2 is Wherein is the predicted value of the scale factor drift of the current / frequency conversion circuit by the temperature compensation model output in the step S17, represents the ambient temperature T n is the drift amount of the scale factor of the current / frequency conversion circuit measured at, represents the measured value of the scale factor drift is the mean value, N is the number of measured values collected; R 2 ranges from [0, 1], and the multiple determination coefficient R 2 is close to 1, indicating that the final temperature compensation model in the step S17 has a good fitting effect on the drift amount of the scale factor of the current / frequency conversion circuit with temperature change.

8. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 4, characterized in that, The temperature compensation model (3) in step S6 is constructed by setting the parameters of the candidate parameter vector X in the matrix form (9) of the temperature compensation model to zero, where x is the parameter in the candidate parameter vector X that does not belong to the selected parameter set Θ. When constructing the measurement sample matrix m of the candidate parameter vector X, the row vector of the measurement sample values corresponding to the parameter x is also set to a zero vector. Based on the least squares algorithm, with the minimization of the temperature compensation residual as the constraint condition, the non-zero elements of the obtained linear regression coefficient estimate m are substituted into step S6 to obtain the temperature compensation model (3); the temperature compensation model (8) in step S16 is constructed by setting the parameters of the candidate parameter vector X in the matrix form (9) of the temperature compensation model to zero. When constructing the measurement sample matrix of the candidate parameter vector X, the row vector of the measurement sample values corresponding to the parameter x is also set to a zero vector. Based on the least squares algorithm, with the minimization of the temperature compensation residual as the constraint condition, the non-zero elements of the obtained linear regression coefficient estimate are substituted into step S16 to obtain the temperature compensation model (8). is the parameter in the candidate parameter vector X that does not belong to the selected parameter set Θ. When constructing the measurement sample matrix m of the candidate parameter vector X, the row vector of the measurement sample values corresponding to the parameter x is also set to a zero vector. Based on the least squares algorithm, with the minimization of the temperature compensation residual as the constraint condition, the non-zero elements of the obtained linear regression coefficient estimate are substituted into step S16 to obtain the temperature compensation model (8).

9. The temperature compensation method for the current / frequency conversion circuit based on multiple linear regression according to claim 8, wherein Measure and record the real-time temperature of the current / frequency conversion circuit, and calculate all the parameters in the selected parameter set Θ Using the temperature compensation model output by the step S17, obtain an estimated value of the scale factor drift of the current / frequency conversion circuit, and subtract the estimated value from the measured value of the scale factor of the current / frequency conversion circuit to achieve high-precision compensation for the scale factor of the current / frequency conversion circuit.

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