Phase feedback temperature tracing method based on Kalman filtering

Abstract

The invention discloses a phase feedback temperature tracing method based on Kalman filtering, and the method comprises the following steps: building an observation equation of a corresponding relation between light intensity and temperature, and a state equation of object temperature evolution, carrying out the Taylor expansion of a non-linear part in the observation equation through an extended Kalman filtering method, keeping a first-order linear term, and obtaining a second-order linear term; obtaining an extended Kalman filtering main equation; building an interferometer module, receiving a light intensity signal through a photoelectric detector, and converting the light intensity signal into an electric signal; acquiring an electric signal through acquisition equipment; and the electric signal is used as the input of an extended Kalman filtering main equation, so that extended Kalman filtering is carried out, the calculation of an estimated value of the temperature and an error covariance matrix is completed, and the temperature information is obtained. According to the method, the temperature of the object can be tracked under the condition that a traditional temperature sensor is not used, so that the problem that the traditional temperature sensor cannot work normally in a complex electromagnetic environment is solved.

Description

Technical Field

[0001] The invention relates to the technical field of temperature sensing, and in particular to a phase feedback temperature tracking method based on Kalman filtering. Background Art

[0002] Temperature is a common physical quantity in daily life. In many cases, it is necessary to measure the temperature of an object to more accurately evaluate its state. For example, motors and transformers need to measure their temperature to prevent accidents caused by overheating of the device. In the field of quantum precision measurement, atomic magnetometers need to have an accurate understanding of the temperature of the atomic gas chamber to determine whether it has sufficient density of vaporized alkali metal atoms. Currently, common temperature sensors are generally electrical temperature sensors, which output temperature changes as electrical signals for identification, such as thermocouples, thermistors, etc. However, due to their inherent characteristics, this sensor has certain limitations, such as the inability to work normally in complex electromagnetic environments and inaccurate temperature estimates. Therefore, a method is needed to accurately measure the temperature of an object in a complex electromagnetic environment. Summary of the invention

[0003] In view of the shortcomings of the prior art, the present invention proposes a phase feedback temperature tracking method based on Kalman filtering, which has high temperature measurement accuracy, a wide temperature measurement range, and can accurately track temperature information in a complex electromagnetic environment. The present invention uses the thermal expansion properties of optical fiber and the thermo-optical effect to link the interference phase change of the optical fiber interferometer with the temperature change, and successfully tracks the temperature change through Kalman filtering, thereby realizing the use of an all-optical path to transmit temperature information, and achieving the purpose of accurately tracking temperature information in a complex electromagnetic environment.

[0004] In order to solve the above technical problems, the technical solution of the present invention is:

[0005] A phase feedback temperature tracking method based on Kalman filtering includes the following steps:

[0006] Step 1: Establish an observation equation for the corresponding relationship between light intensity and temperature, as well as a state equation for the temperature evolution of an object, and perform Taylor expansion on the nonlinear part of the observation equation by using an extended Kalman filter method, retaining the first-order linear term, to obtain the extended Kalman filter main equation;

[0007] Step 2: Build an interferometer module, receive the light intensity signal through a photodetector, and convert the light intensity signal into an electrical signal;

[0008] Step 3, collecting electrical signals through a collection device;

[0009] Step 4: Use the electrical signal as the input of the extended Kalman filter main equation to perform the extended Kalman filter, thereby completing the calculation of the temperature estimate and the error covariance matrix, thereby obtaining the temperature information.

[0010] Preferably, the interference phase φ of the interferometer is affected by the optical path difference L, the wavelength λ of the light, and the refractive index n, and the corresponding relationship is as follows:

[0011]

[0012] From the thermo-optic effect, we know that the refractive index n will change with temperature. The relationship between the light intensity I and the interference phase φ is as follows:

[0013]

[0014] The observation equation expression of the corresponding relationship between light intensity and temperature is as follows:

[0015]

[0016]

[0017] Among them, h represents the nonlinear mapping relationship between temperature T and light intensity I. It shows the change of refractive index n with temperature T in the thermo-optical effect. k represents the temperature value at time k, I dif represents the light intensity value at time k, I m represents the amplitude, v k is the observation noise.

[0018] As a preference, when the temperature is rising, assuming that a heating device heats the object with power P(t), according to the law of energy conservation, it can be obtained that:

[0019]

[0020] Where m is the mass of the object, c is the specific heat capacity, Characterizes the rate of change of an object's temperature over time.

[0021] Considering that a completely thermally isolated environment cannot be achieved, and heat loss is affected by multiple factors such as conduction, convection, and radiation, in order to simplify the model, the heat loss Q is specified, assuming that it is only affected by Newton's law of cooling:

[0022]

[0023] Where β is the cooling constant and T0 is the ambient temperature.

[0024] The final temperature change rate can be obtained from this:

[0025]

[0026] Use the previous Euler method to discretize it to obtain the state equation when heating:

[0027]

[0028] in, is the process noise, represents the discretized time step, u(k)= , represents the control item related to the heat source power.

[0029] As a preference, when in a cooling state, since there is no external heat source, u(k)=0, thus:

[0030]

[0031] Preferably, when the temperature changes, the extended Kalman filter main equation is:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] in, Represents the prior estimate of temperature at time k, b=βT0 , Represents the posterior estimate of temperature at time k; K k is the Kalman gain, is the prior estimate error covariance, is the posterior estimation error covariance; A k With H k are the state Jacobian matrix and the measurement Jacobian matrix respectively. u(k) is the control item related to the heat source. When there is no external heat source, u(k)=0.

[0038] Preferably, the state Jacobian matrix and the measurement Jacobian matrix are defined as:

[0039]

[0040]

[0041] in represents the posterior estimate of the temperature at time k-1, Represents the prior estimate of temperature at time k.

[0042] Preferably, the interferometer module comprises a laser, a half-wave plate, a polarization beam splitter, a beam splitter, a first reflector, a second reflector and a photodetector.

[0043] Preferably, the method for the interferometer module to output an interference signal is as follows: a laser emits a laser, and the emitted laser passes through a half-wave plate and then passes through a polarization beam splitter to decompose the incident light into two beams of light; one of the beams of light after passing through the polarization beam splitter is taken as the input of the Michelson interferometer, passes through a 50:50 beam splitter, enters the two arms of the interferometer, is reflected by a first mirror and a second mirror respectively, and then is combined at the beam splitter, thereby outputting an interference signal.

[0044] Preferably, the output of the Michelson interferometer is finally received by a photodetector, and the optical signal is converted into an electrical signal as the output of the interferometer module.

[0045] Preferably, one of the optical paths after beam splitting by the beam splitter in the Michelson interferometer is the experimental arm, and the other optical path after beam splitting is the reference arm, and a temperature control device is provided in the experimental arm.

[0046] Preferably, the extended Kalman filter main equation is written into a data processing device, the output end of the interferometer module is connected to the input end of the acquisition device, and the output end of the acquisition device is connected to the data processing device.

[0047] The present invention has the following characteristics and beneficial effects:

[0048] 1. Kalman filtering is used to track the temperature of the optical fiber, using a new method that is different from the traditional temperature sensing method.

[0049] 2. It can be used to replace traditional temperature sensors and is not easily affected by electromagnetic interference and radio frequency interference.

[0050] 3. Due to the advantages of Kalman filtering itself, when the model is correct, it can greatly reduce the impact of environmental noise, improve the system's anti-interference ability, and make the obtained temperature results more accurate.

[0051] 4. The temperature information transmission process is an all-optical channel and will not introduce additional electromagnetic noise.

[0052] 5. Use photoelectric detectors to collect phase information and convert interference phase changes into changes in voltage amplitude for subsequent data processing.

[0053] 6. A Michelson interferometer is used to sense the interference phase change caused by temperature change. It has a simple structure and high sensitivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0055] Figure 1 A flow chart of a Kalman filter algorithm according to an embodiment of the present invention;

[0056] Figure 2 is a module block diagram of an embodiment of the present invention;

[0057] Figure 3 is a device diagram of an embodiment of the present invention;

[0058] Figure 4 It is a simulation result diagram of an embodiment of the present invention;

[0059] Figure 5 is a posterior covariance graph of an embodiment of the present invention;

[0060] Figure 6 2 is an error diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0061] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0062] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0063] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0064] Example 1

[0065] The present invention provides a phase feedback temperature tracking method based on Kalman filtering, comprising the following steps:

[0066] Step 1: Establish the observation equation of the corresponding relationship between light intensity and temperature, as well as the state equation of the temperature evolution of the object, and use the extended Kalman filter method to perform Taylor expansion on the nonlinear part of the observation equation, retain the first-order linear terms, and obtain the extended Kalman filter main equation.

[0067] Specifically, the working mechanism of the present invention is: when the laser wavelength When stable, the interference phase Affected by the optical path difference L1-L2 and the fiber refractive index Influence:

[0068]

[0069] As the temperature changes, the properties of the optical fiber itself will change. From the thermo-optical effect, we know that its refractive index will change with temperature. Therefore, when the temperature changes, the optical path difference between the two arms of the Michelson interferometer will change due to the change in the refractive index of the optical fiber, which will cause the interference phase to change. When the temperature rises, the optical fiber will also expand due to the heat, causing the optical path of its two arms to change, which will also cause the optical path difference between the two arms of the Michelson interferometer to change. According to the principles of constructive and destructive interference, as the interference phase changes, the light intensity will also change, which can be used to judge the temperature change, that is, as the temperature changes, the output voltage value and period of the photodetector change. Therefore, the interference phase can be used to track the temperature, thereby realizing the detection of temperature changes without using traditional electrical temperature sensors.

[0070] In this embodiment, it is proposed to use Kalman filtering to complete the tracking of temperature signals through light intensity signals. Kalman filtering is an optimal linear estimation method under the condition of minimum mean square error. It relies on the state space equation and uses the measured value and the prior estimated value at the current moment to perform data fusion according to certain weights to reduce the mean square error and reduce the influence of noise. The advantages of Kalman filtering are that it has a small amount of calculation and good recursiveness, so it is easy to implement on embedded devices. Kalman filtering is also often used to estimate quantities that cannot be directly measured. It uses observation data and theoretical models to map the state quantity to be estimated to the observation domain, thereby realizing the estimation of the state quantity. Since conventional temperature sensors are not used, temperature is difficult to measure directly, and because temperature changes can be reflected by changes in interference phase, it meets the conditions of Kalman filtering; therefore, the Kalman filtering algorithm can be used to track temperature through changes in light intensity.

[0071] Furthermore, since the system studied in the present invention is a nonlinear system, it is necessary to introduce an extended Kalman filter. The extended Kalman filter is a variant of the Kalman filter. The nonlinear system is linearized by Taylor expansion and truncating the first-order terms so that it meets the conditions of the Kalman filter. According to the relationship between the change of temperature and light intensity, a state space equation is constructed, and the light intensity is used as the observed quantity and the temperature is used as the state quantity. The temperature condition is tracked using the Kalman filter, so that the temperature change condition can be obtained without using a temperature sensor. And because the temperature information is transmitted through optical fiber, it is not interfered by electromagnetic noise and can correctly reflect the temperature change in a complex electromagnetic environment.

[0072] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Based on this, an embodiment of the present invention provides a phase feedback temperature tracking method based on Kalman filtering. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0073] In this embodiment, Kalman filtering is used to track the temperature of an object in a cooling state through light intensity values, thereby replacing the traditional electrical temperature sensor. The modeling principle is: as the temperature changes, according to the thermo-optical effect, it can be known that the refractive index of the optical fiber will change with the temperature change, and the change in the refractive index causes the change in the interference phase, which is reflected by the change in light intensity.

[0074] Specifically, according to the basic principle of interference, the interferometer output light intensity is decomposed into a DC component and an AC component. The DC component reflects the amplitude of the interferometer output light intensity. The AC component forms a strict mapping relationship with the interference phase through the cosine function. The change in the interference phase is positively correlated with the change in the fiber refractive index n and the optical path difference L, and negatively correlated with the change in the laser wavelength λ. Based on the thermo-optical effect, it is found that the temperature is negatively correlated with the refractive index n. When the temperature changes, the interference light intensity changes. In this way, a mapping relationship between temperature and light intensity is established, and then the observation equation is constructed. From this, the observation equation can be deduced:

[0075]

[0076]

[0077] The observation equation describes the state variable temperature and the observed light intensity Among them, h represents the nonlinear mapping relationship between light intensity and temperature. It represents the change of refractive index with temperature in the thermo-optic effect, v k is the observation noise, which satisfies Gaussian distribution and its covariance matrix is .

[0078] Furthermore, according to the law of conservation of energy, the heat absorbed by the object is equivalent to the heat provided by the heat source. Since a completely thermally isolated environment cannot be achieved, there is bound to be heat loss. Factors affecting the heat loss include heat conduction, heat convection and heat radiation. The heat loss can be described as being proportional to the heat dissipation coefficient, the difference between the object temperature and the ambient temperature, and the surface area of ​​the object. According to the basic laws of thermodynamics, the temperature change rate is inversely proportional to the mass and specific heat capacity of the object, and is proportional to the heat absorbed by the object. In this way, a differential equation for the temperature change rate and time can be established. The differential equation is discretized into a difference equation through the preceding term Euler method to establish a mapping relationship between temperature and time, and then the state equation root is constructed. It can be deduced that the state equation when the temperature is lowered is:

[0079]

[0080] in, is process noise, which satisfies Gaussian distribution and its covariance matrix is The state equation describes the temperature state at the previous moment. The current temperature state impact.

[0081] Since the model is nonlinear, it needs to be linearized to make it meet the conditions for use of Kalman filtering. The nonlinear part can be linearized in the first order using Taylor expansion, and the state Jacobian matrix can be introduced. and the measure Jacobian matrix , which is defined as follows:

[0082]

[0083]

[0084] Jacobian matrix of the measurement Describes the local linear relationship between the observed quantity and the state quantity at a certain moment, the state Jacobian matrix Describes the local linear relationship between the current state and the previous state.

[0085] In a further arrangement of this embodiment, the extended Kalman filter main equation is obtained by the following steps:

[0086] Obtaining the control input item and the state transfer matrix through the state equation to obtain the state transfer information of the system, predicting the state at the current moment based on the a posteriori estimate value, the state transfer matrix and the control input item at the previous moment to obtain the a priori estimate value; calculating the a priori estimate error covariance based on the a posteriori estimate error covariance, the process noise covariance and the state transfer matrix;

[0087] When the observation equation is a nonlinear equation, the observation Jacobian matrix is ​​obtained by linearizing the observation equation according to the extended Kalman filter method to obtain the nonlinear mapping relationship between the system state quantity and the observation quantity;

[0088] According to the minimum mean square error criterion, the Kalman gain is obtained from the prior estimation error covariance, the observation noise covariance and the observation Jacobian matrix;

[0089] The Kalman gain is used to perform weighted fusion of the observed value and the prior estimate, and the prior estimate is corrected to give the optimal posterior estimate, i.e., the temperature tracking value; and the posterior estimate error covariance at the current moment is updated based on the Kalman gain and the observed Jacobian matrix.

[0090] The method of obtaining the main equation of the extended Kalman filter constitutes a closed-loop iterative calculation process, which achieves the optimal estimation of the state of the dynamic system by real-time fusion of predicted values ​​and observed values.

[0091] It should be noted that when in the cooling state, since there is no external heat source, the state equation is:

[0092]

[0093] And its prior estimation error covariance matrix:

[0094]

[0095] According to the optimal estimation theory, the calculation formula of Kalman gain can be obtained:

[0096]

[0097] The Kalman gain can then be used to derive the expression of the a posteriori estimate of temperature and the a posteriori estimate error covariance matrix:

[0098]

[0099]

[0100] Where Z k is the observed light intensity value. So far, the Kalman filter model of this example has been established.

[0101] Step 2: Build an interferometer module, receive the light intensity signal through a photodetector, and convert the light intensity signal into an electrical signal.

[0102] Specifically, Figure 2 and Figure 3 As shown, in this embodiment, the interferometer module includes a laser, a half-wave plate, a polarization beam splitter, a beam splitter, a first mirror, a second mirror, and a photodetector.

[0103] In this embodiment, the laser output light is adjusted in polarization direction by a half-wave plate, and then the incident light is decomposed into two beams of light with mutually orthogonal polarization directions by a polarization beam splitter. The half-wave plate and the polarization beam splitter constitute an optical power attenuator, and the optical power can be adjusted by adjusting the half-wave plate without adjusting the laser output optical power.

[0104] In this embodiment, the laser output light enters the optical power attenuator and then enters the beam splitter to be split into two beams with the same frequency and polarization direction, and then enters the two arms of the interferometer to meet the interference condition.

[0105] In this embodiment, the first reflector and the second reflector reflect the light entering the two arms of the interferometer, so that the light is combined at the beam splitter to generate interference.

[0106] In this embodiment, the photoelectric detector converts the light intensity signal of the interferometer into an electrical signal, which can more conveniently realize the collection of the light intensity signal.

[0107] In this embodiment, the device is as follows Figure 2 As shown, the temperature control module simulates the temperature change.

[0108] Step 3, collecting electrical signals through a collection device;

[0109] In this embodiment, the acquisition device model is PCI4462, which has a maximum sampling rate of 204.8kS / s and a sampling bit number of 24 bits, and can obtain light intensity signals with sufficient accuracy to achieve more accurate tracking of temperature information. The light intensity data is received through the acquisition card and communication is established with the computer.

[0110] Step 4: Use the electrical signal as the input of the extended Kalman filter main equation to perform the extended Kalman filter, thereby completing the calculation of the temperature estimate and the error covariance matrix, thereby obtaining the temperature information.

[0111] It should be noted that, in this embodiment, the data processing device is a computer, which executes the flowchart of the Kalman filter algorithm, such as Figure 1 shown.

[0112] In order to verify the tracking effect of the present invention on temperature changes, the present embodiment uses software to perform simulation. First, a temperature drop curve is generated according to the Newton cooling formula; then, the light intensity value with noise at the corresponding moment is generated according to the relationship between temperature and light intensity. Finally, these generated light intensity values ​​are used as observation data and processed as input of Kalman filter. Figure 5 It can be seen that its posterior covariance matrix changes periodically. This is because the observation equation is a cosine function, and the observation value will change periodically, so the measurement Jacobian matrix will also change periodically, which in turn causes its posterior covariance matrix to change periodically; this proves that the filter can effectively use the observation data and absorb its internal information. The Kalman filter result value can be seen in Figure 4 , it can be seen that the Kalman filter result value is almost the same as the true value, and its error value is Figure 6 It can be seen that the error is small, except for some noise points that are all within 10 -3 The magnitude of the Kalman filter confirms the feasibility of temperature tracking.

[0113] The specific method is as follows:

[0114] 1. Establish the state space equation. Establish the state space equation of the relationship between the interferometer output light intensity and temperature when the temperature changes, that is, the observation equation; and the state equation of the object temperature evolution.

[0115] 2. Calculate the Jacobian matrix. Since the Kalman filter cannot correctly handle nonlinear situations, the nonlinear parts of the state equation and observation equation are Taylor expanded to retain their first-order linear terms, which is the extended Kalman filter method.

[0116] 3. Establish the main equation of the extended Kalman filter. According to the state space equation, the main equation of the extended Kalman filter is listed to track the temperature information.

[0117] 4. Build the interferometer optical path. Use one arm of the beam splitter as the experimental arm to sense temperature changes, and the other arm as the reference arm.

[0118] 5. Convert light intensity signals into electrical signals. The light intensity changes caused by the interference phase changes in the interferometer are converted into electrical signals through photodetectors.

[0119] 6. Light intensity signal acquisition: The output of the photodetector is received by the acquisition device and connected to the data processing device for data processing.

[0120] 7. Data processing and temperature tracking. The light intensity information is used on the data processing device to perform extended Kalman filtering according to the main equation listed in step 3, so as to complete the calculation of the temperature estimate, Kalman gain and error covariance matrix, and thus obtain the temperature information.

[0121] Example 2

[0122] The difference between this embodiment and embodiment 1 is that, when the temperature is in the rising state, assuming that the heating device heats the object with a constant power P, according to the law of energy conservation, it can be obtained that:

[0123]

[0124] Where m is the mass of the object, c is the specific heat capacity, Characterizes the rate of change of an object's temperature over time.

[0125] Considering that a completely thermally isolated environment cannot be achieved, and heat loss is affected by multiple factors such as conduction, convection, and radiation, in order to simplify the model, the heat loss Q is specified as follows:

[0126]

[0127] Among them, h is the equivalent heat transfer coefficient, A is the surface area of ​​the object, and T is the temperature of the object.

[0128] From this we can get:

[0129]

[0130] Right now:

[0131]

[0132] Use the previous Euler method to discretize it to obtain the state equation when heating:

[0133]

[0134] Where u(k)= , , Represents the discretized time step.

[0135] When the temperature rises, the first equation of the extended Kalman filter main equation is:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] in, .

[0142] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A phase feedback temperature tracking method based on Kalman filtering, characterized in that: The steps include: Step 1: Establish an observation equation for the corresponding relationship between light intensity and temperature, as well as a state equation for the temperature evolution of an object, and perform Taylor expansion on the nonlinear part of the observation equation by using an extended Kalman filter method, retaining the first-order linear term, to obtain the extended Kalman filter main equation; Step 2: Build an interferometer module, receive the light intensity signal through a photodetector, and convert the light intensity signal into an electrical signal; Step 3, collecting electrical signals through a collection device; Step 4: Use the electrical signal as the input of the extended Kalman filter main equation to perform the extended Kalman filter, thereby completing the calculation of the temperature estimate and the error covariance matrix, thereby obtaining the temperature information.

2. The phase feedback temperature tracking method based on Kalman filtering according to claim 1 is characterized in that: According to the basic principle of interference, the interferometer output light intensity is decomposed into a DC component and an AC component. The DC component reflects the amplitude of the interferometer output light intensity. The AC component forms a strict mapping relationship with the interference phase through a cosine function. The change in the interference phase is positively correlated with the change in the optical fiber refractive index n and the optical path difference L, and is negatively correlated with the change in the laser wavelength λ. Based on the thermo-optical effect, it is obtained that the temperature is negatively correlated with the refractive index n. When the temperature changes, it causes the change in the interference light intensity. In this way, a mapping relationship between temperature and light intensity is established, and then the observation equation is constructed.

3. The phase feedback temperature tracking method based on Kalman filtering according to claim 2 is characterized in that: According to the law of conservation of energy, the heat absorbed by an object is equivalent to the heat provided by the heat source. Since a completely thermally isolated environment cannot be achieved, heat loss is bound to occur. Factors affecting the heat loss include heat conduction, heat convection, and heat radiation. The heat loss can be described as being proportional to the heat dissipation coefficient, the difference between the object temperature and the ambient temperature, and the surface area of ​​the object. According to the basic laws of thermodynamics, the temperature change rate is inversely proportional to the mass and specific heat capacity of the object, and is proportional to the heat absorbed by the object. In this way, a differential equation for the temperature change rate and time can be established. The differential equation is discretized into a difference equation through the preceding term Euler method, so as to establish a mapping relationship between temperature and time, and then construct the state equation.

4. The phase feedback temperature tracking method based on Kalman filtering according to claim 1 is characterized in that: The extended Kalman filter main equation is obtained by the following steps: Obtaining the control input item and the state transfer matrix through the state equation to obtain the state transfer information of the system, and predicting the state at the current moment based on the a posteriori estimate value, the state transfer matrix and the control input item at the previous moment to obtain the a priori estimate value; The prior estimation error covariance is calculated based on the posterior estimation error covariance, the process noise covariance and the state transfer matrix; When the observation equation is a nonlinear equation, the observation Jacobian matrix is ​​obtained by linearizing the observation equation according to the extended Kalman filter method to obtain the nonlinear mapping relationship between the system state quantity and the observation quantity; According to the minimum mean square error criterion, the Kalman gain is obtained from the prior estimation error covariance, the observation noise covariance and the observation Jacobian matrix; The Kalman gain is used to perform weighted fusion of the observed value and the prior estimate, and the prior estimate is corrected to give the optimal posterior estimate, i.e., the temperature tracking value; and the posterior estimate error covariance at the current moment is updated based on the Kalman gain and the observed Jacobian matrix.

5. The phase feedback temperature tracking method based on Kalman filtering according to claim 1 is characterized in that: The method for obtaining the extended Kalman filter main equation constitutes a closed-loop iterative calculation process, and realizes the optimal estimation of the dynamic system state by real-time fusion of predicted values ​​and observed values.

6. The phase feedback temperature tracking method based on Kalman filtering according to claim 4 is characterized in that: The observation Jacobian matrix is ​​obtained by Taylor expansion of the observation equation while retaining its first-order linear terms; further, in each filtering cycle, the observation Jacobian matrix needs to be recalculated based on the prior estimate at the current moment.

7. The phase feedback temperature tracking method based on Kalman filtering according to claim 1 is characterized in that: The interferometer module includes a laser, a half-wave plate, a polarization beam splitter, a beam splitter, a first reflector, a second reflector and a photodetector.

8. The phase feedback temperature tracking method based on Kalman filtering according to claim 7 is characterized in that: The method for the interferometer module to output an interference signal is as follows: a laser emits a laser, and the emitted laser passes through a half-wave plate and then passes through a polarization beam splitter to decompose the incident light into two beams of light; one of the beams of light after passing through the polarization beam splitter is taken as the input of the Michelson interferometer, passes through a 50:50 beam splitter, enters the two arms of the interferometer, is reflected by a first mirror and a second mirror respectively, and then is combined at the beam splitter, thereby outputting an interference signal.

9. The phase feedback temperature tracking method based on Kalman filtering according to claim 8, characterized in that: The output of the Michelson interferometer is finally received by a photodetector, which converts the optical signal into an electrical signal as the output of the interferometer module.

10. A phase feedback temperature tracking method based on Kalman filtering according to claim 9, characterized in that: In the Michelson interferometer, one of the optical paths after beam splitting by the beam splitter is the experimental arm, and the other optical path after beam splitting is the reference arm. A temperature control device is arranged in the experimental arm.

11. A phase feedback temperature tracking method based on Kalman filtering according to any one of claims 1 to 10, characterized in that: The extended Kalman filter main equation is written into the data processing device, the output end of the interferometer module is connected to the input end of the acquisition device, and the output end of the acquisition device is connected to the data processing device.

Images