A Phase Feedback Temperature Tracking Method Based on Kalman Filter

Abstract

The present invention discloses a phase feedback temperature tracking method based on Kalman filtering, which includes the following steps: establishing an observation equation for the correspondence between light intensity and temperature, and a state equation for the temperature evolution of an object, and performing Taylor expansion on the nonlinear part in the observation equation through the extended Kalman filtering method, retaining the first-order linear term to obtain the main equation of the extended Kalman filter; building an interferometer module, receiving the light intensity signal through a photodetector, and converting the light intensity signal into an electrical signal; collecting the electrical signal through a collection device; using the electrical signal as the input of the main equation of the extended Kalman filter, thereby performing extended Kalman filtering to complete the calculation of the estimated value of the temperature and the error covariance matrix, so as to obtain temperature information. This method can track the temperature of an object without using a traditional temperature sensor to solve the problem that the traditional temperature sensor cannot work properly in a complex electromagnetic environment.

Description

Technical Field

[0001] The present invention relates to the technical field of temperature sensing, and specifically refers 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 occasions, it is necessary to measure the temperature of an object to more accurately evaluate its state. For example, motors, transformers, etc. all need to measure their temperatures to prevent accidents caused by overheating of the devices. In the field of quantum precision measurement, atomic magnetometers need to have an accurate understanding of the temperature of the atomic vapor cell to determine whether it has a 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, such sensors have certain limitations, such as being unable to work properly in complex electromagnetic environments and having inaccurate temperature estimates. Therefore, a method that can accurately measure the temperature of an object in a complex electromagnetic environment is needed. Summary of the Invention

[0003] In view of the deficiencies of the prior art, the present invention proposes a phase feedback temperature tracking method based on Kalman filtering. This method has high temperature measurement accuracy, a wide temperature measurement range, and can accurately track temperature information in a complex electromagnetic environment. The present invention utilizes the thermal expansion property and thermo-optic effect of optical fibers to relate the interference phase change of an optical fiber interferometer to temperature change, and successfully tracks the temperature change through Kalman filtering, thereby realizing the conduction of temperature information through an all-optical path and achieving the purpose of accurately tracking temperature information in a complex electromagnetic environment.

[0004] To solve the above technical problems, the technical solution of the present invention is as follows:

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

[0006] Step 1: Establish an observation equation for the correspondence between light intensity and temperature, and a state equation for the evolution of the object's temperature, and perform a Taylor expansion on the non-linear part in the observation equation through the extended Kalman filtering method, retaining the first-order linear term to obtain the main equation of the extended Kalman filter;

[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: Collect the electrical signal through a collection device;

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

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

[0011]

[0012] According to the thermo-optic effect, the refractive index n changes with temperature. And the light intensity I and the interference phase φ have the following relationship:

[0013]

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

[0015]

[0016]

[0017] Among them, h represents the non-linear mapping relationship between the temperature T and the light intensity I. represents the change of the refractive index n with the temperature T in the thermo-optic effect, T 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] Preferably, when in the heating state, assume that there is a heating device heating an object with a power P(t). According to the law of conservation of energy, it can be obtained that:

[0019]

[0020] Among them, m is the mass of the object, c is the specific heat capacity. characterizes the change rate of the object's temperature with time.

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

[0022]

[0023] Among them, β is the cooling constant, and T0 is the ambient temperature.

[0024] Thus, the final temperature change rate can be obtained:

[0025]

[0026] Discretize it using the above Euler's method to obtain the state equation during heating:

[0027]

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

[0029] Preferably, when in the cooling state, since there is no external heat source, then u(k) = 0, and thus we can obtain:

[0030]

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

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] where represents the prior estimate value of the temperature at time k, b = βT0 , represents the posterior estimate value of the temperature at time k; K k is the Kalman gain, is the prior estimate error covariance, is the posterior estimate error covariance; A k and H k are the state Jacobian matrix and the measurement Jacobian matrix respectively, u(k) is the control term related to the heat source, and 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] where represents the posterior estimate of the temperature at time k-1, represents the prior estimate of the temperature at time k.

[0042] Preferably, 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.

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

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

[0045] Preferably, in the Michelson interferometer, one of the optical paths after the beam splitter is the experimental arm, and the other optical path after the beam splitter 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 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.

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

[0048] First, the Kalman filter is used to track the fiber temperature, and a new method different from the traditional temperature sensing method is used.

[0049] Second, it can be used to replace the traditional temperature sensor and is not easily affected by electromagnetic interference and radio frequency interference.

[0050] Third, due to the advantages of the Kalman filter itself, when the model is correct, it can greatly reduce the influence of environmental noise, improve the anti-interference ability of the system, and make the obtained temperature results more accurate.

[0051] Fourth, the temperature information transmission process is an all-optical path and will not introduce additional electromagnetic noise.

[0052] Fifth, a photodetector is used to collect the phase information, and the interference phase change is converted into a change in voltage amplitude for subsequent data processing.

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

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0055] Figure 1 It is the flowchart of the Kalman filtering algorithm according to the embodiment of the present invention;

[0056] Figure 2 It is the block diagram of the module according to the embodiment of the present invention;

[0057] Figure 3 It is the device diagram according to the embodiment of the present invention;

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

[0059] Figure 5 It is the posterior covariance diagram according to the embodiment of the present invention;

[0060] Figure 6 It is the error diagram according to the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0062] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is 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 a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0063] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installation", "connection", and "coupling" 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 an indirect connection through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0064] Embodiment 1

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

[0066] Step 1: Establish an observation equation for the correspondence between light intensity and temperature, and a state equation for the evolution of the object's temperature, and perform Taylor expansion on the nonlinear part in the observation equation by the extended Kalman filtering method, retaining the first-order linear term to obtain the main equation of the extended Kalman filter.

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

[0068]

[0069] As the temperature changes, the properties of the optical fiber itself will change. According to the thermo-optic effect, its refractive index will change with the temperature. Therefore, when the temperature changes, due to the change in the refractive index of the optical fiber, the optical path difference between the two arms of the Michelson interferometer will change, thereby causing the interference phase to change. When the temperature rises, the optical fiber will also expand due to heat, resulting in a change in the optical path of its two arms, and thus also causing a change in the optical path difference between the two arms of the Michelson interferometer. According to the principle of constructive interference and destructive interference, as the interference phase changes, the light intensity will also change accordingly. The change in temperature can be judged based on this, that is, as the temperature changes, the output voltage value and period of the photodetector change. Therefore, the temperature can be tracked by using the interference phase, so as to detect the temperature change without using a traditional electrical temperature sensor.

[0070] In this embodiment, it is proposed to use Kalman filtering to track the temperature signal through the light intensity signal. Kalman filtering is an optimal linear estimation method under the condition of minimum mean square error. It depends on the state space equation and uses the measured value and the prior estimate value at the current moment to perform data fusion according to certain weights to reduce the mean square error and the influence of noise. The advantage of Kalman filtering is 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 the observed data and the theoretical model to map the state quantity to be estimated to the observation domain, so as to realize the estimation of the state quantity. Since a conventional temperature sensor is not used, the temperature is difficult to measure directly. And because the temperature change can be reflected by the change of the interference phase, which meets the conditions of Kalman filtering; therefore, the Kalman filtering algorithm can be used to track the temperature through the change of the light intensity.

[0071] Furthermore, since the system studied in the present invention is a nonlinear system, it is necessary to introduce the extended Kalman filter. The extended Kalman filter is a variant of the Kalman filter. By performing Taylor expansion on the nonlinear system and intercepting the first-order term for linearization, it meets the conditions of the Kalman filter. According to the variation relationship between the temperature and the light intensity, a state space equation is constructed. Taking the light intensity as the observable quantity and the temperature as the state quantity, the Kalman filter is used to track the temperature situation, so that the temperature change situation can be known without using a temperature sensor. And because the temperature information is transmitted through the optical fiber, it is not affected 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 clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Based on this, the 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 used 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 the light intensity value, thus replacing the traditional electrical temperature sensor. Its modeling principle is: as the temperature changes, according to the thermo-optic effect, it can be known that the refractive index of the optical fiber changes with the temperature change, and the change of the refractive index causes the change of the interference phase, and the change of the interference phase is reflected by the change of the light intensity.

[0074] Specifically, according to the basic principle of interference, the output light intensity of the interferometer is decomposed into a DC component and an AC component. The DC component reflects the amplitude of the output light intensity of the interferometer. 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 refractive index n of the optical fiber and the change in the optical path difference L, and negatively correlated with the change in the laser wavelength λ. Based on the thermo-optic effect, it is obtained that the temperature is negatively correlated with the refractive index n. When the temperature changes, it causes a change in the interference light intensity, thereby establishing a mapping relationship between the temperature and the light intensity, and further constructing the observation equation. From this, its observation equation can be deduced:

[0075]

[0076]

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

[0078] Furthermore, 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, there must be heat loss. The 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, it can be known that the temperature change rate is inversely proportional to the mass and specific heat capacity of the object, and directly proportional to the heat absorbed by the object. Based on this, a differential equation of the temperature change rate with respect to time can be established. The differential equation is discretized into a difference equation by the forward Euler method, thereby establishing a mapping relationship between the temperature and time, and further constructing the root of the state equation. Its state equation during cooling can be deduced as:

[0079]

[0080] Among them, is the process noise, which satisfies the Gaussian distribution, and its covariance matrix is . The state equation describes the influence of the temperature state quantity at the previous moment on the temperature state quantity at the current moment.

[0081] Moreover, since this model is non-linear, it is necessary to linearize it to meet the usage conditions of the Kalman filter. The Taylor expansion can be used to perform first-order linearization on its non-linear part, and the state Jacobian matrix is introduced. and the measurement Jacobian matrix , and their definitions are as follows:

[0082]

[0083]

[0084] The measurement Jacobian matrix describes the local linearization relationship between the observed quantity and the state quantity at a certain moment, and the state Jacobian matrix describes the local linearization relationship between the state at the current moment and the state at the previous moment.

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

[0086] Obtain the control input term and the state transition matrix through the state equation to obtain the state transition information of the system. Based on the posterior estimate value at the previous moment, the state transition matrix, and the control input term, predict the state at the current moment to obtain the prior estimate value; calculate the prior estimate error covariance according to the posterior estimate error covariance, the process noise covariance, and the state transition matrix;

[0087] In the case where the observation equation is a non-linear equation, according to the extended Kalman filter method, linearize it to obtain the observation Jacobian matrix to obtain the non-linear mapping relationship between the system state quantity and the observed quantity;

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

[0089] Use the Kalman gain to perform weighted fusion on the observed value and the prior estimate value, correct the prior estimate value, so as to give the optimal posterior estimate value, that is, the temperature tracking value; and update the posterior estimate error covariance at the current moment based on the Kalman gain and the observation Jacobian matrix.

[0090] 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 fusing the predicted value and the observed value in real time.

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

[0092]

[0093] and its prior estimation error covariance matrix:

[0094]

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

[0096]

[0097] Furthermore, from the Kalman gain, the expressions of the posterior estimation value of the temperature and the posterior estimation error covariance matrix can be deduced:

[0098]

[0099]

[0100] where Z k is the observed light intensity value. Thus, the establishment of the Kalman filter model in this example is completed.

[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, as Figure 2 and Figure 3 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 light emitted by the laser passes through the half-wave plate to adjust the polarization direction of the laser, and then the incident light is decomposed into two beams of light with orthogonal polarization directions through the polarization beam splitter. The half-wave plate and the polarization beam splitter form an optical power attenuator. Without adjusting the optical power of the light emitted by the laser, the optical power can be adjusted by adjusting the half-wave plate.

[0104] In this embodiment, after the light emitted by the laser enters the optical power attenuator, it enters the beam splitter, and is split into two beams of light with the same frequency and the same polarization direction, so as to enter the two arms of the interferometer to meet the interference conditions.

[0105] In this embodiment, the first mirror and the second mirror reflect the light entering the two arms of the interferometer, so that they are combined at the beam splitter to produce an interference phenomenon.

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

[0107] In this embodiment, the device is as Figure 2 shown, and the change of temperature is simulated by the temperature control module.

[0108] Step 3: Collect the electrical signal through a collection device;

[0109] In this embodiment, the model of the collection device is PCI4462, whose maximum sampling rate reaches 204.8 kS / s and has 24-bit sampling bits, which can obtain the light intensity signal with sufficient accuracy to achieve more accurate tracking of temperature information. The collection card is used to complete the reception of the light intensity data and establish communication with the computer terminal.

[0110] Step 4: Use the electrical signal as the input of the extended Kalman filter main equation, and then perform extended Kalman filtering to complete the calculation of the estimated value of the temperature and the error covariance matrix, so as to obtain the temperature information.

[0111] It should be noted that in this embodiment, the data processing device is a computer, and its flowchart for executing the Kalman filter algorithm is as Figure 1 shown.

[0112] In order to verify the tracking effect of the present invention on temperature changes, a simulation is carried out using software in this embodiment. First, a temperature drop curve is generated according to Newton's cooling formula; then, according to the relationship between temperature and light intensity, the light intensity values with noise at corresponding moments are generated. Finally, these generated light intensity values are used as observation data and processed as the input of the Kalman filter. It can be Figure 5 seen that its posterior covariance matrix changes periodically. This is because the observation equation is a cosine function and the observed values 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 utilize the observation data and absorb its internal information. The Kalman filter result value is shown in Figure 4 , and it can be seen that the Kalman filter result value almost coincides with the true value, while its error value is shown in Figure 6 , and it can be seen that its error is small, and except for individual noise points, they are all in the order of 10 -3 , which proves the feasibility of using the Kalman filter to track the temperature.

[0113] The specific method is as follows:

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

[0115] 2. Calculate the Jacobian matrix. Since the Kalman filter cannot correctly handle the non-linear situation, the non-linear parts in the state equation and the observation equation are expanded by Taylor series, and the first-order linear terms are retained, that is, the extended Kalman filter method.

[0116] 3. Establish the main equation of the extended Kalman filter. List the main equation of the extended Kalman filter according to the state space equation to trace the temperature information.

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

[0118] 5. Convert the light intensity signal into an electrical signal. Convert the light intensity change caused by the interference phase change of the interferometer into an electrical signal through a photodetector.

[0119] 6. Collect the light intensity signal. Receive the output of the photodetector through a collection device and connect it to a data processing device for data processing.

[0120] 7. Data processing and temperature tracing. Use the read light intensity information 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 estimated value of temperature, Kalman gain and error covariance matrix, and thus obtain the temperature information.

[0121] Embodiment 2

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

[0123]

[0124] where m is the mass of the object and c is the specific heat capacity, represents the rate of change of the object's temperature with time.

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

[0126]

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

[0128] From this, it can be obtained that:

[0129]

[0130] That is:

[0131]

[0132] Use the forward Euler method to discretize it to obtain the state equation during heating:

[0133]

[0134] where u(k) = , , represents the discretized time step.

[0135] When heating up, the first equation of the extended Kalman filter main equation is:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] where .

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

Claims

1. A phase feedback temperature tracking method based on Kalman filtering, characterized in that It includes the following steps: Step 1: Establish an observation equation for the correspondence between light intensity and temperature, and a state equation for the temperature evolution of an object. Then, perform a Taylor expansion on the nonlinear part in the observation equation using the extended Kalman filter method, retaining the first-order linear term to obtain the main equation of the extended Kalman filter; The method for constructing the observation equation is as follows: According to the basic principle of interference, the output light intensity of the interferometer is decomposed into a direct current component and an alternating current component. The direct current component reflects the amplitude of the output light intensity of the interferometer, and the alternating current component forms a strict mapping relationship with the interference phase through a cosine function. The change amount of the interference phase is positively correlated with the change amounts of the optical fiber refractive index n , optical path difference L , and negatively correlated with the change amount of the laser wavelength λ . Based on the thermo-optic effect, it is obtained that the temperature is negatively correlated with the refractive index n . When the temperature changes, it causes a change in the interference light intensity, thereby establishing a mapping relationship between the temperature and the light intensity, and further constructing the observation 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: Collect the electrical signal through a collection device; Step 4: Use the electrical signal as the input of the main equation of the extended Kalman filter, thereby performing extended Kalman filtering to complete the calculation of the estimated value of temperature and the error covariance matrix, and thus obtain temperature information.

2. The phase feedback temperature tracking method based on Kalman filtering according to claim 1, characterized in that The heat loss is 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, it is known that the temperature change rate is inversely proportional to the mass and specific heat capacity of the object and directly proportional to the heat absorbed by the object. Based on this, a differential equation of the temperature change rate with respect to time is established. The differential equation is discretized into a difference equation by the forward Euler method to establish the mapping relationship between temperature and time, and then the state equation is constructed.

3. A phase feedback temperature tracking method based on Kalman filtering according to claim 1, characterized in that The main equation of the extended Kalman filter is obtained through the following steps: Obtain the control input term and the state transition matrix through the state equation to obtain the state transition information of the system. Based on the posterior estimate value at the previous moment, the state transition matrix, and the control input term, predict the state at the current moment to obtain the prior estimate value; Calculate the prior estimate error covariance according to the posterior estimate error covariance, the process noise covariance, and the state transition matrix; In the case where the observation equation is a nonlinear equation, according to the extended Kalman filter method, linearize it to obtain the observation Jacobian matrix to obtain the nonlinear mapping relationship between the system state quantity and the observed quantity; According to the minimum mean square error criterion, calculate the Kalman gain from the prior estimate error covariance, the observation noise covariance, and the observation Jacobian matrix; Use the Kalman gain to perform weighted fusion of the observed value and the prior estimate value, correct the prior estimate value, and thus give the optimal posterior estimate value, that is, the temperature tracking value; and update the posterior estimate error covariance at the current moment based on the Kalman gain and the observation Jacobian matrix.

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

5. A phase feedback temperature tracking method based on Kalman filtering according to claim 3, characterized in that The observation Jacobian matrix is obtained by performing a Taylor expansion on the observation equation and retaining its first-order linear term; In each filtering period, it is necessary to recalculate the observation Jacobian matrix based on the prior estimate value at the current moment.

6. A phase feedback temperature tracking method based on Kalman filtering according to claim 1, characterized in that, 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.

7. A phase feedback temperature tracking method based on Kalman filtering according to claim 6, characterized in that, The method for the interferometer module to output an interference signal is as follows: The laser emits laser light, and the emitted laser light passes through a half-wave plate and then 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, enters the two arms of the interferometer after passing through a 50:50 beam splitter, is reflected by the first mirror and the second mirror respectively, and then recombined at the beam splitter, thereby outputting an interference signal.

8. A phase feedback temperature tracking method based on Kalman filtering according to claim 7, characterized in that The output of the Michelson interferometer is finally received by a photodetector, which converts the optical signal into an electrical signal and serves as the output of the interferometer module.

9. A phase feedback temperature tracking method based on Kalman filtering according to claim 8, characterized in that One of the optical paths after the beam splitting by the beam splitter in the Michelson interferometer is the experimental arm, and the other optical path after the beam splitting is the reference arm. A temperature control device is provided in the experimental arm.

10. A phase feedback temperature tracking method based on Kalman filtering according to any one of claims 1-9, 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.

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