Method for estimating tilt-length coupling coefficient when optical path noise exists in space gravitational wave detector

Abstract

The invention discloses a tilt-length coupling coefficient estimation method when optical path noise exists in a space gravitational wave detector, and belongs to the technical field of noise analysis and data processing of the space gravitational wave detector. In combination with a convolutional neural network and an adaptive time delay interference technology, a link polluted by optical path noise is automatically identified through the convolutional neural network, then time delay interference observed quantity capable of suppressing contribution of the polluted link is constructed, and an optimal time delay interference combination is automatically screened out. Complete offset of laser frequency noise and effective avoidance of abnormal links are realized; meanwhile, by introducing an edge likelihood function regression method, a tilt-length coupling coefficient can be estimated with high precision without assuming a noise power spectral density model, so that tilt-length noise is effectively deducted, and the sensitivity and reliability of gravitational wave signal extraction are greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of noise analysis and data processing technology for space gravitational wave detectors, and more specifically, relates to a method for estimating the tilt-length coupling coefficient in a space gravitational wave detector when optical path noise exists. Background Technology

[0002] Gravitational waves are ripples in spacetime caused by the motion of massive celestial bodies, capable of carrying information from the depths of the universe. Space-based gravitational wave detection programs (such as LISA, Tianqin, and Taiji) detect low-frequency gravitational wave signals by constructing laser interferometers spanning millions of kilometers in space. Because the space environment effectively avoids interference from ground-based noise, space-based gravitational wave detectors play an irreplaceable role in low-frequency gravitational wave observation, filling the frequency gap in ground-based detection. However, in actual detection processes, the phase noise caused by laser frequency instability is far higher than the intensity of the gravitational wave signal, necessitating the use of time-delay interferometry to suppress this noise.

[0003] Space-based gravitational wave detectors employ inter-satellite interferometry spanning millions of kilometers, and their sensitivity depends on the suppression and calibration of various residual noises. With current noise subtraction techniques, in the low-frequency range (<0.01 Hz), residual acceleration noise from the test mass primarily dominates. In the mid-frequency range (0.01–1 Hz), optical path noise and tilt-length coupling become key factors limiting sensitivity. Tilt-length noise is generated by the angular jitter of optical elements, mapped to an equivalent length change through geometric coupling. It can be suppressed by measuring the coupling coefficient and subtracting its contribution from the data. It should be noted that tilt-length noise describes a form of equivalent measurement noise generated under a known physical mechanism. Specifically, when angular jitter (also known as tilt noise) occurs in optical elements or the optical platform, due to non-ideal factors such as finite spot size, wavefront curvature, optical axis offset, and assembly errors in the optical system, the angular disturbance is transformed into an equivalent optical path length change through geometric coupling, thus manifesting as a noise component in the interferometric phase readout that is difficult to distinguish from the actual length change. Therefore, tilt-length noise is used to emphasize the physical nature of angular jitter after being mapped by the optical system and ultimately manifested as length noise in interferometry. Its essence is the coupling result between angular perturbation and equivalent length change, rather than simply angular noise itself.

[0004] If tilt-length coupling noise is not removed, it will be directly superimposed on the interferometric results. Furthermore, its spectral characteristics in the mid-frequency band overlap with optical path noise and the effective frequency band of the gravitational wave signal, making it difficult to distinguish using simple filtering or frequency domain separation methods. This will lead to an increase in the noise floor, thereby reducing the signal-to-noise ratio of the gravitational wave signal and affecting the reliability of system sensitivity assessment and subsequent scientific data analysis. Therefore, it is necessary to estimate the tilt-length coupling coefficient to reconstruct the equivalent length noise introduced by angular jitter and subtract this noise component from the time-delayed interferometric output signal. This will improve the interferometric accuracy of the space gravitational wave detector and suppress the main noise source in the mid-frequency band.

[0005] However, as optical path noise increases, its power spectral density and tilt-length noise exhibit similar characteristics in the mid-frequency band, making it impossible for traditional spectral differentiation methods to reliably separate the two. This leads to increased tilt-length coefficient estimation errors, which in turn affect gravitational wave signal recovery. Optical path noise originates from minute variations in the optical path length within the optical system. These variations can be caused by factors such as structural thermal expansion due to temperature gradients, deformation or stress relaxation of optical components, assembly errors of optical components, wavefront distortion, and micro-vibrations of mechanical support structures. Since the accuracy of the tilt-length coupling coefficient estimation algorithm depends on the measurement accuracy of angular jitter in the input data and the interference output signal, an increase in optical path noise significantly degrades the estimation accuracy and uncertainty of the coupling coefficient, thus affecting the gravitational wave signal extraction effect. Summary of the Invention

[0006] In view of the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for estimating the tilt-length coupling coefficient in a space gravitational wave detector when there is optical path noise, thereby improving the estimation accuracy of the tilt-length noise coupling coefficient.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a method for estimating the tilt-length coupling coefficient in a space gravitational wave detector when optical path noise exists is provided, comprising: S1, acquire phase measurement data of each optical link of the space interferometer and angle jitter measurement data provided by the onboard attitude control system; S2, perform short-time Fourier transform on the phase measurement data to obtain a power spectral density image, and input the power spectral density image into a convolutional neural network for abnormal link identification to obtain optical links with abnormal optical path noise; S3, based on the optical link with optical path noise anomaly, select the optimal time delay interference combination so that the time delay interference based on the optimal time delay interference combination can completely cancel the laser frequency noise and eliminate the influence of the optical link with optical path noise anomaly. S4. Based on the optimal time-delay interference combination, time-delay interference is performed to obtain the interference output signal. Based on the interference output signal and the angle jitter measurement data, frequency domain power spectrum regression analysis is performed using the marginal likelihood function to obtain the optimal estimate of the tilt-length coupling coefficient. The tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change.

[0008] According to the tilt-length coupling coefficient estimation method in space gravitational wave detectors with optical path noise, the convolutional neural network includes an input layer, multiple convolutional layers, pooling layers, fully connected layers, and an output layer. The input layer receives the power spectral density image of the phase measurement data of each optical link. The convolutional layers extract the frequency domain features of the power spectral density image. The pooling layers perform dimensionality reduction on the frequency domain features output by the convolutional layers. The fully connected layers perform nonlinear mapping on the dimensionality-reduced features output by the pooling layers. The output layer maps the output of the fully connected layers to a noise state label corresponding to each optical link.

[0009] Based on the tilt-length coupling coefficient estimation method for optical path noise in space gravitational wave detectors, and considering the optical link with optical path noise anomalies, an optimal time-delay interferometry combination is selected. This ensures that time-delay interferometry based on the optimal time-delay interferometry combination can completely cancel laser frequency noise and eliminate the influence of the optical link with optical path noise anomalies. Specifically, this includes: Based on the time delay operators corresponding to the optical path length of different optical links and the polynomial coefficients of the time delay operators, the phase measurement data of each optical link in the space gravitational wave detector are expressed as a linear superposition of various noise terms, including laser frequency noise and optical path noise, and a set of linear constraint equations under the condition of laser frequency noise cancellation is obtained. The coefficients of the time delay operator polynomial corresponding to the optical link with optical path noise anomaly are set to 0 as an additional constraint. Based on the additional constraints, the linear constraint equations are solved to obtain the optimal time-delay interference combination.

[0010] Based on the tilt-length coupling coefficient estimation method for optical path noise in space gravitational wave detectors described above, the linear constraint equations are as follows:

[0011] in, Indicates optical link Time delay operator, Indicates optical link reverse link Time delay operator, and Optical links and The time delay operator polynomial.

[0012] Based on the aforementioned method for estimating the tilt-length coupling coefficient in a space gravitational wave detector when optical path noise exists, and using the interferometric output signal and the angular jitter measurement data, frequency domain power spectrum regression analysis is performed using the marginal likelihood function to obtain the optimal estimate of the tilt-length coupling coefficient, specifically including: Multiple estimates are set for the tilt-length coupling coefficient; The angle jitter measurement data are weighted based on each estimated value of the tilt-length coupling coefficient to obtain the tilt-length noise estimation component corresponding to the corresponding estimated value. The tilt-length noise estimation component corresponding to each estimated value is then removed from the interferometric output signal to obtain the residual signal corresponding to each estimated value. The residual signals corresponding to each estimate are converted to the frequency domain, and the average power spectral density of the residual signals at each sampling frequency is calculated. Based on the average power spectral density of the residual signal corresponding to each estimate at each sampling frequency, and the marginal likelihood function, the marginal likelihood function value corresponding to each estimate is calculated, and the estimate corresponding to the maximum marginal likelihood function value is selected as the optimal estimate of the tilt-length coupling coefficient.

[0013] Based on the tilt-length coupling coefficient estimation method for optical path noise in space gravitational wave detectors described above, the edge likelihood function is:

[0014] in, This represents the marginal likelihood function with respect to the tilt-length coupling coefficient; This indicates that in the optical link between the transmitter (TX) and receiver (RX), tilt-length noise originates from angular jitter. The tilt-length coupling coefficient to the interference phase, These represent the angular jitter components of the device orientation in two mutually orthogonal directions, used to characterize the small angular deviation of an optical platform or optical element from its ideal orientation. This represents the discrete Fourier transform result of the residual signal at frequency k; The average power spectral density of the residual signal at frequency k; This represents the value of the theoretical noise power spectrum model at frequency k; The number of independent spectrum segments used for estimation; is the set of sampling frequencies; C is a constant term independent of the parameters.

[0015] According to a second aspect of the present invention, a tilt-length coupling coefficient estimation system is provided for a space gravitational wave detector in the presence of optical path noise, comprising: The data acquisition unit is used to acquire phase measurement data from each optical link of the space interferometer and angle jitter measurement data provided by the onboard attitude control system; An abnormal link identification unit is used to perform a short-time Fourier transform on the phase measurement data to obtain a power spectral density image, and input the power spectral density image into a convolutional neural network to identify abnormal links and obtain optical links with abnormal optical path noise. The time delay interference selection unit is used to select the optimal time delay interference combination based on the optical link with optical path noise anomaly, so that the time delay interference based on the optimal time delay interference combination can completely cancel the laser frequency noise and eliminate the influence of the optical link with optical path noise anomaly. The coupling coefficient estimation unit is used to perform time-delay interference based on the optimal time-delay interference combination to obtain the interference output signal, and to perform frequency domain power spectrum regression analysis using the marginal likelihood function based on the interference output signal and the angle jitter measurement data to obtain the optimal estimate of the tilt-length coupling coefficient; the tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change.

[0016] According to a third aspect of the present invention, an electronic device is provided, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0017] According to a fourth aspect of the invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to perform the method as described in the first aspect.

[0018] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: When optical path noise anomalies occur in one or more optical links of a space gravitational wave detector, a combination of convolutional neural networks and adaptive time-delay interferometry is used. In the data analysis stage, the convolutional neural network first automatically identifies the links contaminated by optical path noise, and then constructs time-delay interferometric observations that can suppress the contribution of contaminated links. The optimal time-delay interferometric combination is automatically selected to achieve complete cancellation of laser frequency noise and effective avoidance of abnormal links. At the same time, by introducing the marginal likelihood function regression method, the tilt-length coupling coefficient can be estimated with high accuracy without assuming a noise power spectral density model, thereby achieving effective subtraction of tilt-length noise and significantly improving the sensitivity and reliability of gravitational wave signal extraction. Attached Figure Description

[0019] Figure 1 A schematic flowchart illustrating the tilt-length coupling coefficient estimation method for a space gravitational wave detector with optical path noise, as provided in an embodiment of the present invention. Figure 2 This is a block diagram of the convolutional neural network structure and a schematic diagram of the main parameter configuration provided in the embodiments of the present invention; Figure 3 The time delay interference combination provided in the embodiments of the present invention A spacetime diagram; Figure 4 The time delay interference combination provided in the embodiments of the present invention A spacetime diagram; Figure 5 The time delay interference combination provided in the embodiments of the present invention A spacetime diagram; Figure 6 The time delay interference combination provided in the embodiments of the present invention A spacetime diagram; Figure 7 The time delay interference combination provided in the embodiments of the present invention A spacetime diagram; Figure 8 The figure shows the estimation results of the tilt-length coupling coefficient based on edge likelihood function regression under the optical path noise anomaly provided in the embodiments of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] This invention provides a method for estimating the tilt-length coupling coefficient in a space gravitational wave detector when optical path noise is present, such as... Figure 1 As shown, it includes: S1, acquire phase measurement data of each optical link of the space interferometer and angle jitter measurement data provided by the onboard attitude control system; S2, perform short-time Fourier transform on the phase measurement data to obtain a power spectral density image, and input the power spectral density image into a convolutional neural network for abnormal link identification to obtain optical links with abnormal optical path noise; S3, based on the optical link with optical path noise anomaly, select the optimal time delay interference combination so that the time delay interference based on the optimal time delay interference combination can completely cancel the laser frequency noise and eliminate the influence of the optical link with optical path noise anomaly. S4. Based on the optimal time-delay interference combination, time-delay interference is performed to obtain the interference output signal. Based on the interference output signal and the angle jitter measurement data, frequency domain power spectrum regression analysis is performed using the marginal likelihood function to obtain the optimal estimate of the tilt-length coupling coefficient. The tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change.

[0022] Specifically, in the basic link configuration of the space gravitational wave detector, three satellites form an equilateral triangle array, and each optical link consists of a transmitter and a receiver. The phase measurement data on each optical link includes the phase difference between the optical signals at the transmitter and receiver on the corresponding link. This phase difference is the result of multiple physical effects during the actual measurement process, and it inherently includes the combined response of factors such as laser frequency noise, optical path noise, and tilt-length noise during interferometric readout, reflecting the phase change of each optical link under actual operating conditions. Since the laser frequency noise is of a high magnitude, it needs to be canceled by time-delayed interferometry. However, during actual measurements, optical path noise may be abnormally amplified on some optical links, thus disrupting the ideal noise cancellation relationship. Therefore, before constructing the time-delayed interferometry combination, the original phase measurement data needs to be preprocessed by downsampling, filtering, and interpolation.

[0023] This process involves using high-pass filtering to remove low-frequency drift from the raw phase data of each optical link. Subsequently, a sliding window adaptive smoothing algorithm is employed to suppress transient pulse interference, ensuring the stability of the time-domain data. Finally, the processed signals are time-delay synchronized to guarantee that the alignment accuracy of data from different optical links on the time axis is better than 1 / 10 of the sampling interval. The phase measurement data obtained from each optical link after this processing step can be directly used for optical path noise identification and subsequent time-delay interferometry construction. Simultaneously, angular jitter measurement data provided by the onboard attitude control system is also acquired.

[0024] After preprocessing the phase measurement data, this embodiment of the invention employs a convolutional neural network to identify anomalies in the optical path noise of each optical link, thereby determining which optical links have optical path noise levels that significantly deviate from the normal range, thus providing a basis for subsequent selection of time-delayed interferometric combinations. Specifically, the phase measurement data of each optical link can be subjected to a short-time Fourier transform to obtain the corresponding power spectral density image, and the power spectral density image of each optical link can be input into a convolutional neural network for anomaly link identification to identify optical links with abnormal optical path noise.

[0025] In some embodiments, the overall structure of the convolutional neural network is as follows: Figure 2 As shown, the convolutional neural network includes an input layer, multiple convolutional layers, pooling layers, a fully connected layer, and an output layer. The input layer receives the power spectral density image of the phase measurement data from each optical link. The convolutional layers extract the frequency domain features of the power spectral density image. The pooling layers perform dimensionality reduction on the frequency domain features output by the convolutional layers. The fully connected layer performs nonlinear mapping on the dimensionality-reduced features output by the pooling layers. The output layer (e.g., a Softmax or Sigmoid output layer) maps the output of the fully connected layer to a noise state label corresponding to each optical link. The noise state label indicates whether there are optical path noise anomalies in the corresponding optical link. To improve recognition accuracy, the convolutional neural network can employ a sample augmentation strategy with noise injection during the training phase. The input data is obtained through different simulated optical noise scenarios, and the parameters of the convolutional neural network are adjusted during training by minimizing the cross-entropy loss function.

[0026] After identifying optical links with abnormal optical path noise, the time-delay interferometry equation can be solved using a geometric construction method based on the identification result. The optimal time-delay interferometry combination can then be selected to avoid these optical links with abnormal optical path noise, while ensuring complete cancellation of laser frequency noise. The optimal time-delay interferometry combination describes the time-delay operator and its polynomial coefficients for each optical link signal, and is used to perform time-delay interferometry processing on each optical link signal.

[0027] Specifically, the basic principle of time-delay interferometry is to apply specific time-delay operators and their corresponding weighting coefficients (i.e., the time-delay operator polynomial coefficients) between different link signals, so that the laser frequency noise is precisely canceled in the constructed interferometric combination. Therefore, a geometric construction method can be used to construct the time-delay interferometric combination for the phase measurement data of each optical link. That is, the phase measurement data of each optical link is regarded as a data stream propagating along the corresponding optical path direction. By introducing a time-delay operator corresponding to the optical path length on the time axis, the time-delay operator polynomial coefficients of each optical link are solved using an optimization algorithm to construct the optimal time-delay interferometric combination. This achieves weighted, delayed, and linear combination of different link signals, ensuring that the condition for complete cancellation of laser frequency noise is met and eliminating the contribution of identified optical path noise anomalous links.

[0028] In some embodiments, based on the time delay operators corresponding to the optical path lengths of different optical links and the polynomial coefficients of the time delay operators, the phase measurement signals of each optical link in the space gravitational wave detector can be expressed as a linear superposition of various noise terms, including laser frequency noise and optical path noise, to obtain a set of linear constraint equations under the condition of laser frequency noise cancellation. The time delay operators corresponding to each optical link can be determined based on the optical path length of the corresponding optical link. The linear constraint equations of the time-delay interferometry combination can be expressed as three laser noise cancellation equations, each corresponding to the laser frequency noise contribution of a satellite. For any optical link, its phase measurement data can be expressed as the sum of signal terms, laser frequency noise terms, optical path noise terms, and tilt-length noise terms. By solving the polynomial coefficients of the time delay operators that satisfy the above linear constraint equations, an optimal time-delay interferometry combination can be constructed. Time-delay interferometry processing based on this optimal combination can achieve laser frequency noise cancellation.

[0029] Based on this, since any optical link may theoretically experience optical path noise anomalies during the operation of a space gravitational wave detector, but the simultaneous occurrence of anomalies in multiple links is an extremely low-probability event. To address the possibility of sudden local link anomalies during normal detector operation, this embodiment of the invention sets additional constraints to eliminate the impact of optical links with optical path noise anomalies. Specifically, when an optical link with optical path noise anomalies is identified, the coefficients of the polynomial of the time delay operator corresponding to that optical link are set to 0 as an additional constraint. This indicates that the phase measurement data of the corresponding optical link does not participate in the weighted superposition during the time-delay interference process, ensuring that the signal of the corresponding optical link is avoided during the time-delay interference process. Mathematically, the above additional constraints are equivalent to adding linear constraints to the original linear constraint equations, shrinking the solution space to a subspace that does not contain the abnormal link data stream. As long as the number of remaining links and the degrees of freedom of the time delay operator satisfy the solvability condition of the equations, a time-delay interference combination that satisfies the laser frequency noise cancellation requirement and has the ability to avoid abnormal links can be obtained. This improves the operational stability of the system under sudden noise anomaly conditions while ensuring complete cancellation of laser frequency noise. Based on the above additional constraints, solving the linear constraint equations yields the optimal time-delay interference combination that has specific data avoidance capabilities and completely cancels out laser frequency noise.

[0030] In some embodiments, the system of linear constraint equations is as follows:

[0031] in, Indicates optical link Time delay operator, Indicates optical link reverse link Time delay operator, and Optical links and The time delay operator polynomial.

[0032] Figure 3-7The spatiotemporal delay path structures of several optimal time-delay interferometric combinations are illustrated as examples. Table 2 shows the optical links that each optimal time-delay interferometric combination can avoid. In Table 2, "Avoid Data Stream 1" and "Avoid Data Stream 2" list the two sets of measurement data streams that each time-delay interferometric combination can avoid. The data stream outside the parentheses represents the directly avoided link, while the data stream inside the parentheses represents the link that can be avoided after index rotation. The avoided data stream indicates that the phase measurement signal of the optical link does not participate in the superposition in the corresponding time-delay interferometric combination, thus avoiding the influence of optical path noise of that link on the combined output. Index rotation refers to the cyclical replacement of link indices, which can generate several mathematically equivalent but physically different combination forms from the same type of time-delay interferometric combination, thereby enabling the combination to avoid different optical link data streams. As shown in the figure, even in the event of anomalies in a single or dual link, the optimal time delay interference combination selected by the method proposed in this embodiment of the invention can still completely cancel out the laser frequency noise, while avoiding contaminated data stream signals, thus providing a stable input for the subsequent estimation of the tilt-length coupling coefficient.

[0033]

[0034] After determining the optimal time-delay interferometric combination, time-delay interferometric processing is performed using this optimal combination to obtain the interferometric output signal. Subsequently, based on the interferometric output signal and the angle jitter measurement data obtained in step S1, the tilt-length coupling coefficient is estimated in the frequency domain using the marginal likelihood function regression method to subtract tilt-length noise. Tilt-length noise is caused by the attitude change of the satellite optical platform, and its phase response has a linear coupling relationship with the attitude angle signal. The tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change. Let the interferometric output signal be Y(f) and the angle jitter measurement data be Φ(f), then the relationship between them can be expressed as Y(f) = C·Φ(f) + N(f), where C is the tilt-length coupling coefficient to be estimated, and N(f) is the noise term. Traditional least squares methods can lead to estimation bias when the noise variance is unknown or non-stationary. Therefore, this invention introduces the marginal likelihood function method, which integrates and marginalizes the noise power spectral density, thereby avoiding explicit assumptions about the noise spectral density and improving the stability of coefficient estimation.

[0035] In some embodiments, multiple estimates can be set for the tilt-length coupling coefficient. Based on each estimate of the tilt-length coupling coefficient, the angle jitter measurement data is weighted to obtain the corresponding tilt-length noise estimation component. This tilt-length noise estimation component is then removed from the interferometric output signal to obtain the residual signal for each estimate. Subsequently, the residual signals for each estimate are converted to the frequency domain, and the average power spectral density of the residual signals at each sampling frequency is calculated. Next, based on the average power spectral density of the residual signals for each estimate at each sampling frequency, and the marginal likelihood function, the marginal likelihood function value for each estimate is calculated. The estimate with the largest marginal likelihood function value is selected as the optimal estimate of the tilt-length coupling coefficient. This marginal likelihood function regression method can accurately recover the coupling coefficient even under conditions of enhanced optical path noise or link anomalies.

[0036] In other embodiments, the edge likelihood function is:

[0037] in, This represents the marginal likelihood function with respect to the tilt-length coupling coefficient; This indicates that in the optical link between the transmitter (TX) and receiver (RX), tilt-length noise originates from angular jitter. The tilt-length coupling coefficient to the interference phase, These represent the angular jitter components of the device orientation in two mutually orthogonal directions, used to characterize the small angular deviation of an optical platform or optical element from its ideal orientation. This represents the discrete Fourier transform result of the residual signal at frequency k. Let k be the average power spectral density of the residual signal at frequency k. This represents the value of the theoretical noise power spectrum model at frequency k; The number of independent spectrum segments used for estimation; is the set of sampling frequencies; C is a constant term independent of the parameters.

[0038] Figure 8 The estimation results of the tilt-length coupling coefficient are shown for two optical links with optical path noise anomalies, demonstrating that the method proposed in this embodiment still has good robustness and accuracy under multi-link anomaly conditions. Table 2 shows the optimal time-delay interferometry combination selected under optical path noise anomaly conditions. Then, the actual tilt-length coupling coefficient is compared with its optimal estimate.

[0039]

[0040] As shown in Table 2, the optimal estimated value obtained by the method proposed in the embodiments of the present invention is highly consistent with the true value, with a maximum deviation of less than 2%, which verifies the effectiveness of the method proposed in the embodiments of the present invention.

[0041] In summary, the method provided by this invention, when optical path noise anomalies occur in one or more optical links of a space gravitational wave detector, combines convolutional neural networks and adaptive time-delay interferometry. During the data analysis phase, the convolutional neural network automatically identifies the links contaminated by optical path noise. Then, it constructs time-delay interferometric observations that suppress the contribution of the contaminated links, automatically selecting the optimal time-delay interferometric combination to achieve complete cancellation of laser frequency noise and effective avoidance of abnormal links. Simultaneously, by introducing the marginal likelihood function regression method, the tilt-length coupling coefficient can be estimated with high accuracy without assuming a noise power spectral density model, thereby achieving effective subtraction of tilt-length noise and significantly improving the sensitivity and reliability of gravitational wave signal extraction.

[0042] The tilt-length coupling coefficient estimation system for optical path noise in a space gravitational wave detector provided by the present invention is described below. The tilt-length coupling coefficient estimation system for optical path noise in a space gravitational wave detector described below can be referred to in correspondence with the tilt-length coupling coefficient estimation method for optical path noise in a space gravitational wave detector described above.

[0043] This invention provides a tilt-length coupling coefficient estimation system for space gravitational wave detectors when optical path noise exists, comprising: The data acquisition unit is used to acquire phase measurement data from each optical link of the space interferometer and angle jitter measurement data provided by the onboard attitude control system; An abnormal link identification unit is used to perform a short-time Fourier transform on the phase measurement data to obtain a power spectral density image, and input the power spectral density image into a convolutional neural network to identify abnormal links and obtain optical links with abnormal optical path noise. The time delay interference selection unit is used to select the optimal time delay interference combination based on the optical link with optical path noise anomaly, so that the time delay interference based on the optimal time delay interference combination can completely cancel the laser frequency noise and eliminate the influence of the optical link with optical path noise anomaly. The coupling coefficient estimation unit is used to perform time-delay interference based on the optimal time-delay interference combination to obtain the interference output signal, and to perform frequency domain power spectrum regression analysis using the marginal likelihood function based on the interference output signal and the angle jitter measurement data to obtain the optimal estimate of the tilt-length coupling coefficient; the tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change.

[0044] This invention provides an electronic device, including: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0045] This invention provides a computer-readable storage medium storing computer instructions that cause a processor to perform the method described in any of the above embodiments.

[0046] This invention provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the method described in any of the above embodiments.

[0047] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating the tilt-length coupling coefficient in a space gravitational wave detector when optical path noise exists, characterized in that, include: S1, acquire phase measurement data of each optical link of the space interferometer and angle jitter measurement data provided by the onboard attitude control system; S2, perform short-time Fourier transform on the phase measurement data to obtain a power spectral density image, and input the power spectral density image into a convolutional neural network for abnormal link identification to obtain optical links with abnormal optical path noise; S3, based on the optical link with optical path noise anomaly, select the optimal time delay interference combination so that the time delay interference based on the optimal time delay interference combination can completely cancel the laser frequency noise and eliminate the influence of the optical link with optical path noise anomaly. S4. Based on the optimal time-delay interference combination, time-delay interference is performed to obtain the interference output signal. Based on the interference output signal and the angle jitter measurement data, frequency domain power spectrum regression analysis is performed using the marginal likelihood function to obtain the optimal estimate of the tilt-length coupling coefficient. The tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change.

2. The tilt-length coupling coefficient estimation method for a space gravitational wave detector with optical path noise as described in claim 1, characterized in that, The convolutional neural network includes an input layer, multiple convolutional layers, pooling layers, a fully connected layer, and an output layer. The input layer receives the power spectral density image of the phase measurement data from each optical link. The convolutional layers extract the frequency domain features of the power spectral density image. The pooling layers perform dimensionality reduction on the frequency domain features output by the convolutional layers. The fully connected layer performs nonlinear mapping on the dimensionality-reduced features output by the pooling layers. The output layer maps the output of the fully connected layer to a noise state label corresponding to each optical link.

3. The tilt-length coupling coefficient estimation method for a space gravitational wave detector with optical path noise as described in claim 1 or 2, characterized in that, Based on the optical link exhibiting optical path noise anomalies, an optimal time-delay interference combination is selected, such that time-delay interference based on this optimal combination can completely cancel laser frequency noise and eliminate the influence of the optical link exhibiting optical path noise anomalies. Specifically, this includes: Based on the time delay operators corresponding to the optical path length of different optical links and the polynomial coefficients of the time delay operators, the phase measurement data of each optical link in the space gravitational wave detector are expressed as a linear superposition of various noise terms, including laser frequency noise and optical path noise, and a set of linear constraint equations under the condition of laser frequency noise cancellation is obtained. The coefficients of the time delay operator polynomial corresponding to the optical link with optical path noise anomaly are set to 0 as an additional constraint. Based on the additional constraints, the linear constraint equations are solved to obtain the optimal time-delay interference combination.

4. The tilt-length coupling coefficient estimation method for a space gravitational wave detector with optical path noise as described in claim 3, characterized in that, The linear constraint equations are as follows: in, Indicates optical link Time delay operator, Indicates optical link reverse link Time delay operator, and Optical links and The time delay operator polynomial.

5. The tilt-length coupling coefficient estimation method for a space gravitational wave detector with optical path noise as described in claim 1 or 2, characterized in that, Based on the interferometric output signal and the angular jitter measurement data, frequency domain power spectrum regression analysis is performed using the edge likelihood function to obtain the optimal estimate of the tilt-length coupling coefficient, specifically including: Multiple estimates are set for the tilt-length coupling coefficient; The angle jitter measurement data are weighted based on each estimated value of the tilt-length coupling coefficient to obtain the tilt-length noise estimation component corresponding to the corresponding estimated value. The tilt-length noise estimation component corresponding to each estimated value is then removed from the interferometric output signal to obtain the residual signal corresponding to each estimated value. The residual signals corresponding to each estimate are converted to the frequency domain, and the average power spectral density of the residual signals at each sampling frequency is calculated. Based on the average power spectral density of the residual signal corresponding to each estimate at each sampling frequency, and the marginal likelihood function, the marginal likelihood function value corresponding to each estimate is calculated, and the estimate corresponding to the maximum marginal likelihood function value is selected as the optimal estimate of the tilt-length coupling coefficient.

6. The tilt-length coupling coefficient estimation method for a space gravitational wave detector with optical path noise as described in claim 5, characterized in that, The marginal likelihood function is: in, This represents the marginal likelihood function with respect to the tilt-length coupling coefficient; This indicates that in the optical link between the transmitter (TX) and receiver (RX), tilt-length noise originates from angular jitter. The tilt-length coupling coefficient to the interference phase, These represent the angular jitter components of the device orientation in two mutually orthogonal directions, used to characterize the small angular deviation of an optical platform or optical element from its ideal orientation. This represents the discrete Fourier transform result of the residual signal at frequency k; The average power spectral density of the residual signal at frequency k; This represents the value of the theoretical noise power spectrum model at frequency k; The number of independent spectrum segments used for estimation; is the set of sampling frequencies; C is a constant term independent of the parameters.

7. A tilt-length coupling coefficient estimation system for a space gravitational wave detector with optical path noise, characterized in that, include: The data acquisition unit is used to acquire phase measurement data from each optical link of the space interferometer and angle jitter measurement data provided by the onboard attitude control system; An abnormal link identification unit is used to perform a short-time Fourier transform on the phase measurement data to obtain a power spectral density image, and input the power spectral density image into a convolutional neural network to identify abnormal links and obtain optical links with abnormal optical path noise. The time delay interference selection unit is used to select the optimal time delay interference combination based on the optical link with optical path noise anomaly, so that the time delay interference based on the optimal time delay interference combination can completely cancel the laser frequency noise and eliminate the influence of the optical link with optical path noise anomaly. The coupling coefficient estimation unit is used to perform time-delay interference based on the optimal time-delay interference combination to obtain the interference output signal, and to perform frequency domain power spectrum regression analysis using the marginal likelihood function based on the interference output signal and the angle jitter measurement data to obtain the optimal estimate of the tilt-length coupling coefficient; the tilt-length coupling coefficient characterizes the degree of coupling between angle jitter and equivalent length change.

8. An electronic device, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in any one of claims 1-6.

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