A time domain correction method and system based on local adaptive thin plate spline interpolation

Abstract

This invention provides a time-domain correction method based on local adaptive thin-plate spline interpolation, comprising the following steps: S10, separating the pilot signal from the mixed measurement signal, performing fine phase tracking on the pilot signal, and extracting the phase noise sequence introduced by clock jitter; S20, converting the phase noise sequence into jitter at the sampling time; S30, determining the ideal sampling time, selecting several original sampling points adjacent to each ideal sampling time, obtaining a local interpolation subset, evaluating the jitter intensity of the local interpolation subset, and performing adaptive interpolation calculation accordingly to obtain the signal value at the ideal sampling time; S40, outputting the uniformly sampled signal sequence after interpolation reconstruction; this invention also provides a time-domain correction system based on local adaptive thin-plate spline interpolation. This invention solves the problems of poor real-time performance and weak adaptability of traditional TPS interpolation, achieving high-precision suppression of clock jitter noise and meeting the stringent requirements of phase measurement for space gravitational wave detection.

Description

Technical Field

[0001] This invention relates to the field of space gravitational wave detection technology, and in particular to a time-domain correction method and system based on local adaptive thin-plate spline interpolation. Background Technology

[0002] In fields such as space gravitational wave detection and high-precision inter-satellite clock comparison, clock jitter of the spaceborne ultra-stable oscillator (USO) can cause the sampling time of the ADC to deviate from the ideal value, resulting in non-uniform digitization of the input signal and introducing significant phase noise. This noise can seriously interfere with the extraction and identification of weak gravitational wave signals and is one of the core factors restricting the accuracy of phase measurement.

[0003] In existing technologies, pilot-assisted time-domain correction methods are commonly used to suppress clock jitter noise: first, the phase noise of the pilot signal is extracted from the mixed z-measurement signal and converted into jitter at the sampling time; then, the signal at the ideal sampling time is reconstructed using an interpolation algorithm. Among these methods, thin-plate spline (TPS) interpolation, as a classic radial basis function interpolation method, possesses second-order smoothness C. 2 The variational optimality of minimizing bending energy is theoretically more suitable for high-precision reconstruction of non-uniform sampled signals, but its application in time-domain correction faces engineering bottlenecks.

[0004] 1. The computational complexity of traditional global TPS interpolation is O(n³) (where n is the number of sampling points), which has poor real-time performance and cannot meet the high-speed real-time requirements of inter-satellite signal processing;

[0005] 2. Using a fixed kernel function and polynomial basis makes it difficult to adapt to scenarios with dynamically changing clock jitter intensity (such as jitter abrupt changes caused by inter-satellite Doppler frequency offset), resulting in insufficient robustness;

[0006] 3. Without targeted optimization of the time-domain correction framework with pilot assistance, it cannot be directly integrated into existing phase measurement systems.

[0007] In view of this, the present invention is proposed. Summary of the Invention

[0008] To address the shortcomings of the aforementioned technologies, this invention provides a time-domain correction method based on local adaptive thin-plate spline interpolation. This method can achieve high-precision suppression of clock jitter noise, meet the stringent requirements of phase measurement for space gravitational wave detection, solve the problems of poor real-time performance and weak adaptability of TPS interpolation, and improve the accuracy of interpolation and enhance the smoothness of signal data.

[0009] The technical solution provided by this invention is as follows:

[0010] On one hand, this invention discloses a time-domain correction method based on local adaptive thin-plate spline interpolation, comprising the following steps:

[0011] S10. Separate the pilot signal from the mixed measurement signal, perform fine phase tracking on the pilot signal, and extract the phase noise sequence introduced by clock jitter;

[0012] S20. Based on the linear relationship between the pilot signal frequency and the phase noise, the phase noise sequence is converted into the jitter Δτ at the sampling time. cal ;

[0013] S30. Determine the ideal sampling time, select several original sampling points near each ideal sampling time, obtain a local interpolation subset, evaluate the jitter intensity of the local interpolation subset, and perform adaptive interpolation calculation accordingly to obtain the signal value at the ideal sampling time.

[0014] S40. Based on the signal value at the ideal sampling time obtained in step S30, output the uniformly sampled signal sequence after interpolation reconstruction.

[0015] In some embodiments, step S10, which involves separating the pilot signal from the mixed measurement signal and performing fine phase tracking on the pilot signal, includes:

[0016] With a center frequency of f pt The passband range is f pt The pilot signal is separated by a 200th-order linear phase FIR filter with ±0.5MHz; a second-order phase-locked loop is used to perform fine phase tracking on the pilot signal, wherein the normalized bandwidth of the second-order phase-locked loop is set to 0.001 and the loop bandwidth is 40kHz.

[0017] In some embodiments, the conversion formula for converting the phase noise sequence into jitter at the sampling time in step S20 is as follows:

[0018] ;

[0019] Where, Δτ cal f represents the time deviation between the ideal sampling time and the actual sampling time, in ps; pt Let f be the center frequency of the pilot signal, and f pt 5MHz; the value covers the typical clock jitter range for space gravitational wave detection; φ pilot (t) represents the phase error, i.e., the phase offset of the signal.

[0020] In some embodiments, step S30 specifically includes:

[0021] S301. Determine the ideal sampling time: Obtain the original signal sequence S(t') of the ADC non-uniform sampling, based on the jitter amount Δτ. cal Calculate the ideal sampling time, and the formula for calculating the ideal sampling time is: t comp =t'-Δτ cal ;

[0022] S302, Local Neighborhood Filtering: For each ideal sampling time, filter the k nearest original sampling points to form a local interpolation subset, and transform the global TPS interpolation into local TPS interpolation.

[0023] S303. Evaluate the jitter intensity of the local interpolation subset: The jitter intensity is calculated by determining the standard deviation of the jitter amount corresponding to the local interpolation subset. The formula for calculating the standard deviation of the jitter amount is as follows:

[0024] ;

[0025] in This represents the average jitter of a local subset;

[0026] S304, Adaptive interpolation calculation: Preset jitter intensity threshold τ th According to σ τ With τ th By comparing the results, dynamically switching between the TPS kernel function and the polynomial basis form, constructing and solving a system of local TPS interpolation equations, the signal value S(t) at the ideal sampling time is obtained. comp ).

[0027] In some embodiments, k in step S302 is a preset number of neighborhood points, where 5 ≤ k ≤ 20.

[0028] In some embodiments, the preset jitter intensity threshold τ in step S304 th According to σ τ With τ th The comparison results dynamically switch between the TPS kernel function and the polynomial basis form, including:

[0029] When σ τ ≤ τ th It employs a first-order polynomial basis and the standard TPS kernel function, where the standard TPS kernel function has the following form: Φ(r) is the time difference between the ideal and actual sampling times, and the first-order polynomial basis is... ;

[0030] When σ τ > τ th It employs a second-order polynomial basis and an improved TPS kernel function, wherein the improved TPS kernel function takes the form of: ;

[0031] The basis of the second-order polynomial is: .

[0032] In some embodiments, the local TPS interpolation equations are in block matrix form:

[0033]

[0034] Where Φ is a k×k local kernel matrix, Ξ is a k×(d+1) polynomial basis matrix (where d is the polynomial basis order, d=1 or 2), c is the kernel function coefficient vector, a is the polynomial basis coefficient vector, and S is the local subset signal value vector; the Cholesky decomposition method is used to solve the system of equations, and the signal values ​​are calculated after obtaining the coefficients.

[0035] .

[0036] On the other hand, the present invention also discloses a time-domain correction system based on local adaptive thin plate spline interpolation, which applies any of the time-domain correction methods based on local adaptive thin plate spline interpolation mentioned above. The time-domain correction system adopts a modular architecture, including a pilot phase noise extraction unit, a jitter calculation unit, a local adaptive TPS interpolation unit, and a signal output unit, and the various unit modules are interconnected.

[0037] In some embodiments, the pilot phase noise extraction unit separates the pilot signal from the mixed measurement signal, tracks the pilot phase change through a second-order PLL, and extracts the phase noise sequence φ. p ᵢ lot (t), output to the jitter calculation unit;

[0038] The jitter calculation unit receives the phase noise sequence output by the pilot phase noise extraction unit and converts the phase noise into jitter Δτ at the sampling time according to the conversion formula. cal The output is fed to a local adaptive TPS interpolation unit, where the conversion formula is as follows:

[0039] .

[0040] In some embodiments, the local adaptive TPS interpolation unit includes four sub-modules: a local neighborhood selection module, a jitter intensity evaluation module, a kernel function switching module, and an equation solving module, all of which are designed using an FPGA parallel architecture.

[0041] The functions of each submodule include: the local neighborhood filtering module quickly filters the k nearest sampling points at the ideal sampling time through address mapping logic, where k can be configured through a register;

[0042] The jitter intensity assessment module uses a pipelined architecture to calculate the jitter intensity σ of a local subset. τ The calculation delay is ≤5ns;

[0043] The kernel function switching module pre-stores the hardware calculation logic of the standard TPS core and the improved TPS core, based on the jitter intensity σ. τ With the preset threshold τ th The comparison results automatically switch between kernel function and polynomial basis form;

[0044] The equation solving module uses a parallel Cholesky decomposition accelerator to achieve fast decomposition of the local kernel matrix and coefficient solving, with a computation delay of ≤20ns and support for real-time processing at a sampling rate of 80MHz.

[0045] Compared with the prior art, the beneficial effects of the present invention are:

[0046] This application employs the second-order smoothness (C²) of TPS interpolation, ensuring continuous reconstruction of phase and angular frequency without phase jumps, and a phase error RMS value ≤ 1.8 × 10⁻⁶. -3 The phase measurement accuracy is rad, which is far superior to linear interpolation / Lagrange interpolation / Farrow interpolation, and meets the stringent requirements of picometer-level phase measurement for space gravitational wave detection.

[0047] The radial characteristics of the TPS kernel function make it naturally adaptable to non-uniform sampling caused by clock jitter. Compared with polynomial interpolation, it has less phase distortion and stronger robustness in jitter abrupt regions.

[0048] By changing global interpolation to local neighborhood interpolation and filtering by local neighborhood (k=10), the computational complexity of TPS interpolation is reduced from O(n³) to O(1). The FPGA parallel architecture achieves a computational latency of ≤20ns and supports real-time processing at a sampling rate of 80MHz, thus satisfying the real-time requirements of engineering and solving the bottleneck of traditional TPS interpolation in engineering applications.

[0049] Based on the adaptive kernel function and polynomial basis switching mechanism of jitter intensity, the interpolation strategy can be adjusted according to the dynamic changes of clock jitter. In the jitter-smooth region, the calculation is simplified to ensure real-time performance, and in the jitter-smooth region, the fitting is enhanced to ensure accuracy. It is fully adaptable to the dynamic scenario of inter-satellite Doppler frequency offset.

[0050] It is seamlessly compatible with existing pilot-assisted time-domain correction frameworks, requiring no major modifications to the original system structure. Upgrades can be achieved simply by replacing the interpolation module, reducing engineering implementation costs and facilitating industrial applications.

[0051] All modules adopt an FPGA parallel architecture design, with simple operation logic, low resource consumption, and support for multi-channel signal parallel processing. They can be integrated into existing VPX architecture phase measurement prototypes to meet the miniaturization and low power consumption requirements of spaceborne equipment. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the time-domain correction method based on local adaptive thin-plate spline interpolation in this invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0054] In the description of this invention, it should be noted that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0055] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0056] On the one hand, as attached Figure 1 As shown, this invention discloses a time-domain correction method based on local adaptive thin-plate spline interpolation, comprising the following steps:

[0057] S10, Pilot Phase Noise Extraction

[0058] The pilot signal is separated from the mixed measurement signal, and the pilot signal is subjected to fine phase tracking to extract the phase noise sequence introduced by clock jitter;

[0059] S20, jitter conversion

[0060] Based on the linear relationship between the pilot signal frequency and the phase noise, the phase noise sequence is converted into jitter Δτ at the sampling time. cal ;

[0061] S30, Local Adaptive TPS Interpolation Reconstruction

[0062] Determine the ideal sampling time, select several original sampling points near each ideal sampling time, obtain a local interpolation subset, evaluate the jitter intensity of the local interpolation subset, and perform adaptive interpolation calculation accordingly to obtain the signal value at the ideal sampling time;

[0063] S40, Correction signal output

[0064] Based on the signal value at the ideal sampling time obtained in step S30, output the uniformly sampled signal sequence S(t) after interpolation reconstruction. comp ).

[0065] Obviously, this application is based on pilot phase noise extraction, reduces the computational complexity of TPS interpolation by local neighborhood screening, and achieves adaptive switching between kernel function and polynomial basis by jitter intensity evaluation, and finally completes the high smoothness reconstruction of non-uniform sampling signal.

[0066] In some embodiments, pilot phase noise extraction in S10 specifically includes:

[0067] From the mixed measurement signal, through the center frequency f pt The passband range is f pt The pilot signal is separated by a 200th-order linear phase FIR filter with ±0.5MHz; a second-order phase-locked loop (PLL) is used to perform precise phase tracking on the pilot signal, wherein the normalized bandwidth of the second-order PLL is set to 0.001 and the loop bandwidth is 40kHz; the mixed measurement signal includes the main carrier beat frequency signal, the sideband beat frequency signal, the 5MHz pilot signal and the pseudocode signal.

[0068] In some embodiments, step S20 converts the phase noise sequence into jitter Δτ at the sampling time. cal The conversion formula is:

[0069] ;

[0070] Where, Δτ cal f represents the time deviation between the ideal sampling time and the actual sampling time, in ps; pt Let f be the center frequency of the pilot signal, and f pt The value is 5MHz, covering the typical clock jitter range (1ps~1ns) for space gravitational wave detection; φ pilot (t) represents the phase error, specifically the phase offset of the signal.

[0071] Step S30 specifically includes the following four sub-steps:

[0072] S301. Determine the ideal sampling time: Obtain the original signal sequence S(t') of the ADC non-uniform sampling (t' is the actual sampling time), based on the jitter amount Δτ. cal Calculate the ideal sampling time, and the formula for calculating the ideal sampling time is: t comp =t'-Δτ cal ;

[0073] S302, Local Neighborhood Filtering: For each ideal sampling time t compThe local interpolation subset is formed by selecting the k nearest original sampling points, which transforms the global TPS interpolation into local TPS interpolation, reducing the computational complexity from O(n³) to O(k³) and meeting the real-time requirements; where k is the preset number of neighborhood points, 5≤k≤20; preferably, k=10.

[0074] S303. Evaluate the jitter intensity of the local interpolation subset: The jitter intensity is calculated by determining the standard deviation of the jitter amount corresponding to the local interpolation subset. The formula for calculating the standard deviation of the jitter amount is as follows:

[0075] ;

[0076] in This represents the average jitter of a local subset;

[0077] S304, Adaptive interpolation calculation: Preset jitter intensity threshold τ th According to σ τ With τ th By comparing the results, dynamically switching between the TPS kernel function and the polynomial basis form, constructing and solving a system of local TPS interpolation equations, the signal value S(t) at the ideal sampling time is obtained. comp ).

[0078] Furthermore, the preset jitter intensity threshold τ in step S304 th According to σ τ With τ th The comparison results dynamically switch between the TPS kernel function and the polynomial basis form, including:

[0079] When σ τ ≤ τ th (For regions with smooth jitter), a first-order polynomial basis and a standard TPS kernel function are used, where the standard TPS kernel function takes the form of: Φ(r) is the time difference between the ideal and actual sampling times, and the first-order polynomial basis is... ;

[0080] When σ τ > τ th (In areas of severe jitter), a second-order polynomial basis and an improved TPS kernel function are used, wherein the improved TPS kernel function takes the form of: ;

[0081] The basis of the second-order polynomial is: .

[0082] Furthermore, in step S304, the local TPS interpolation equations are in block matrix form:

[0083]

[0084] Where Φ is a k×k local kernel matrix (elements are the corresponding kernel function values), Ξ is a k×(d+1) polynomial basis matrix (d is the polynomial basis order, 1 or 2), c is the kernel function coefficient vector, a is the polynomial basis coefficient vector, and S is the local subset signal value vector; the Cholesky decomposition method is used to solve the system of equations, and the signal values ​​are calculated after obtaining the coefficients.

[0085] .

[0086] In some embodiments, step S40 outputs the interpolated and reconstructed uniform sampled signal sequence S(t) comp This signal eliminates phase noise introduced by clock jitter and maintains second-order smoothness, and can be directly input to subsequent carrier phase-locked loop, sideband phase extraction module and time delay interference (TDI) processing unit.

[0087] For example, the specific implementation steps of the time-domain correction method based on local adaptive thin-plate spline interpolation in this application are as follows:

[0088] S10, Pilot Phase Noise Extraction: The 5MHz pilot signal is separated by a 200th-order FIR filter of 4.5~5.5MHz, and the phase noise is tracked by a second-order PLL. The extracted phase noise sequence has a resolution of 10ps.

[0089] S20, Jitter Conversion: Based on the formula Δτ cal = The phase noise is converted into jitter, and the conversion error is ≤1ps;

[0090] S30, Local Adaptive TPS Interpolation Reconstruction: For the ideal sampling time t comp Select the 10 nearest original sampling points to form a local subset; calculate the jitter intensity σ of the local subset. τ When σ τ When σ = 30ps (≤ 50ps), a first-order polynomial basis + standard TPS kernel is used; when σ τ When the value is 60ps (>50ps), a second-order polynomial basis + improved TPS kernel is used;

[0091] Construct a system of 12th-order (d=1) or 13th-order (d=2) block equations, solve the coefficients through Cholesky decomposition, and calculate the signal value at the ideal sampling time.

[0092] S40, Correction signal output: Outputs a uniform sampling signal with a sampling rate of 80MHz, which is input to the subsequent carrier phase-locked loop and TDI processing unit.

[0093] Obviously, the correction method in this application is a targeted improvement on traditional TPS interpolation, and it is deeply integrated with the existing pilot-assisted time-domain correction framework. The differences include:

[0094] By changing global interpolation to local neighborhood interpolation, the computational complexity is reduced from O(n³) to O(k³), solving the problem of poor real-time performance; the introduction of adaptive kernel functions and polynomial bases solves the problem of weak adaptability of fixed parameters.

[0095] The second-order smoothness of TPS interpolation ensures continuous reconstruction of phase and angular frequency, resulting in higher accuracy; the radial characteristics of the kernel function are better suited to non-uniform sampling, and the distortion in jitter abrupt regions is smaller.

[0096] By deeply integrating TPS interpolation with the pilot-assisted framework, an adaptive strategy is designed to address the dynamic characteristics of clock jitter. Compared with traditional interpolation algorithms, this approach offers superior correction performance and stronger robustness.

[0097] On the other hand, the present invention also discloses a time-domain correction system based on local adaptive thin-plate spline interpolation, which applies the time-domain correction method based on local adaptive thin-plate spline interpolation as described above, and adopts a modular architecture, including a pilot phase noise extraction unit, a jitter calculation unit, a local adaptive TPS interpolation unit, and a signal output unit, with communication connections between each unit module.

[0098] In some embodiments, the pilot phase noise extraction unit separates the pilot signal from the mixed measurement signal, tracks the pilot phase change through a second-order PLL, and extracts the phase noise sequence φ. p ᵢ lot (t), output to the jitter calculation unit;

[0099] The jitter calculation unit receives the phase noise sequence output by the pilot phase noise extraction unit and converts the phase noise into jitter Δτ at the sampling time according to the conversion formula. cal The output is fed to a local adaptive TPS interpolation unit, where the conversion formula is as follows:

[0100] .

[0101] In some embodiments, the local adaptive TPS interpolation unit includes four sub-modules: a local neighborhood selection module, a jitter intensity evaluation module, a kernel function switching module, and an equation solving module, all of which are designed using an FPGA parallel architecture.

[0102] The functions of each submodule include: the local neighborhood filtering module quickly filters the k nearest sampling points at the ideal sampling time through address mapping logic, where k can be configured through a register;

[0103] The jitter intensity assessment module uses a pipelined architecture to calculate the jitter intensity σ of a local subset. τ The calculation delay is ≤5ns;

[0104] The kernel function switching module pre-stores the hardware calculation logic of the standard TPS core and the improved TPS core, based on the jitter intensity σ. τ With the preset threshold τ th The comparison results automatically switch between kernel function and polynomial basis form;

[0105] The equation solving module uses a parallel Cholesky decomposition accelerator to achieve fast decomposition of the local kernel matrix and coefficient solving, with a computation delay of ≤20ns and support for real-time processing at a sampling rate of 80MHz.

[0106] In some embodiments of this application, the core parameters of the phase measurement system for space gravitational wave detection are configured as follows:

[0107] Mixed measurement signal: main carrier center frequency 15MHz, sideband frequency difference with main carrier 1MHz, pilot signal frequency 5MHz, pseudocode chip rate 1Mbps;

[0108] ADC sampling parameters: sampling rate 80MHz, bit width 14bit;

[0109] Clock jitter range: 1ps~1ns, jitter intensity threshold τ th =50ps;

[0110] TPS interpolation parameters: local neighborhood points k=10, improved TPS kernel adjustment coefficient α=0.01;

[0111] FPGA platform: Based on the AXU9EG development platform, using the VPX architecture, supporting parallel computing and high-speed data transmission.

[0112] The implementation details of the aforementioned time-domain correction system based on local adaptive thin-plate spline interpolation are as follows:

[0113] Hardware platform: It consists of signal transmission board, signal acquisition board, signal processing board, high-precision clock source, and VPX backplane, among which the signal processing board is integrated as the four core units of this application;

[0114] Clock synchronization: A high-precision clock source (rubidium clock / thermostatic clock) provides a unified reference clock for all units, with a clock stability ≤10. −13 / √Hz;

[0115] Interface compatibility: It adopts an SMA interface for analog signal transmission, a GTX interface for high-speed digital signal transmission, and an Ethernet interface for remote control and telemetry, and can be seamlessly integrated with existing phase measurement systems.

[0116] Furthermore, through simulation and hardware testing, the correction effect of the method and system in the above embodiments of this application was verified. The core test results are as follows:

[0117] 1) Phase error: The RMS value of the phase error of the corrected signal is 1.7×10⁻³rad, and the peak error is 7.8×10⁻³rad. Compared with Lagrange interpolation (2.64×10⁻³rad), the accuracy is improved by 31.8%, and compared with Farrow interpolation (3.04×10⁻³rad), the accuracy is improved by 40.8%.

[0118] 2) Real-time performance: The overall computational latency of the FPGA implementation is ≤20ns, supporting real-time processing at a sampling rate of 80MHz, meeting the requirements for inter-satellite signal processing;

[0119] 3) Robustness: It can maintain high accuracy in both areas with gentle jitter and areas with severe jitter. The phase distortion in areas with sudden jitter is ≤8×10⁻³rad, which is suitable for dynamic jitter scenarios caused by inter-satellite Doppler frequency offset.

[0120] 4) System compatibility: No modifications are required to other modules of the existing phase measurement system. After direct integration, the carrier phase-locked loop tracking accuracy is improved by 25%, and the clock noise suppression effect of the TDI module is significantly enhanced.

[0121] It should be further explained that the relevant technical terms in the above embodiments of this application are explained as follows:

[0122] 1. Thin Plate Spline (TPS) Interpolation: A classic radial basis function interpolation method that achieves high smoothness reconstruction of signals by minimizing bending energy. The kernel function is r²lnr, which has second-order smoothness (C²).

[0123] 2. Linear interpolation: The simplest and most intuitive interpolation method, and the basis for other complex interpolation methods. It has low computational complexity, but poor phase compensation accuracy and insufficient signal smoothness, and cannot meet the requirements of picometer-level phase measurement.

[0124] 3. Lagrange interpolation: A method in numerical analysis that uses known data points to construct a polynomial to estimate the value of a function at other locations; it is more accurate than linear interpolation, but higher-order interpolation suffers from Runge phenomenon, has poor adaptability to non-uniform sampling, and exhibits significant phase distortion in jitter and abrupt change regions.

[0125] 4. Farrow interpolation: It flexibly estimates the value of discrete signals at any non-integer sampling point by means of polynomial interpolation. It balances accuracy and real-time performance, but it is difficult to guarantee the high-order continuity of phase and angular frequency. In scenarios where the clock jitter intensity changes dynamically, there is still a lot of room for optimization of phase error.

[0126] 5. Clock jitter: The time deviation of the output clock of the spaceborne ultra-stable oscillator (USO), including ADC aperture jitter and external clock jitter, will cause non-uniform sampling of the ADC and introduce phase noise.

[0127] 6. Pilot-assisted: By adding a pilot signal with known frequency and phase to the mixed measurement signal, the phase noise of the pilot is extracted to characterize clock jitter and provide a basis for time-domain correction.

[0128] 7. Local Neighborhood Selection: Select the k nearest points to the ideal sampling time from the global sampling points to form a local subset, transforming the global TPS interpolation into local TPS interpolation, thus reducing computational complexity.

[0129] 8. Jitter Intensity: The standard deviation of the jitter in a local interpolation subset, characterizing the severity of clock jitter in that region, used for adaptive switching of interpolation parameters.

[0130] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A time domain correction method based on local adaptive thin plate spline interpolation, characterized in that, The method comprises the following steps: S10, separating a pilot signal from the mixed measurement signal, performing fine phase tracking on the pilot signal, and extracting a phase noise sequence introduced by clock jitter; S20, according to the linear relationship between the pilot signal frequency and the phase noise, convert the phase noise sequence into the jitter amount Δτ at the sampling time cal ; S30, determining an ideal sampling time, screening a plurality of original sampling points adjacent to each ideal sampling time, obtaining a local interpolation subset, evaluating the jitter strength of the local interpolation subset, and performing adaptive interpolation calculation accordingly to obtain a signal value at the ideal sampling time; S40, outputting a uniformly sampled signal sequence after interpolation reconstruction according to the signal value at the ideal sampling time obtained in step S30.

2. The time-domain correction method based on local-adaptive thin-plate-spline interpolation according to claim 1, wherein, In step S10, the pilot signal is separated from the mixed measurement signal, and fine phase tracking is performed on the pilot signal, comprising: With a center frequency of f pt The passband range is f pt The pilot signal is separated by a 200th-order linear phase FIR filter with ±0.5MHz; a second-order phase-locked loop is used to perform fine phase tracking on the pilot signal, wherein the normalized bandwidth of the second-order phase-locked loop is set to 0.001 and the loop bandwidth is 40kHz.

3. The time-domain correction method based on local-adaptive thin-plate-spline interpolation according to claim 1, wherein, In step S20, the conversion formula of the phase noise sequence into the jitter amount of the sampling time is: ； Wherein Δτ cal is the time deviation value of ideal sampling time and actual sampling time, unit is ps; f pt is the center frequency of pilot signal, and f pt is 5MHz; The value covers the typical clock jitter range of gravitational wave detection; φ pilot (t) is the phase error, i.e. the phase offset of the signal.

4. The time-domain correction method based on local-adaptive thin-plate-spline interpolation according to claim 3, wherein, Step S30 specifically comprises: S301, determine ideal sampling time: obtain the original signal sequence S(t') of ADC non-uniform sampling, and calculate the ideal sampling time based on the jitter amount Δτ cal The calculation formula of the ideal sampling time is t comp =t'-Δτ cal ; S302, local neighborhood screening: for each ideal sampling time, screening k adjacent original sampling points to form a local interpolation subset, and converting global TPS interpolation into local TPS interpolation; S303, evaluating the jitter strength of the local interpolation subset: calculating the jitter amount standard deviation corresponding to the local interpolation subset as the jitter strength, and the calculation formula of the jitter amount standard deviation is: ； wherein is the mean value of the jitter for the local subset; S304、Adaptive interpolation calculation: preset jitter intensity threshold τ th , according to the comparison result of σ τ and τ th , dynamically switch the TPS kernel function and the polynomial base form, construct the local TPS interpolation equation group and solve it to obtain the signal value S(t comp ) at the ideal sampling time.

5. The time-domain correction method based on local-adaptive thin-plate-spline interpolation according to claim 4, wherein, In step S302, k is a preset number of neighborhood points, and 5≤k≤20.

6. The time-domain correction method based on local-adaptive thin-plate-spline interpolation according to claim 4, wherein, The preset jitter intensity threshold τ in step S304 th , according to the comparison result of σ τ and τ th , dynamically switch the TPS kernel function and the polynomial base form, including: When σ τ ≤ τ th , a first-order polynomial basis and a standard TPS kernel function are adopted, wherein the standard TPS kernel function is in the form of , and Φ(r) is a time difference between ideal and actual sampling times, and the first-order polynomial basis is ; When σ τ > τ th , a second order polynomial basis and an improved TPS kernel function are adopted, wherein the improved TPS kernel function is in the form of ; The second order polynomial basis is .

7. The time-domain correction method based on local-adaptive thin-plate-spline interpolation according to claim 6, wherein, In step S304, the local TPS interpolation equation set is in a block matrix form: ； Wherein Φ is a k×k local kernel matrix, Ξ is a k×(d+1) polynomial basis matrix, c is a kernel function coefficient vector, a is a polynomial basis coefficient vector, and S is a local subset signal value vector; the equation set is solved by using Cholesky decomposition method to obtain the coefficients and then calculate the signal value: 。 8. A time domain correction system based on local adaptive thin plate spline interpolation, characterized in that, The application of the time domain correction method based on local adaptive thin plate spline interpolation according to any one of claims 1-7 adopts a modular architecture, comprising a pilot phase noise extraction unit, a jitter amount calculation unit, a local adaptive TPS interpolation unit, and a signal output unit, and the units are communicatively connected.

9. The local-adaptive thin-plate-spline interpolation based time-domain correction system according to claim 8, wherein, The pilot phase noise extraction unit separates the pilot signal from the mixed measurement signal, tracks the pilot phase variation through a second-order PLL, and extracts a phase noise sequence φ p ᵢ lot (t), and outputs to the jitter amount calculation unit. The jitter calculation unit receives the phase noise sequence output by the pilot phase noise extraction unit and converts the phase noise into jitter Δτ at the sampling time according to the conversion formula. cal The output is sent to the local adaptive TPS interpolation unit, and the conversion formula is as follows: 。 10. The local-adaptive thin-plate-spline interpolation based time-domain correction system according to claim 9, wherein, The local adaptive TPS interpolation unit comprises four sub-modules, i.e., a local neighborhood screening module, a jitter strength evaluation module, a kernel function switching module, and an equation set solving module, all of which are designed by using an FPGA parallel architecture; The functions of each sub-module include that the local neighborhood screening module quickly screens k sampling points adjacent to the ideal sampling time through address mapping logic, and k can be configured through a register; The jitter strength evaluation module calculates the jitter strength σ of the local subset using a pipelined architecture τ with a delay of < 5 ns. The kernel function switching module pre-stores hardware calculation logic of standard TPS kernel and improved TPS kernel, automatically switches the kernel function and the polynomial basis form according to the comparison result of the jitter strength στ and the preset threshold τth; The equation set solving module adopts a parallel Cholesky decomposition accelerator to realize fast decomposition of the local kernel matrix and coefficient solving, and the operation delay is ≤20 ns, supporting 80MHz sampling rate real-time processing.

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