Continuous frequency and phase estimation method for non-stationary non-cooperative satellite signals

Abstract

This invention discloses a method for continuous frequency and phase estimation of non-stationary, non-cooperative satellite signals. The method comprises the following steps: instantaneous estimation of the non-cooperative satellite signal to obtain the initial synchronization parameters as the initial values ​​for the loop; inputting the initial values ​​into the carrier tracking and code tracking loops to obtain the loop phase detection result at the current moment; when the loop phase detection result at the current moment exceeds the noise bandwidth of the loop, using an instantaneous estimation algorithm to estimate the synchronization parameters of the signal at the current moment and compensating for the loop phase detection result, continuing the loop iteration at the next moment; and outputting the continuous estimation results of the signal frequency and phase. This invention fully utilizes the complementary advantages of instantaneous signal parameter estimation and continuous tracking parameter estimation algorithms, greatly improving the stability of continuous frequency and phase estimation of non-stationary signals while meeting the requirements of real-time acquisition and processing of non-cooperative signals.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and more specifically relates to a method for continuous frequency and phase estimation of non-stationary, non-cooperative satellite signals within the field of satellite signal processing technology. This invention can be used to achieve long-term continuous estimation of the frequency and phase of non-stationary, non-cooperative satellite signals even when no prior information about the signal is known. Background Technology

[0002] With the continuous development of satellite technology, satellite communication and satellite navigation systems have been widely used globally. For example, the Global Positioning System (GPS) and the BeiDou Navigation Satellite System provide users with high-precision positioning, navigation, and timing services. Continuous estimation of satellite signal frequency and phase is fundamental to these functions, and its performance directly affects the service quality and reliability of the satellite system. In the field of satellite navigation, continuous estimation of satellite signal frequency and phase involves using a navigation receiver to acquire and track satellite signals. The acquisition process is a two-dimensional search of the satellite signal against a known carrier frequency and ranging code. The tracking process uses a phase-locked loop (PLL) and a code loop to continuously adjust the coarsely estimated carrier frequency and phase, gradually converging to the true signal's frequency and phase. However, for non-cooperative signals, without prior information about the unknown signal, it is impossible to use navigation signal processing methods to obtain a coarse estimate of the satellite signal's parameters. Furthermore, when the signal experiences jitter due to sudden high-dynamic conditions, the carrier tracking loop may exceed its locking range due to sudden frequency and phase jitter, leading to inaccurate subsequent estimation results.

[0003] Changsha Xiandu Technology Co., Ltd. proposed a carrier phase tracking method for weak QAM signals in its patent application "A Carrier Phase Tracking Method for Weak QAM Signals" (Patent Application No.: CN 202310530944.9, Patent Publication No.: CN 116260690 A). The implementation steps of this method are as follows: Based on the fourth power spectrum of the QAM signal, the signal frequency of the QAM signal is initially estimated and compensated; within the loop update period T, the outer signal points in the constellation diagram of the compensated QAM signal undergo fourth power processing to obtain an unsigned modulated QAM signal; the phase error of the continuous data blocks in the unsigned modulated QAM signal is coherently accumulated and initially tracked to obtain the first signal parameter estimate of the unsigned modulated QAM signal; the QAM signal is compensated, and then the outer signal points in the constellation diagram of the compensated QAM signal are phase-detected and phase error accumulated to obtain the second signal parameter estimate. This method utilizes the characteristics of QAM modulated signals to estimate and compensate for the signal frequency using a constellation diagram within the carrier loop update period, thus solving the technical problem of unstable tracking and easy loss of lock in traditional tracking loops under high dynamic and low signal-to-noise ratio conditions. However, this method still has limitations. It is only applicable to QAM modulated signals. For non-cooperative satellite signals, if the modulation type of the signal is not known in advance, it cannot solve the problem of tracking loop loss of lock. During the long-term continuous estimation of the frequency and phase of non-stationary, non-cooperative satellite signals, the problem of losing the ability to track subsequent signals due to loop loss of lock can still occur.

[0004] In his paper "Research on Non-Cooperative Satellite Parameter Estimation Method and Application Based on GPU" (Master's Thesis, Xi'an University of Electronic Science and Technology, 2022), Yang Mixhao proposed a continuous tracking method for carrier and code signals of non-cooperative satellites. The method's implementation steps are as follows: Initial parameter estimation results are obtained through algorithms such as carrier frequency estimation and code frequency and code phase estimation of short-time signals. This process is similar to the acquisition process of spread spectrum signal tracking. During continuous tracking, the phase-locked loop (PLL) requires a relatively accurate initial frequency to converge, and the higher the accuracy of the initial frequency, the shorter the convergence time. Therefore, this method uses the calculation method of the initial carrier phase in the short-time signal for compensation during the phase detection stage of the PLL to obtain a higher accuracy phase estimation result. During code loop tracking, to reduce tracking errors, a joint optimization function for code period and code phase is designed using multiple chip data. A code phase detector is constructed using the early-late method, and the code frequency parameter is introduced into the loop filter. During the loop filtering process, the code phase and code frequency parameters converge to the optimal value of the optimization function. Although this method can continuously estimate the frequency and phase of non-cooperative satellite signals, it still has shortcomings: although it can achieve high-precision carrier tracking and code tracking of non-cooperative satellite signals, the algorithm is complex and the convergence process is slow, making it difficult to meet the needs of real-time signal acquisition and processing in practical engineering. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a continuous frequency and phase estimation method for non-stationary, non-cooperative satellite signals. This method solves the problems in existing technologies where, when there is no prior information about the unknown signal, the algorithm for long-term continuous estimation of satellite signal frequency and phase is too complex to meet the needs of real-time acquisition and processing of non-cooperative satellite signals. Furthermore, it addresses the issue that during tracking, the signal carrier loop and code loop may lose lock due to changes in non-stationary signals, and the unknown signal modulation type makes it impossible to compensate for the loss of lock, thus hindering continuous estimation of subsequent signals.

[0006] To achieve the above objectives, the technical approach of this invention is as follows: This invention obtains the initial parameters for continuous signal tracking through an instantaneous estimation method of non-cooperative satellite signal synchronization parameters. These parameters are then input into a second-order PLL carrier tracking loop and code tracking loop to achieve long-term continuous estimation of signal frequency and phase. This solves the problem of high complexity and practical engineering difficulty in existing carrier tracking and code tracking algorithms. This invention utilizes an M-power spectrum combined with a ZFFT complex modulation frequency shift high-precision carrier frequency estimation algorithm, as well as an instantaneous estimation algorithm for carrier phase and other parameters, to compensate for phase detection errors in the carrier loop. Furthermore, it uses a code frequency estimation algorithm refined from the baseband signal envelope spectrum and CZT spectrum, and an instantaneous estimation algorithm for code phase parameters, to compensate for phase detection errors in the code loop. When a sudden, non-stationary signal causes interference, the frequency estimation result will exceed the loop's allowable error range. At this time, the loop will lose lock and will be unable to continuously estimate the frequency and phase of subsequent signals. After compensating for the loop error using this invention, the loop will converge again, thereby enhancing the loop's robustness to long-term continuous estimation of the frequency and phase of non-stationary signals. This solves the problem of the loop losing its tracking capability due to phase-locked loop lockout during the tracking process of non-stationary, non-cooperative satellite signals.

[0007] To achieve the above objectives, the technical solution adopted by the invention includes the following steps:

[0008] Step 1: Use the instantaneous estimation algorithm to perform instantaneous estimation on the non-cooperative satellite signal to obtain the synchronization parameters at the initial moment, and use the synchronization parameters at the initial moment as the initial value of the loop;

[0009] Step 2: Substitute the initial values ​​into the carrier tracking and code tracking loop to generate the local carrier signal and code sequence at the current moment. Calculate the loop phase detection result at the current moment by comparing the local signal with the received signal.

[0010] Step 3: Determine whether the current loop phase detection result exceeds the loop noise bandwidth range. If it does not exceed the range, use the current loop output result as the initial value of the signal tracking loop at the next moment and then execute Step 2; otherwise, execute Step 4.

[0011] Step 4: Using the same instantaneous estimation algorithm as in Step 1, estimate the synchronization parameters of the signal at the current moment;

[0012] Step 5: Determine whether the current time has reached the user-set task time. If yes, proceed to step 6. Otherwise, calculate the difference between the synchronization parameter of the signal at the current time and the initial estimated value of the synchronization parameter, use the difference to compensate for the loop phase detection result of the current signal segment, and use the result as the initial value of the signal tracking loop at the next time before proceeding to step 2.

[0013] Step 6: Output the continuous estimation results of the signal frequency and phase.

[0014] Furthermore, the instantaneous estimation algorithm is used to perform instantaneous estimation of non-cooperative satellite signals, and the resulting synchronization parameters include carrier frequency, carrier phase, code frequency, code phase, and symbol parsing sequence.

[0015] Furthermore, the instantaneous estimation of the carrier frequency is performed as follows:

[0016] The first step is to perform an FFT Fourier transform on the digital intermediate frequency signal to obtain the frequency domain signal;

[0017] The second step is to perform M-fold frequency multiplication on the frequency domain signal, remove the DC component from the multiplied signal, and then find the horizontal coordinate index value corresponding to the maximum spectral line on the frequency multiplied spectrum. This value is used as a rough estimate of the carrier frequency obtained after M-fold frequency multiplication. The value of M is determined according to the type of different modulation signals. For BPSK signals, it is 2 times the frequency, and for QPSK signals, it is 4 times the frequency.

[0018] The third step involves using the ZFFT algorithm to roughly estimate the carrier frequency and shift the digital intermediate frequency signal to near zero frequency. The signal is then divided into N segments for integration. The maximum spectral line is found on the spectrum of each segment, and a quadratic curve is fitted to the maximum spectral line of each segment to obtain a refined spectrum. The horizontal coordinate index value corresponding to the maximum spectral line of the refined spectrum is found, and this value is used as the carrier frequency of the synchronization parameter. Here, N takes any integer value between 10 and 100.

[0019] Furthermore, the carrier phase is generated based on the carrier frequency of the synchronization parameter. A local carrier signal is generated, and the local carrier signal is phase-shifted by 90° to obtain in-phase and quadrature components. The digital intermediate frequency signal is coherently demodulated, and the two mixed signals obtained after demodulation are low-pass filtered to remove the second harmonic component, resulting in two baseband signals I(t) and Q(t). The two baseband signals are then subjected to arctangent phase detection, and the phase detection result is used as the carrier phase of the synchronization parameter.

[0020] Furthermore, the code frequency is obtained by calculating the envelope spectrum signal x using two baseband signals I(t) and Q(t). e (t)=I(t)+Q(t), find the horizontal coordinate index value corresponding to the maximum spectral line on the envelope spectrum, and use this value as a rough estimate of the code frequency; after performing Z-transform on the envelope spectrum signal through the CZT algorithm, use the spiral model to perform equally segmented angle sampling on the signal Z-transform curve along the z-plane, that is, perform fitting interpolation at the rough estimate of the code frequency of the curve after Z-transformation, find the horizontal coordinate index value corresponding to the maximum spectral line after interpolation, and use this value as the code frequency of the synchronization parameter.

[0021] Furthermore, the code phase is obtained by solving the function according to the following formula, and the optimal solution is used as the code phase of the synchronization parameter:

[0022]

[0023] Where, N c T represents the length of the baseband signal, k represents the sampling point of the baseband signal, τ represents the delay parameter of the baseband signal, and its value ranges from 0 to 1. c0 Let W(t) represent the baseband signal code period, where the period value is the reciprocal of the code frequency at the current moment. Let x′(t) represent the analytical form of the baseband signal, x′(t) = I(t) + jQ(t), where j represents the imaginary unit. c ,τ) represents the weight function, which takes values ​​of T int This represents the time corresponding to the total length of the baseband signal.

[0024] Furthermore, the symbol parsing sequence is obtained by performing binary decision on any baseband signal. Specifically, the sampling points within a chip are accumulated. Since the pseudocode has a bipolar mapping, when the accumulated value is greater than 0, the symbol value is determined to be -1; otherwise, the symbol value is determined to be 1. The symbol decision values ​​are arranged sequentially to obtain the symbol parsing sequence of the synchronization parameters.

[0025] Furthermore, the step of substituting the initial value into the carrier tracking and code tracking loop is as follows:

[0026] The first step is to generate a local carrier signal based on the carrier frequency and carrier phase in the synchronization parameters at the initial moment, and use the symbol parsing sequence in the synchronization parameters at the initial moment as the local pseudocode sequence.

[0027] The second step is to mix the digital intermediate frequency signal with the local carrier signal and then perform low-pass filtering on the mixed signal, thus completing the carrier stripping and obtaining two baseband signals.

[0028] The third step is to process the two baseband signals by advancing and delaying them by half a chip, respectively, to obtain four baseband signals.

[0029] Furthermore, the method of using the difference to compensate for the loop phase detection result obtained by tracking the current signal segment refers to taking the difference between the carrier frequency in the synchronization parameters of the signal at the current moment and the carrier frequency of the initial value of the loop, using the difference to compensate for the loop phase detection result obtained by tracking the signal at the current moment, and using the result as the initial value of the signal tracking loop at the next moment, and using the initial value to generate the local carrier signal in the next loop iteration.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] First, because the present invention obtains the initial estimate value through instantaneous estimation during the carrier and symbol tracking process, and combines the second-order phase-locked loop carrier tracking and code tracking loop, it overcomes the problem of high algorithm complexity and difficulty in practical engineering in the prior art, thus enabling the present invention to meet the real-time acquisition and processing requirements of satellite signals.

[0032] Secondly, because this invention uses an M-power spectrum combined with a ZFFT complex modulation frequency shift high-precision estimation algorithm and a carrier phase and other parameter instantaneous estimation algorithm to compensate for the carrier loop phase detection error, and uses a baseband signal envelope spectrum and CZT spectrum refinement code frequency estimation algorithm and code phase parameter instantaneous estimation algorithm to compensate for the code loop phase detection error, it overcomes the problem in the prior art that when the frequency and phase of non-stationary and non-cooperative satellite signals are continuously estimated for a long time, the signal carrier loop and code loop lose lock due to changes in non-stationary signals during tracking, and the unknown signal modulation type makes it impossible to compensate for the loop lock-out state, ultimately leading to the inability to continuously estimate subsequent signals. This invention enables long-term continuous estimation of the frequency and phase of non-stationary signals. Attached Figure Description

[0033] Figure 1 This is a flowchart of the present invention;

[0034] Figure 2 This is a flowchart illustrating how the instantaneous estimation algorithm is used to obtain the initial estimated parameters according to the present invention.

[0035] Figure 3 This is a flowchart of the ZFFT algorithm of this invention;

[0036] Figure 4 This is a schematic diagram of the ZFFT algorithm of the present invention;

[0037] Figure 5 This is a schematic diagram of the CZT algorithm of the present invention;

[0038] Figure 6 This is a schematic diagram of the code phase estimation algorithm of the present invention;

[0039] Figure 7 This is a flowchart of the tracking loop of the present invention;

[0040] Figure 8 The figure shows the simulation results of the present invention. Figure 8 (a) is a comparison chart of the simulation experiment time of the present invention. Figure 8 (b) is a graph showing the simulation analysis results of stationary signals in the simulation experiment of this invention. Figure 8 (c) is a graph showing the simulation analysis results of stationary signals using existing methods in the simulation experiment of this invention. Figure 8 (d) is a graph showing the simulation analysis results of non-stationary signals using existing methods in the simulation experiment of this invention. Figure 8 (e) is a simulation analysis result of non-stationary signals using the method of this invention in the simulation experiment of this invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0042] Reference Figure 1 The implementation steps of the present invention will be described in further detail below.

[0043] Step 1: Using an instantaneous estimation algorithm, the non-cooperative satellite signal is instantaneously estimated to obtain the synchronization parameters at the initial moment. These initial synchronization parameters are then used as the initial values ​​for the loop. The synchronization parameters include carrier frequency, carrier phase, code frequency, code phase, and symbol resolution sequence.

[0044] Reference Figure 2 The process of instantaneously estimating the synchronization parameters of non-cooperative satellite signals using an instantaneous estimation algorithm is further described. This process is similar to the acquisition process in spread spectrum signal tracking.

[0045] The first step is to acquire the digital intermediate frequency signal S from the front end. IF (t) is transformed to the frequency domain using FFT Fourier transform to obtain the frequency domain signal S. IF (f).

[0046] The second step is to perform frequency multiplication on the frequency domain signal obtained in the previous step, multiplying it by the power of M. The multiplication factor M is adjusted according to the characteristics of different modulation signals; for BPSK signals, it is multiplied by 2, and for QPSK signals, it is multiplied by 4, resulting in the frequency-multiplied signal S. IF (f) M Then, find the horizontal coordinate index corresponding to the maximum value on the spectrum after frequency multiplication. This index value is the rough estimate of the carrier frequency obtained after frequency multiplication to the power of M.

[0047] The third step involves using the ZFFT algorithm to interpolate near the maximum spectral line of the frequency-doubled spectrum from the second step, thereby finding a more refined estimate of the carrier frequency f. c .

[0048] Reference Figure 3 The process of calculating the carrier frequency estimate using the ZFFT algorithm is further described.

[0049] First, the signal is re-modulated using the roughly estimated carrier frequency and shifted to near zero frequency.

[0050] Secondly, the signal is segmented and averaged. After segment extraction, an N-point FFT transform is performed to find the maximum spectral line in the local spectrum of each segment. Then, a quadratic curve fitting is performed on the obtained maximum spectral line value to obtain the refined spectrum. Here, N is the length of the segmented signal.

[0051] The ZFFT algorithm spectrum refinement algorithm, such as Figure 4 As shown.

[0052] The fourth step is to generate a local carrier signal based on the estimated carrier frequency value, and then perform a 90° phase shift on the local carrier signal to obtain in-phase and quadrature components. These components are then mixed with the original signal, i.e., coherent demodulation of the original signal. The two mixed signals obtained after demodulation are then low-pass filtered to remove the second harmonic component, resulting in the baseband signals I(t) and Q(t).

[0053] Fifth, based on the principle that shaping filtering causes periodic fluctuations in the signal during signal generation, the signal envelope spectrum x is calculated using the two baseband signals obtained in step four. e (t)=I(t)+Q(t), find the spectral line position f of the maximum value of the envelope spectrum. index f index The index corresponding to the position of the maximum spectral line is the coarse estimate of the code frequency, f. coderate0 .

[0054] The sixth step involves using the CZT algorithm to interpolate near the maximum spectral line of the envelope spectrum obtained in the fifth step, thereby finding a more refined code frequency estimate f. coderate .

[0055] Reference Figure 5 The CZT algorithm will be further described.

[0056] First, the signal is subjected to a Z-transform to obtain X(z). To enable refined interpolation over a region and to ensure that the Z-transform can take values ​​along a more generalized path in the z-plane, a spiral model can be used to perform equally secant sampling of the signal's Z-transform curve along the z-plane, defining the sampling point as z... k =AW -k The spectrum after interval refinement is represented as X(z) k ).

[0057] Secondly, through X(z) k Find the point X with the maximum amplitude in the range. m To obtain its corresponding frequency point f m This is a more accurate estimate of the carrier frequency.

[0058] Step 7: Based on the baseband signal obtained in step 4 and the code frequency estimate obtained in step 6, establish the optimization function J(T) cSolving the above function yields the code phase estimation result τ.

[0059] Reference Figure 6 The code phase estimation algorithm is further described below. The algorithm works by integrating the received baseband signal within an integration window, and then establishing an optimization function using the integration result, delay parameters, and symbol period parameters. When Tc = Tc0, the integration window width is exactly equal to the symbol width. If τ = Tc / 2 at this time, then at T... int If the integral for each integration window within the time interval is zero, and the sum of the integrals of all integration windows is also zero, then the optimization function reaches its minimum. If τ is located near the edge of the integration window, then each integration window exactly contains a complete symbol period, and the absolute value of the integral within the integration window reaches its maximum value, i.e., Τ. int The overall integral reaches its maximum value, and the optimization function also reaches its maximum value. If τ is located near the edge of the integration window and the symbol period parameter Tc deviates from the true symbol period Tc0, then the position of each integration window edge relative to the symbol flip point will cumulatively shift, and consequently, the optimization function obtained by summing the absolute values ​​of the piecewise integrations will deviate from its maximum value.

[0060] The optimization function established above is expressed as follows:

[0061]

[0062] Where, N c T represents the length of the baseband signal, k represents the sampling point of the baseband signal, τ represents the delay parameter of the baseband signal, and its value ranges from 0 to 1. c0 Let W(t) represent the baseband signal code period, where the period value is the reciprocal of the code frequency at the current moment. Let x′(t) represent the analytical form of the baseband signal, x′(t) = I(t) + jQ(t), where j represents the imaginary unit. c ,τ) represents the weight function, which takes values ​​of T int This represents the time corresponding to the total length of the baseband signal.

[0063] Find the optimal solution of the function Γ(τ) and use the optimal solution as the code phase of the initial estimate;

[0064] The eighth step involves binary decision-making on the baseband signal. Specifically, sampling points within a single chip are accumulated. If the accumulated value is greater than 0, the symbol is determined to be -1 due to the bipolar mapping of the pseudocode. If the accumulated value is less than 0, the symbol is determined to be 1. After the decision-making process for the entire baseband signal is completed, a symbol parsing sequence is obtained, which is considered the pseudocode sequence of the satellite signal.

[0065] Step 2: Based on the initial parameters of the instantaneous estimation of the non-cooperative satellite signal, input them into the carrier and symbol tracking loop to achieve long-term continuous estimation of the frequency and phase of the non-cooperative satellite signal.

[0066] Reference Figure 7 The loop tracking process of the present invention will be further described below.

[0067] The synchronization parameter estimates obtained in step 1 are used as initial values ​​and substituted into the carrier and symbol tracking loop. The specific tracking loop process is as follows:

[0068] The first step is to represent the acquired digital intermediate frequency signal as... Where A is the signal amplitude, f IF For carrier frequency.

[0069] The second step is to use the carrier frequency f from the synchronization parameters obtained in step 1. c Initial phase of carrier Symbol frequency f coderate And by substituting the initial symbol phase τ, the local carrier signal S is generated. loc (t)=cos(2πf c t)+jsin(2πf c t), the code element parsing sequence is used as the local pseudocode sequence.

[0070] The third step is to mix the digital intermediate frequency signal with the local carrier signal and then perform low-pass filtering on the mixed signal, thus completing the carrier frequency stripping and obtaining two baseband signals I(t) and Q(t).

[0071] The fourth step involves adjusting the phase of the I / Q baseband signals obtained in the third step of this process by adding a phase advance and a delay code Δτ to obtain four baseband signals: one leading and one lagging. E (t), I L (t), Q E (t) and Q L (t).

[0072] Step 3: Decision is made on the loop phase detection result in Step 2 to determine whether the loop phase detection result of the signal to be processed exceeds the allowable error range of the loop.

[0073] Perform carrier phase detection on the I and Q components of the baseband signal obtained in step 2 to obtain the phase detection error. The four baseband signals obtained from the lead and lag processing are correlated with the pseudocode sequence. After integration and clearing, the correlation results are used for code ring phase detection to obtain the code phase detection error τ. e :

[0074]

[0075] If a sudden interference signal occurs during continuous signal tracking, the signal frequency will fluctuate due to the Doppler effect. Since the loop's tracking capability is limited, if the frequency fluctuation exceeds the loop's frequency lock-in range, a loss of lock-in will occur. This invention makes a judgment on the loop frequency tracking result by using half the loop noise bandwidth as a threshold. The phase detection error result is compared with the threshold. If the phase detection error does not exceed the threshold, the loop operates normally and gradually converges to a stable value.

[0076] Step 4: Combine the instantaneous estimation algorithm to re-estimate the non-stationary signal that exceeds the phase detection error range, and use the estimation result to compensate for the loop tracking error to ensure the loop's ability to track subsequent signals.

[0077] The loop tracking noise bandwidth is set to the decision threshold in step 3. When the frequency error result after phase detection exceeds the threshold, the frequency value tracked by the loop will exceed the locking range of the loop. Therefore, it is considered that the signal is subjected to sudden interference at this time. If it is not controlled, when the loop continues to process the subsequent signal, it will bring in the error value obtained this time, causing the phase-locked loop to lose lock. The loop will lose its tracking ability and will be unable to continue to estimate the frequency and phase of the non-stationary satellite signal.

[0078] This invention addresses the aforementioned problem by implementing control measures when the frequency error exceeds the loop noise bandwidth. In this case, the original digital intermediate frequency (IF) signal received by the loop is transformed to the frequency domain. Since the instantaneous synchronization parameter estimation algorithm used in step 1 has high accuracy in estimating signal parameters, the synchronization parameters of this signal segment are then instantaneously estimated. This involves repeating steps two through seven of step 1 to obtain accurate frequency and phase changes for this signal segment. The estimated parameters of this signal segment are then used to correct the loop tracking deviation. Specifically, the difference between the estimated frequency of this signal segment and the initial frequency value of the loop is used to replace the loop phase detection error result obtained from tracking this signal segment. Subsequently, in the next loop iteration, the frequency and phase values ​​of the generated local signal are replaced with the highly accurate instantaneously estimated synchronization parameter values. The loop's frequency tracking value stabilizes within the frequency lock range, thus maintaining the loop lock and ensuring long-term continuous estimation of the frequency and phase of subsequent signals.

[0079] The effects of the present invention will be further explained below with reference to simulation experiments.

[0080] 1. Simulation conditions.

[0081] The hardware platform for the simulation experiment of this invention is: a central processing unit of Intel(R) Core(TM) i5-12500H CPU@2.50GHz and 16G of memory.

[0082] The software platform for the simulation experiment of this invention is: Windows 11 operating system and MATLAB R2022b.

[0083] The simulation experiment of this invention uses measured BeiDou satellite signals with a digital sampling rate of 50Msps, a total data length of 50s, a digital intermediate frequency of 12.5MHz, a code rate of 2.046Mbps, a signal-to-noise ratio of 10dB, a carrier tracking phase-locked loop noise bandwidth of 20Hz, and a code tracking phase-locked loop noise bandwidth of 10Hz.

[0084] 2. Simulation content and result analysis.

[0085] There are two simulation experiments for this invention.

[0086] Simulation Experiment 1 compares the processing time of the same non-cooperative satellite signal using existing technology and the method of this invention. Since the different signal data lengths in the carrier loop and code loop processing affect the processing time of the loop tracking method, simulation experiments are conducted on the method of this invention and existing technology under different segment lengths, and the algorithm time consumption results are plotted, as shown in the figure. Figure 8 As shown in (a).

[0087] The existing technology used in simulation experiment 1 of this invention is:

[0088] In his paper "Research on Non-cooperative Satellite Parameter Estimation Method and Application Based on GPU" (Master's Thesis, Xi'an University of Electronic Science and Technology, 2022), Yang Mixhao proposed a method for long-term continuous estimation of the frequency and phase of non-cooperative satellite signals.

[0089] Simulation Experiment 2 addresses the problem of lost-locking during the continuous frequency and phase estimation process in existing technologies for tracking non-stationary signals over long periods, leading to a loss of loop tracking capability. The method described in this invention improves upon these existing technologies. Simulation Experiment 2 also uses measured satellite signals with a sampling rate of 50 Mbps and a digital intermediate frequency of 12.5 MHz. Simulation Experiment 2 uses two sets of signals for comparison: one set of stationary signals and the other set of non-stationary signals, i.e., signals with sudden interference. The experimental results are as follows: Figure 8 (b) Figure 8 (c) Figure 8 As shown in (d).

[0090] The existing technology used in simulation experiment 2 of this invention refers to,

[0091] Changsha Xiandu Technology Co., Ltd. proposed a method for compensating for tracking non-stationary signals in its patent application document "A carrier phase tracking method for weak QAM signals" (patent application number: CN 202310530944.9, patent publication number: CN 116260690 A).

[0092] The following combination Figure 8 The simulation diagrams further illustrate the effects of the present invention.

[0093] Simulation Experiment 1 consists of five sets of simulation experiments with segmented signal lengths of 1ms, 5ms, 10ms, 50ms, and 100ms respectively for continuous estimation of the signal length of non-cooperative satellite signals. The simulation experiments compare the time consumption of the method of this invention and the existing technology for long-term continuous estimation of the frequency and phase of non-cooperative satellite signals under different segmented signal lengths.

[0094] Figure 8 In (a), the horizontal axis represents the length of the loop segmented signal, and the vertical axis represents the running time of the method. Among the two curves, the blue curve represents the time consumed by the method of the present invention, and the yellow curve represents the time consumed by the prior art method.

[0095] from Figure 8 (a) It can be seen that, under MATLAB simulation, the time taken by the method of the present invention is between 90s and 300s, while the time taken by the existing technology is basically within 600s to 700s. In actual engineering, the segment length of loop tracking is usually taken as 10ms. Therefore, by comparison, it can be found that the time taken by the present invention is reduced by 5 times compared with the existing technology when the segment length is 10ms, which greatly improves the efficiency of the algorithm and meets the needs of real-time signal processing in actual engineering.

[0096] Simulation Experiment 2 uses the method of this invention and existing techniques to analyze and process two groups of satellite signals, one stationary and one non-stationary. The experimental results are as follows: Figure 8 As shown, for the analysis of stationary signals, both existing techniques and the method of this invention can achieve long-term continuous estimation of signal frequency and phase.

[0097] Figure 8 (b) and Figure 8 In (c), the horizontal axis represents the number of loop iterations. The first graph shows the continuous estimation results of the carrier frequency, and the vertical axis represents the carrier frequency. The second graph shows the continuous estimation results of the carrier phase, and the vertical axis represents the carrier phase. The third graph shows the continuous estimation results of the code frequency, and the vertical axis represents the code frequency. The fourth graph shows the continuous estimation results of the code phase, and the vertical axis represents the code phase.

[0098] Depend on Figure 8 (b) and Figure 8(c) The comparison of the two sets of experiments shows that the existing technology requires a certain amount of time to converge and finally track a stable frequency result for the carrier frequency and code frequency tracking process. However, the method of the present invention has a high accuracy in estimating the signal synchronization parameters in the instantaneous estimation. Therefore, the convergence time of the loop is greatly reduced and a stable frequency result is tracked quickly.

[0099] For the analysis of non-stationary signals, by Figure 8 (d) It can be seen that in the process of tracking non-stationary signals using existing technology, when a sudden interference occurs, the frequency tracking result of the loop will exceed the stable frequency range of the loop, causing all subsequent frequency analysis results of the signal to be inaccurate, and it will be impossible to continue to accurately estimate the signal frequency and phase.

[0100] like Figure 8 As shown in (e), after improvement using the method of this invention, when the loop frequency tracking result exceeds the stable frequency range of the loop, an instantaneous estimation algorithm is immediately used to correct and compensate the frequency, so that the loop continues to remain locked, in order to achieve long-term continuous estimation of subsequent signal frequency and phase. Figure 8 In (e), the horizontal axis represents the number of loop iterations. The first graph shows the continuous estimation results of the carrier frequency, and the vertical axis represents the carrier frequency. The second graph shows the continuous estimation results of the code frequency, and the vertical axis represents the code frequency.

Claims

1. A method for frequency and phase continuity estimation of non-stationary, non-cooperative satellite signals, characterized in that, Synchronization parameters are obtained through instantaneous estimation. These parameters are then substituted into the carrier tracking and code tracking loops to obtain the current loop phase detection result. The loop phase detection result is then compensated. The process includes the following steps: Step 1: Use an instantaneous estimation algorithm to perform instantaneous estimation on the non-stationary, non-cooperative satellite signal to obtain the synchronization parameters at the initial moment. Use the synchronization parameters at the initial moment as the initial values ​​for the carrier tracking and code tracking loops. The instantaneous estimation algorithm is used to perform instantaneous estimation of non-stationary, non-cooperative satellite signals. The initial synchronization parameters obtained include carrier frequency, carrier phase, code frequency, code phase, and symbol parsing sequence. Step 2: Substitute the initial values ​​into the carrier tracking and code tracking loop to generate the local carrier signal and code sequence at the current moment. Calculate the loop phase detection result at the current moment by comparing the local signal with the received signal. The steps for incorporating the initial values ​​into the carrier tracking and code tracking loops are as follows: The first step is to generate a local carrier signal based on the carrier frequency and carrier phase in the synchronization parameters at the initial moment, and use the symbol parsing sequence in the synchronization parameters at the initial moment as the local pseudocode sequence. The second step is to mix the digital intermediate frequency signal with the local carrier signal and then perform low-pass filtering on the mixed signal, thus completing the carrier stripping and obtaining two baseband signals. The third step is to process the two baseband signals by advancing and delaying them by half a chip, respectively, to obtain four baseband signals. Step 3: Determine whether the current loop phase detection result exceeds the noise bandwidth range of the carrier tracking and code tracking loops. If it does not exceed the noise bandwidth range, use the current loop phase detection result as the initial value of the carrier tracking and code tracking loops at the next moment and then execute Step 2. Otherwise, proceed to step 4; Step 4: Use the same instantaneous estimation algorithm as in Step 1 to estimate the synchronization parameters at the current moment; Step 5: Determine whether the current time has reached the user-set task time. If yes, proceed to step 6. Otherwise, calculate the difference between the synchronization parameters at the current time and the synchronization parameters at the initial time, use the difference to compensate for the loop phase detection result of this signal segment, and use the loop phase detection result as the initial value of the carrier tracking and code tracking loop at the next time before proceeding to step 2. Step 6: Output the continuous estimation results of the frequency and phase of the non-stationary, non-cooperative satellite signal.

2. The method for frequency and phase continuity estimation of non-stationary, non-cooperative satellite signals according to claim 1, characterized in that, The instantaneous estimation steps for the carrier frequency are as follows: The first step is to perform an FFT Fourier transform on the digital intermediate frequency signal to obtain the frequency domain signal; The second step is to perform M-fold frequency multiplication on the frequency domain signal, remove the DC component from the multiplied signal, and then find the horizontal coordinate index value corresponding to the maximum spectral line on the frequency multiplied spectrum. This horizontal coordinate index value is used as a rough estimate of the carrier frequency obtained after M-fold frequency multiplication. The value of M is determined according to the type of different modulation signals. For BPSK signals, it is 2 times the frequency, and for QPSK signals, it is 4 times the frequency. The third step involves using the ZFFT algorithm to roughly estimate the carrier frequency and shift the digital intermediate frequency signal to near zero frequency. The signal is then divided into N segments for integration. An FFT Fourier transform is performed on each segment, and the maximum spectral line is found in the spectrum of each segment. A quadratic curve fitting is performed on the maximum spectral line of each segment to obtain the refined spectrum. The horizontal coordinate index value corresponding to the maximum spectral line of the refined spectrum is found, and this horizontal coordinate index value is used as the carrier frequency of the synchronization parameter. Here, N takes any integer value between 10 and 100.

3. The method for frequency and phase continuity estimation of non-stationary, non-cooperative satellite signals according to claim 2, characterized in that, The carrier phase is generated based on the carrier frequency of the synchronization parameters. A local carrier signal is generated, and the local carrier signal is phase-shifted by 90° to obtain in-phase and quadrature components. The digital intermediate frequency signal is then coherently demodulated. The two demodulated mixed signals are then low-pass filtered to remove the second harmonic component, resulting in two baseband signals. and The two baseband signals are subjected to arctangent phase detection, and the phase detection result is used as the carrier phase of the synchronization parameter.

4. The method for frequency and phase continuity estimation of non-stationary, non-cooperative satellite signals according to claim 3, characterized in that, The code frequency is achieved using two baseband signals. and Find the envelope spectrum signal The process involves finding the abscissa index value corresponding to the maximum spectral line on the envelope spectrum and using this abscissa index value as a rough estimate of the code frequency. After performing a Z-transform on the envelope spectrum signal using the CZT algorithm, a spiral model is used to perform equally secant sampling on the signal's Z-transform curve along the z-plane. That is, fitting and interpolating are performed at the rough estimate of the code frequency on the Z-transform curve. The abscissa index value corresponding to the maximum spectral line after fitting and interpolation is found, and this abscissa index value is used as the code frequency of the synchronization parameter.

5. The method for frequency and phase continuity estimation of non-stationary, non-cooperative satellite signals according to claim 4, characterized in that, The code phase is calculated using the following formula: The optimal solution is used as the code phase of the synchronization parameter: ； in, Indicates the length of the baseband signal. Indicates the sampling points of the baseband signal. This represents the delay parameter of the baseband signal, with a value ranging from 0 to 1. This represents the baseband signal code period, which is the reciprocal of the code frequency at the current moment. This represents the analytical form of the baseband signal. , Represents the imaginary unit. This represents the weighting function, whose values ​​are... , This represents the time corresponding to the total length of the baseband signal.

6. The method for frequency and phase continuity estimation of non-stationary, non-cooperative satellite signals according to claim 1, characterized in that, The step 5 step of using the difference to compensate for the loop phase detection result of the current signal segment means taking the difference between the carrier frequency in the synchronization parameters at the current time and the carrier frequency in the synchronization parameters at the initial time, using the difference to compensate for the loop phase detection result of the current signal segment, and using the loop phase detection result as the initial value of the carrier tracking and code tracking loop at the next time moment. The local carrier signal is generated using the initial value in the next loop iteration.

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