A carrier synchronization method for telemetry and ranging signal fusion based on two-stage EKF

Abstract

The present invention discloses a carrier synchronization method for the fusion of telemetry and ranging signals based on a two-stage EKF, which solves technical problems such as slow carrier synchronization speed and difficult loop filter coefficient design in a system where regenerated pseudo-code ranging and high-order modulated telemetry signals are simultaneously transmitted. In the system of the present invention, carrier synchronization with large frequency offsets is achieved through an extended Kalman filter carrier synchronization algorithm, and EKF carrier synchronization from coarse to fine is achieved through a synchronous locking detector. Rapid frequency pulling is achieved through the coarse synchronization stage, and precise frequency tracking is performed in the fine synchronization stage, maintaining low residual phase noise, thereby improving synchronization speed and stability. The present invention has good telemetry signal demodulation performance and is suitable for space communications with large frequency shifts.

Description

Technical Field

[0001] The present invention belongs to the field of space communication, and in particular relates to a carrier synchronization method for fusing telemetry and ranging signals based on a two-stage EKF. Background Art

[0002] In recent years, within the framework of the Consultative Committee for Space Data Systems (CCSDS), research has been conducted on systems capable of simultaneously transmitting high-speed telemetry and ranging signals. NASA has combined Gaussian minimum shift keying (GMSK) with regenerated pseudo-noise (PN) ranging, a technique denoted as GMSK+PN. The receiver first estimates the transmitted telemetry bits, regenerates and removes the estimated GMSK signal from the received signal, and then uses a set of correlators to estimate the round-trip delay between the ranging code chips and the received ranging signal.

[0003] However, frequency allocation regulations limit near-Earth space research (SR) missions operating in the X-band (8.4-8.45 GHz) for telemetry, tracking, and command (TT&C) to a bandwidth of 10 MHz. Consequently, when using GMSK, SR missions are limited to data rates of approximately 10 Mbps, hindering the generation of effective data. Therefore, to overcome current data rate limitations, these missions must efficiently utilize the available X-band bandwidth. For this reason, high-order modulation schemes are essential.

[0004] In space communications scenarios, the high-speed relative motion between the transmitter and receiver can produce a Doppler shift in the carrier frequency. Carrier synchronization requires recovering a local carrier with the same frequency and phase as the received carrier to adjust the local carrier phase. Carrier synchronization technology is of great research significance for ensuring high-quality communication in space links, and a phase-locked loop (PLL) is commonly used in engineering to estimate Doppler shift. A PLL is a closed-loop phase control system that uses an external reference signal to control the frequency and phase of an oscillating signal within the loop. PLLs offer the advantages of accurate tracking and good stability, and can estimate the unknown phase of the signal itself. However, their performance is affected by the loop bandwidth. If the Doppler shift is too large, a larger loop bandwidth is usually required, which results in more noise entering the loop and reducing tracking accuracy. Therefore, it is not suitable for environments with a wide range of Doppler shifts. These and other similar issues limit the application of traditional Doppler shift estimation methods.

[0005] The Kalman filter (KF) is known as an optimal recursive linear filter in terms of minimum mean square error. KFs offer better adaptability than traditional PLLs whenever the system environment changes. The extended Kalman filter (EKF) is a nonlinear version of the KF used to estimate the state of dynamic systems. The EKF algorithm provides high adaptability by automatically adjusting filter parameters based on dynamic system changes and optimally estimating system states in the presence of strong noise. Therefore, given the insufficient carrier synchronization of a PLL that simultaneously transmits PN ranging and filtered phase-shift keying (PSK) signals, and taking into account the advantages of the EKF, a carrier synchronization method for telemetry and ranging signal fusion based on a two-stage EKF was designed. Summary of the Invention

[0006] To address the above problems, the present invention discloses a carrier synchronization method based on the fusion of telemetry and ranging signals using a two-stage EKF. The entire synchronization process is divided into two stages through a locking detector: coarse synchronization and fine synchronization. In the coarse synchronization stage, a faster-responding filter is used to quickly capture the range of frequency offset; in the fine synchronization stage, a slower-responding but more precise filter is used to accurately calculate and track the offset. The method can adaptively identify different stages and assign appropriate EKF parameters to each stage, thereby improving the speed and stability of synchronization.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] A carrier synchronization method for telemetry and ranging signal fusion based on a two-stage EKF comprises the following steps:

[0009] Step S1: Input the telemetry and pseudo-code received signal r(t) with Doppler frequency offset into the matched filter to obtain y k , and then sent into the carrier synchronization loop, the channel is an additive white Gaussian noise channel;

[0010] Step S2: Determine the state vector and observation vector in the carrier synchronization algorithm based on EKF, and determine the state vector as in is the phase at the kth moment; ω k is the phase deviation at the kth moment; the received signal is input through the matched filter as observed variables;

[0011] Step S3: Set the initial values ​​of the state variables and initial noise variance for the EKF algorithm and P 0|0 The initial mode of EKF is the coarse synchronization mode, and the process noise factor q under the coarse synchronization mode is selected k; Perform iterative estimation based on the decision-making EKF carrier synchronization algorithm, wherein the iterative process includes step S4, step S5, and step S6;

[0012] Step S4, the first process of the EKF algorithm is the prediction process, according to the process noise covariance matrix Q k , the estimated value of the state at the previous moment and update error covariance P k-1|k-1 , using the state equation to estimate the predicted state vector and the prediction error covariance P k|k-1 ;

[0013] Step S5, based on the EKF algorithm correction calculation phase of the decision, the decision symbol is obtained according to the hard decision detector module As the transmitted symbol, and calculate the Jacobian matrix H k and the predicted observed values

[0014] Step S6, the second process of the EKF algorithm is the measurement update process, according to the prediction error covariance P k|k-1 , Jacobian matrix H k , measurement noise covariance R k Calculate the Kalman gain coefficient matrix K k , and finally predict the current state value Observed residual value and the Kalman gain K k To calculate the updated state vector and update error covariance P k|k , one iteration is completed here;

[0015] Step S7: The k-th moment state vector estimated by the EKF iteration in step S6 is in Carrier regeneration is performed to obtain So the signal y after matched filtering is k Perform phase correction and obtain the input signal of the hard decision PSK detector as y' k , the judgment symbol is obtained by the judgment module Return to step S4;

[0016] Step S8, the synchronization lock detector module includes a distance discriminator and a sliding average filter. The distance discriminator detects the phase correction symbol y' k With hard decision detector output Is the distance between them less than the threshold σ? th1 Determine the output error o k Is 1 or 0; the sliding average filter uses a length of N LdThe sliding window of the distance discriminator output o k Perform average filtering to obtain By With the threshold σ th2 Compare and get the preset process noise factor q under the current synchronization stage k .

[0017] First, in step S1, the received signal r(t) is:

[0018]

[0019] where d k is the telemetry data symbol, T s is the telemetry data symbol period, q(t) is the square root raised cosine (SRRC) shaped pulse; is the modulation index of the pseudo-code ranging signal, g sin / sq (t) represents the impulse response of the shaping filter; c k is the pseudo code ranging sequence, with a value of ±1; and the T2B and T4B sequences recommended by CCSDS are selected; The Doppler frequency shift f d and constant phase offset The uncompensated carrier phase error caused by u(t) is zero-mean complex Gaussian white noise;

[0020] After matched filtering and ideal sampling, the received discrete baseband signal y k It can be expressed as:

[0021]

[0022] Secondly, in step S2, the formula of the observation vector is:

[0023]

[0024] The observation transfer matrix In-phase and quadrature components of the received signal and is the observation vector y k Elements, and is the transmitted symbol pair, and Represents the measurement noise of the in-phase component and quadrature component of the received signal respectively. The covariance matrix R of the measurement noise is k =r k I, I is the identity matrix, r k The formula is

[0025]

[0026] Where C / N0(dB-Hz)=SNR(dB)+10log 10 (B(Hz)), B is the received signal bandwidth.

[0027] Next, in step S4, the formula for predicting the state vector is:

[0028]

[0029] The transition matrix

[0030] Prediction error covariance P k|k-1 for

[0031]

[0032] Furthermore, in step S5, the Jacobian matrix H k The formula is:

[0033]

[0034] Predicted observations for

[0035]

[0036] Next, in step S6, the Kalman gain K k for:

[0037] Observation residue for:

[0038]

[0039] Update the state vector for:

[0040]

[0041] Update error covariance P k∣k for:

[0042] P k|k =P k|k-1 -K k H k P k|k-1 .

[0043] Finally, in step S8, the distance discriminator formula is:

[0044]

[0045] The sliding average filter formula is:

[0046]

[0047] The output of the Genlock Detector block is:

[0048]

[0049] The beneficial effects of the present invention are:

[0050] The present invention proposes a carrier synchronization method based on the fusion of telemetry and ranging signals using a two-stage EKF. This is because the existing PLL carrier synchronization method for simultaneously transmitting PN ranging and filtered phase-shift keying (PSK) signals suffers from insufficient tracking accuracy in large frequency offset environments. EKF carrier synchronization can track weaker signals and detect the state of the synchronization process through a synchronization lock detector, adjusting the EKF filter parameters and then updating the noise covariance to achieve more accurate and stable estimation. Therefore, the EKF algorithm is introduced into the model of simultaneously transmitting PN ranging and filtered phase-shift keying (PSK) signals. This synchronization algorithm can quickly lock the signal in the coarse synchronization stage and maintain a low carrier frequency deviation estimate (MSE) in the fine synchronization stage, with excellent performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the present invention.

[0052] Figure 2 It is a frequency offset synchronization curve.

[0053] Figure 3 It is the MSE comparison chart of normalized carrier frequency deviation estimation. DETAILED DESCRIPTION

[0054] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0055] As shown in the figure, the carrier synchronization method for telemetry and ranging signal fusion based on two-stage EKF of the present invention is based on the carrier synchronization algorithm based on extended Kalman filter, and a synchronization lock detection module is added to select the process noise covariance matrix parameter Q of the EKF filter. k The process noise factor q in k , thereby achieving coarse-to-fine carrier synchronization.

[0056] Specifically, the carrier synchronization method includes the following steps:

[0057] Step S1: Input the telemetry and pseudo-code received signal r(t) with Doppler frequency offset into the matched filter to obtain y k , and then sent into the carrier synchronization loop, the channel is an additive white Gaussian noise channel.

[0058] Step S2: Determine the state vector and observation vector in the carrier synchronization algorithm based on EKF, and determine the state vector as in is the phase at the kth moment; ω k is the phase deviation at the kth moment; the received signal is input through the matched filter as observed variables;

[0059] Step S3: Set the initial values ​​of the state variables and initial noise variance for the EKF algorithm and P 0|0 The initial mode of EKF is the coarse synchronization mode, and the process noise factor q under the coarse synchronization mode is selected k ; Perform iterative estimation based on the decision-making EKF carrier synchronization algorithm, wherein the iterative process includes step S4, step S5, and step S6;

[0060] Step S4, the first process of the EKF algorithm is the prediction process, according to the process noise covariance matrix Q k , the estimated value of the state at the previous moment and update error covariance P k-1|k-1 , using the state equation to estimate the predicted state vector and the prediction error covariance P k|k-1 ;

[0061] Step S5, based on the EKF algorithm correction calculation phase of the decision, the decision symbol is obtained according to the hard decision detector module As the transmitted symbol, and calculate the Jacobian matrix H k and the predicted observed values

[0062] Step S6, the second process of the EKF algorithm is the measurement update process, according to the prediction error covariance P k|k-1 , Jacobian matrix H k , measurement noise covariance R k Calculate the Kalman gain coefficient matrix K k , and finally predict the current state value Observed residual value and the Kalman gain K k To calculate the updated state vector and update error covariance P k|k , one iteration is completed here;

[0063] Step S7: The k-th moment state vector estimated by the EKF iteration in step S6 is in Carrier regeneration is performed to obtain So the signal y after matched filtering is k Perform phase correction and obtain the input signal of the hard decision PSK detector as y' k , the judgment symbol is obtained by the judgment module Return to step S4;

[0064] Step S8, the synchronization lock detector module includes a distance discriminator and a sliding average filter. The distance discriminator detects the phase correction symbol y' k With hard decision detector output Is the distance between them less than the threshold σ? th1 Determine the output error o k Is 1 or 0; the sliding average filter uses a length of N Ld The sliding window of the distance discriminator output o k Perform average filtering to obtain By With the threshold σ th2 Compare and get the preset process noise factor q under the current synchronization stage k .

[0065] like Figure 1 As shown, first, in step S1, the received signal r(t) is:

[0066]

[0067] where d k is the telemetry data symbol, T s is the telemetry data symbol period, q(t) is the square root raised cosine (SRRC) shaped pulse; is the modulation index of the pseudo-code ranging signal, g sin / sq (t) represents the impulse response of the shaping filter; c k is the pseudo code ranging sequence, with a value of ±1; and the T2B and T4B sequences recommended by CCSDS are selected; The Doppler frequency shift f d and constant phase offset The uncompensated carrier phase error caused by u(t) is zero-mean complex Gaussian white noise;

[0068] After matched filtering and ideal sampling, the received discrete baseband signal y k It can be expressed as:

[0069]

[0070] Since the modulation index m of the pseudo code ranging signal RG Since the received signal is less affected by the PN ranging signal after carrier synchronization and is sent to the PSK demodulator, it is less likely to be interfered with by the PN ranging signal. However, since the PSK demodulator input noise contains mixed noise of the ranging signal, its power is higher than that of the pure channel noise. Therefore, compared with the case of transmitting only telemetry data (h = 0), the signal-to-noise ratio of the telemetry signal in the composite signal is reduced, and the bit error rate performance is lost. The lost power is

[0071]

[0072] Where J0(·) is the 0th order Bessel function; when h=0.1, P LTM =0.11dB; when h=0.2, P LTM =0.43dB. At this time, the ranging signal caused obvious interference to the telemetry.

[0073] Secondly, in step S2, the formula of the observation vector is:

[0074]

[0075] The observation transfer matrix In-phase and quadrature components of the received signal and is the observation vector y k Elements, and is the transmitted symbol pair, and Represents the measurement noise of the in-phase component and quadrature component of the received signal respectively. The covariance matrix R of the measurement noise is k =r k I, I is the identity matrix, r k The formula is

[0076]

[0077] Where C / N0(dB-Hz)=SNR(dB)+10log 10 (B(Hz)), B is the received signal bandwidth.

[0078] Next, in step S4, the formula for predicting the state vector is:

[0079]

[0080] The transition matrix

[0081] Prediction error covariance P k|k-1 for

[0082]

[0083] Furthermore, in step S5, the Jacobian matrix H k The formula is:

[0084]

[0085] Predicted observations for

[0086]

[0087] Next, in step S6, the Kalman gain K k for: Observation residue for:

[0088]

[0089] Update the state vector for:

[0090]

[0091] Update error covariance P k∣k for:

[0092] P k|k =P k|k-1 -K k H k P k|k-1

[0093] Finally, in step S5, the distance discriminator formula is:

[0094]

[0095] In the presence of frequency error, the received signal constellation point will deviate from the expected constellation point position.

[0096] The sliding average filter formula is:

[0097]

[0098] The sliding average filter uses a length of N L The sliding window of d is used for average filtering to reduce the impact of noise and improve the stability and smoothness of the signal.

[0099] The synchronization lock detector determines whether the current system is in a locked state, thereby determining the synchronization stage of the loop.Ld , σ th1 and σ th2 The output of the synchronous lock detector is given by:

[0100]

[0101] Switching carrier synchronization modes is accompanied by changes in the q value output by the genlock detector. This shift from coarse to fine EKF carrier synchronization allows for fast frequency pulling and low steady-state error. In coarse synchronization mode, a larger q1 value enables rapid convergence. Once the genlock detector detects lock, it switches to q2, or fine synchronization mode, for precise phase tracking.

[0102] In order to verify the effect of the present invention, the following simulation is set:

[0103] Select simulation parameters: telemetry code rate Rs = 4Msymbol / s, PN code chip rate Rc = 4Mchip / s, and the ranging signal weighting factor h is 0.1. The parameters of the two-stage synchronization algorithm based on EKF are shown in the following table

[0104] Table 1. Detailed settings of coefficients in the scheme of the present invention

[0105] Roll-off factor <![CDATA[σ th1 ]]> <![CDATA[σ th2 ]]> <![CDATA[N Ld ]]> <![CDATA[q1]]> <![CDATA[q2]]> QPSK+PN 0.35 0.64 0.6 24 5e-2 1e-7

[0106] like Figure 2 As shown, under the QPSK+PN modulated signal, the signal-to-noise ratio is 10dB and the normalized frequency offset is 0.09. The figure shows the capture curve of the frequency offset under different q values. It can be seen that when the q value increases within a certain range, the capture curve of the frequency offset can achieve faster frequency traction, but it fluctuates greatly in the steady state, resulting in a large steady-state error. In this regard, compared with the fixed q value, as shown in the figure, the frequency offset traction speed of the two-stage synchronization algorithm is faster and the steady-state error is smaller. The q1 and q2 of the two stages in the analysis table of the present invention are the optimal values, and reducing the q2 value does not significantly improve the performance.

[0107] like Figure 3As shown, the present invention obtains the carrier frequency deviation estimation MSE for EKFs with different q values. Compared with the EKF with a constant q value of q = 5e-5, the two-stage EKF carrier synchronization loop (coarse synchronization process) can quickly lock large frequency offset signals with a larger bandwidth. In steady state (fine synchronization process), compared with the EKF with a constant q value of q = 5e-3, it can suppress the impact of noise on the tracking signal with a smaller bandwidth, maintaining a lower carrier frequency deviation estimation MSE. In terms of performance, the carrier synchronization technology based on the two-stage EKF outperforms the fixed-bandwidth EKF carrier synchronization algorithm in both synchronization speed and stability.

[0108] It should be noted that the above content merely illustrates the technical idea of ​​the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.

Claims

1. A carrier synchronization method for telemetry and ranging signal fusion based on a two-stage EKF, characterized in that: The method is based on the carrier synchronization algorithm based on the extended Kalman filter EKF, and adds a synchronization lock detector module to select the process noise covariance matrix Q of the EKF filter. k The process noise factor q in k , thereby achieving coarse-to-fine carrier synchronization; specifically, the carrier synchronization method includes the following steps: Step S1: Input the telemetry and pseudo-code received signal r(t) with Doppler frequency offset into the matched filter to obtain y k , and then sent into the carrier synchronization loop, the channel is an additive white Gaussian noise channel; Step S2: Determine the state vector and observation vector in the carrier synchronization algorithm based on EKF, and determine the state vector as in is the phase at the kth moment; ω k is the phase deviation at the kth moment; the received signal is filtered by matched filtering. As the observation vector; the in-phase and quadrature components of the received signal and is the observation vector y k Elements of Step S3: Set the initial value of the error covariance of the state variable and the initial noise to the carrier synchronization algorithm based on EKF and P 0|0 The initial mode of EKF is the coarse synchronization mode, and the process noise factor q under the coarse synchronization mode is selected k ; Perform iterative estimation based on the decision-making EKF carrier synchronization algorithm, wherein the iterative process includes step S4, step S5, and step S6; Step S4: The first process of the EKF-based carrier synchronization algorithm is the prediction process. k , the state vector at the previous moment and update error covariance P k-1|k-1 , use the state equation to estimate the state vector of the current moment k and the prediction error covariance P k|k-1 ; Step S5, based on the EKF carrier synchronization algorithm correction calculation phase, the decision symbol is obtained according to the hard decision detector module As the transmitted symbol, and calculate the Jacobian matrix H k and the predicted observed values Step S6: The second process of the EKF-based carrier synchronization algorithm is the measurement update process. k|k-1 , Jacobian matrix H k , measurement noise covariance matrix R k Calculate the Kalman gain coefficient matrix K k , and finally predict the state vector of the current moment k Observed residual value And the Kalman gain coefficient matrix K k To calculate the updated state vector and update error covariance P k|k , one iteration is completed here; Step S7: The k-th moment state vector estimated by the EKF iteration in step S6 is in Carrier regeneration is performed to obtain So the signal y after matched filtering is k Perform phase correction and obtain the input signal of the hard decision detector module as y' k , the decision symbol is obtained by the hard decision detector module Return to step S4; Step S8, the synchronization lock detector module includes a distance discriminator and a sliding average filter. The distance discriminator detects the phase correction symbol y' k and the hard decision detector module output Is the distance between them less than the threshold σ? th1 Determine the output error o k Is 1 or 0; the sliding average filter uses a length of N Ld The sliding window of the distance discriminator output error o k Perform average filtering to obtain By With the threshold σ th2 Compare and get the preset process noise factor q under the current synchronization stage k .

2. A carrier synchronization method for telemetry and ranging signal fusion based on a two-stage EKF according to claim 1, characterized in that: In step S1, the received signal r(t) is: where d k is the telemetry data symbol, T s is the telemetry data symbol period, q(t) is the square root raised cosine shaped pulse; is the modulation index of the pseudo-code ranging signal, h is the ranging signal weighting factor, g sin / sq (t) represents the impulse response of the shaping filter; c k is the pseudo code ranging sequence, with a value of ±1; and the T2B and T4B sequences recommended by CCSDS are selected; The Doppler frequency shift f d and constant phase offset The uncompensated carrier phase error caused by u(t) is zero-mean complex Gaussian white noise; After matched filtering and ideal sampling, the received discrete baseband signal y k Expressed as:

3. The carrier synchronization method for telemetry and ranging signal fusion based on a two-stage EKF according to claim 1, characterized in that: In step S2, the formula of the observation vector is: The observed value In-phase and quadrature components of the received signal and is the observation vector y k Elements, and is the transmitted symbol pair, and Respectively represent the measurement noise of the in-phase component and the orthogonal component of the received signal; measurement noise The covariance matrix R of the measurement noise is k =r k I, I is the identity matrix, r k The formula is: Where C / N0(dB-Hz)=SNR(dB)+10log 10 (B(Hz)), B is the received signal bandwidth.

4. The carrier synchronization method for telemetry and ranging signal fusion based on a two-stage EKF according to claim 1, characterized in that: In step S4, the formula for predicting the state vector is: The transition matrix Prediction error covariance P k|k-1 for:

5. The carrier synchronization method for telemetry and ranging signal fusion based on two-stage EKF according to claim 1, characterized in that: In step S5, the Jacobian matrix H k The formula is: Predicted observations for:

6. The carrier synchronization method for telemetry and ranging signal fusion based on two-stage EKF according to claim 1, characterized in that: In step S6, the Kalman gain coefficient matrix K k for: Observed residual value for: Update the state vector for: Update error covariance P k∣k for: P k∣k =P k∣k-1 -K k H k P k∣k-1 。 7. The carrier synchronization method for telemetry and ranging signal fusion based on two-stage EKF according to claim 1, characterized in that: In step S8, the distance discriminator formula is: The sliding average filter formula is: The output of the Genlock Detector block is:

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