Self-adaptive Kalman filtering assisted high-dynamic time division navigation signal tracking method

Abstract

The invention relates to a high-dynamic time division navigation signal tracking method assisted by adaptive Kalman filtering, and belongs to the technical field of satellite navigation. Aiming at the problems of tracking delay, precision reduction and easy lock loss caused by discontinuous loop update in a high dynamic environment in the existing time division navigation signal tracking method, the method comprises the steps of carrier and code stripping, time-slot error identification, adaptive Kalman filter AKF preprocessing and loop filtering and tracking of three-order FLL-assisted four-order PLL. And full-time-slot continuous tracking is realized. The core of the method is that process noise covariance is adaptively adjusted through AKF, optimal estimation and smoothing are carried out on errors, and then processing is carried out through a post-stage loop filter. According to the method, the tracking continuity, robustness and precision in a high dynamic environment are effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation technology and relates to an adaptive Kalman filter-assisted high dynamic time-division navigation signal tracking method. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) play an indispensable role in modern positioning, navigation, and timing. Their core principle is based on the transmission and reception of spread spectrum modulated signals. Traditional navigation signals commonly employ binary phase-shift keying (BPSK) direct sequence spread spectrum modulation (DSSM), and its signal tracking schemes are relatively mature. In engineering practice, receivers typically use phase-locked loops (PLLs) for precise carrier tracking, with frequency-locked loops (FLLs) as a backup to suppress large frequency deviations or rapid dynamic changes. A common implementation is a cascaded structure of FLLs and PLLs. This approach achieves a good balance between implementation complexity and steady-state tracking jitter under conditions of stable or moderate platform dynamics.

[0003] However, when the carrier platform experiences non-stationary dynamic stress caused by high acceleration or jerk, the aforementioned fixed-parameter carrier tracking loop faces significant challenges. The loop must strike a difficult trade-off between increasing bandwidth to keep up with rapid dynamics and decreasing bandwidth to suppress measurement noise. While excessively wide bandwidth can improve the ability to track dynamic stress, it introduces too much noise, leading to deterioration in tracking accuracy; conversely, excessively narrow bandwidth cannot adapt to high dynamic changes and is prone to loss of lock.

[0004] In recent years, code shift keying (CPS) modulation has attracted attention due to its significant advantages in navigation message transmission rates. Some studies have proposed carrier tracking methods for CPS signals. However, these methods place high demands on initial signal alignment conditions and the carrier-to-noise ratio (CNR). Only when the CNR exceeds a certain threshold can its performance rival that of binary phase shift keying (BPSK) modulation tracking at the same code rate. In low CNR or high dynamic environments, the tracking performance and robustness of this method remain limited.

[0005] To comprehensively utilize the superior ranging performance of binary phase-shift keying (BPS) modulation and the high information transmission rate of code shift keying (CPS), time-division multiplexing (TDD) navigation signal structures combining BPS and CPS have emerged and become a research hotspot. However, most existing TDD navigation signal tracking techniques employ a strategy of updating the tracking loop only in the BPS slots and freezing the loop parameters in the CPS slots. This means that phase detection, filtering, and numerically controlled oscillator (CNC) updates for both the carrier and code loops are concentrated within the BPS slots, resulting in intermittent loop updates and a 50% reduction in the effective update rate. This half-duty-cycle update method directly prolongs the loop convergence time and significantly weakens the real-time tracking capability for fast-changing Doppler frequencies in highly dynamic scenarios.

[0006] In summary, existing technologies have significant shortcomings when handling time-division navigation signal tracking in highly dynamic environments: either they sacrifice tracking information from code shift keying (CPSK) slots, leading to discontinuous loop updates, or they exhibit tracking lag, increased jitter, or even loss of lock under high dynamic stress. Currently, there is a lack of a solution that can achieve continuous updates throughout the entire signal frame period while effectively coping with high dynamic stress and ensuring tracking robustness. This technical bottleneck is precisely the core problem that the adaptive Kalman filter-assisted continuous tracking method for highly dynamic time-division navigation signals proposed in this invention aims to solve. Summary of the Invention

[0007] In view of this, the purpose of the present invention is to provide an adaptive Kalman filter-assisted high dynamic time-division navigation signal tracking method.

[0008] To achieve the above objectives, the present invention provides the following technical solution: An adaptive Kalman filter-assisted high dynamic time-division navigation signal tracking method includes the following steps: S1. Carrier and code stripping step: The received time-division digital intermediate frequency signal is mixed with the local carrier generated by the locally carrier numerically controlled oscillator (NCO) to complete carrier stripping and obtain I-channel and Q-channel baseband signals; The I-channel and Q-channel baseband signals are correlated with the local PRN code generated by the local pseudo random noise (PRN) code generator to complete code stripping; S2. Error identification steps: In the Binary Phase Shift Keying (BPSK) time slot, calculate the carrier phase error using the correlation results of the instantaneous branch, and calculate the code phase error using the correlation results of the leading and lagging branches; in the Code Shift Keying (CSK) time slot, use the maximum correlation peak criterion to determine the current CSK symbol, and calculate the carrier phase error using the correlation results of the instantaneous branch corresponding to the symbol, and calculate the code phase error using the correlation results of the leading and lagging branches corresponding to half a chip before and after it; S3. Adaptive Kalman Filter (AKF) preprocessing steps: The carrier phase error and frequency error obtained in S2 are used as observation values ​​and input to the adaptive Kalman filter for preprocessing; the adaptive Kalman filter dynamically adjusts its process noise covariance matrix by estimating the statistical characteristics of the innovation sequence in real time, and outputs the error state estimate after optimal estimation and noise suppression. S4. Loop Filtering and Tracking Steps: The error state estimate preprocessed in S3 is fed into the subsequent loop filter for smoothing and prediction. The loop filter adopts a structure of a third-order frequency-locked loop (FLL) assisted by a fourth-order phase-locked loop (PLL). The control signal processed by the loop filter drives the carrier NCO and the code NCO respectively, adjusting the frequency and phase of the local reproducible carrier and the phase of the local PRN code to complete closed-loop tracking.

[0009] Furthermore, the time-division digital intermediate frequency signal is a BPSK-CSK time-division multiplexed signal, wherein during the transmission frame period... Within the system, BPSK direct-sequence spread spectrum and CSK signal are transmitted in an alternating time-slot manner. Starting from time slot zero, BPSK modulated signal is transmitted in even-numbered time slots and CSK modulated signal is transmitted in odd-numbered time slots.

[0010] Furthermore, in the error identification step, the carrier phase error is calculated using a two-quadrant arctangent phase detector in the BPSK time slot and a four-quadrant arctangent phase detector in the CSK time slot.

[0011] Furthermore, in the error identification step, the code phase error is calculated using a normalized incoherent lead-hysteresis amplitude detector in both the BPSK and CSK time slots.

[0012] Furthermore, in the code stripping step, in the BPSK time slot, the local PRN code generator generates three code copy signals with phase leading, phase instantaneous, and phase lagging; in the CSK time slot, the local PRN code generator generates M groups of code copies, each group including three code copy signals with phase leading, phase instantaneous, and phase lagging, where M is the CSK modulation order.

[0013] Furthermore, the specific method by which the adaptive Kalman filter dynamically adjusts its process noise covariance matrix includes: calculating the sample covariance estimate of the innovation sequence. And according to the formula Calculate the adaptive factor ,in For the observation matrix, Here is the state transition matrix. for k The posterior error covariance matrix at time -1 To observe the noise covariance matrix, The process noise covariance matrix; then using Adjust the noise covariance matrix during the process.

[0014] Furthermore, the sample covariance estimate of the novel sequence The formula is calculated using the window estimation method. ,in For the new information sequence, This refers to the window size.

[0015] Furthermore, the filter parameters of the third-order FLL in the loop filter are set as follows: , , ,in , The bandwidth of the FLL; the filter parameters of the fourth-order PLL are set to... , , , ,in , This refers to the bandwidth of the PLL.

[0016] Furthermore, the state vector of the adaptive Kalman filter includes carrier phase, carrier frequency, and carrier frequency change rate.

[0017] The beneficial effects of this invention are as follows: (1) Full-time slot continuous tracking of time-division navigation signals was achieved. By adopting targeted error identification methods in different modulation time slots and using adaptive Kalman filtering for signal preprocessing, the half-duty cycle working mode of the loop freezing update in the CSK time slot in the existing technology was changed, which significantly improved the effective update rate and convergence speed of the tracking loop.

[0018] (2) The introduced adaptive Kalman filter can adjust the filtering parameters in real time according to the dynamic stress and noise level of the signal. Combined with the subsequent high-order loop filter, it effectively suppresses the dynamic stress and noise interference caused by high acceleration and jerk, and reduces the risk of loss of lock.

[0019] (3) The adaptive Kalman filter provides a smoother and more accurate error state estimate by performing optimal estimation and noise suppression on the original error. The cascaded mechanism of the dual filter combines the advantages of optimal estimation and classical loop, making the loop output more stable, maximizing the power of the in-phase branch signal, and minimizing the power of the quadrature branch signal.

[0020] (4) This method effectively utilizes signal energy in the CSK time slot for loop updates and reduces correlator resource consumption through optimized design of the CSK local code copy, thus improving performance while taking into account implementation efficiency.

[0021] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a block diagram of the continuous tracking loop for time-division navigation signals in an embodiment of the present invention; Figure 2 This is a structural diagram of a third-order FLL-assisted fourth-order PLL loop filter in an embodiment of the present invention; Figure 3 This is a block diagram of the AKF-assisted enhanced carrier tracking loop in an embodiment of the present invention; Figure 4 This is a flowchart of the AKF-assisted filtering algorithm in an embodiment of the present invention; Figure 5 The IQ demodulation bit data diagram of time-division navigation signals using a traditional carrier tracking loop filter under high dynamic conditions; Figure 6 This is a diagram of IQ demodulated bit data of the time-division navigation signal under high dynamic conditions using an adaptive dual filtering algorithm in an embodiment of the present invention. Detailed Implementation

[0023] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0024] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0025] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present 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, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0026] I. Time-division navigation signal tracking: BPSK-CSK time-division navigation modulation signal refers to the signal generated during the transmission frame period. Within the system, BPSK direct-sequence spread spectrum (DSSS) signals and CSK signals are transmitted alternately in time slots using time-division multiplexing. Starting from time slot zero, even-numbered time slots transmit and receive BPSK modulated signals, while odd-numbered time slots transmit and receive CSK modulated signals. The time interval between the two transmissions is the transmission duration of a single time slot. The two signals use different pseudo-random noise (PRN) codes, but the code lengths are the same. With bit rate All are the same, single chip width With bit rate They are reciprocals of each other, that is Then the transmission duration of a single timeslot Thus, the entire transmission frame period is obtained. ,in The total number of time slots for transmitting the two modulated signals is [number]. One time slot. Continue defining the signal sampling frequency as... The number of sampling points in a single time slot is .

[0027] Traditional navigation signals are transmitted to the receiver after being modulated by a BPSK carrier. This BPSK signal is generated using direct sequence spread spectrum. (Navigation message data) Spreading code generated by pseudocode generator Modulation is performed using analog-to-digital (ADC) modulation to generate the baseband spread spectrum signal. Subsequently, BPSK carrier modulation was performed to obtain the radio frequency signal. CSK modulation belongs to the spread spectrum communication system. Its core principle is to use different cyclic shift states of a reference PRN code to represent different modulation symbols. For a code length of... PRN codes, theoretically exist There is only one cyclic shift state, therefore at most 323 cyclic shift states can be defined. A different CSK symbol. In CSK modulation, the reference PRN code is delayed by a code delayer. Perform a circular shift to generate A code sequence that is delayed on a chip Each code sequence corresponds to a unique CSK symbol. The delay between these symbols is fixed and equal, with the unit being the chip period. .

[0028] The analog intermediate frequency signal received by the receiver is defined as follows:

[0029]

[0030]

[0031] Where A is the carrier amplitude. It is a baseband spread spectrum signal. The received signal frequency is equal to the sum of the nominal intermediate frequency (IF) and the Doppler frequency. The initial phase of the carrier. It is additive white Gaussian noise. For BPSK time slot pseudocode sequences, This is a BPSK modulated navigation message data sequence. For the first A cyclic shift code sequence correspond A different CSK symbol, Represents the code length index, which is an integer and Then define , Indicates the first The cyclic shift amount of the code sequence corresponding to each CSK symbol. This represents a rectangular pulse used to generate pseudocode waveforms for BPSK and CSK time slots. Represents the time slot number, which is an integer and The analog intermediate frequency digital signal can then be converted into a digital intermediate frequency signal by analog-to-digital conversion.

[0032] The time-division tracking architecture is as follows: Figure 1As shown, it mainly consists of a carrier tracking loop and a code tracking loop, including carrier mixing and code correlation operations, carrier loop discriminator and code loop discriminator, carrier loop filter and code loop filter, carrier NCO and code NCO, etc. The tracking processes of BPSK modulated signals and CSK modulated signals in different time slots share the carrier loop filter and code loop filter, but the local code generator and carrier discriminator are different. The code loops in both time slots use a traditional second-order delay-locked loop (DLL). Unlike the pure PLL used in the carrier loop of traditional navigation tracking signals, this paper adopts a high-order FLL-assisted FLL, i.e., a third-order FLL-assisted PLL filter structure, to better cope with high dynamic environments. The specific third-order FLL-assisted fourth-order PLL loop filter is shown below. Figure 2 As shown, the specific derivation process of the filter parameters will not be detailed here. Based on empirical values, the filter parameters of a third-order FLL can be set as follows: , , , in This is the bandwidth of the FLL; the parameters of the fourth-order PLL filter can be obtained through empirical reasoning: , , , , ,in It refers to the bandwidth of the PLL.

[0033] The navigation tracking process is relatively fixed. This article first provides a clear introduction to the principle and process. For the received modulated signals in different time slots, the received digital intermediate frequency signals in different time slots after down-conversion and analog-to-digital conversion are first multiplied and mixed with the cosine and sine signals locally reproduced in different time slots generated by the carrier NCO. The purpose of this carrier tracking is to try to make the replicated carrier signal consistent with the received carrier intermediate frequency signal, thereby completely achieving carrier stripping through the mixing mechanism.

[0034] After carrier stripping, the I and Q data signals are correlated with local pseudo-random codes generated by the code NCO in different time slots: In the BPSK time slot, the code generator generates only three code replica signals with corresponding phase-leading, phase-instantaneous, and phase-lagging characteristics, with each of these three code replica signals differing by half a chip; correspondingly, in the CSK time slot, for the cyclic shift generated... Each CSK symbol corresponds to the code NCO. The code is grouped into replicas, each containing three code replica signals: one with leading phase, one with instantaneous phase, and one with lagging phase. The three replica signals in each group are also separated by a half-chip phase difference. That is, the correlators for the leading and lagging codes are spaced one chip apart. Therefore, the leading code replica signal of the current CSK symbol can be effectively shared with the lagging code replica signal of the previous CSK symbol. Consequently, the number of local CSK signals that the code NCO needs to reproduce is reduced to one-third of the original. Note that the code correlation operation within the BPSK time slot only uses the six correlators within the CSK time slot, i.e., three each for the I and Q branches. The purpose of this code correlation operation is to remove the pseudo-random code from the received signal by copying a pseudo-code with the same phase as the pseudo-random code in the received signal and then multiplying and correlating the received signal with the copied pseudo-code.

[0035] The I and Q correlation results from the instantaneous branch after carrier stripping and code stripping are input into the carrier loop discriminator to calculate the current carrier phase error and carrier frequency error. The I and Q correlation results from the lag and lead branches are input into the code loop discriminator to calculate the current code phase error. Within the BPSK time slot, the carrier discriminator uses a two-quadrant arctangent function, which exhibits good phase detection characteristics in both high and low SNR environments, and its phase detection slope is unaffected by signal amplitude. Based on the premise that the code phase error after signal acquisition is within ±0.5 chip lengths, the normalized incoherent lead-lag amplitude method is the optimal choice for the code discrimination function in this tracking process. That is, within this range, the normalized incoherent lead-lag amplitude discriminator can output the true code tracking error under noise-free conditions. This discriminator is preferred because its response is unaffected by signal amplitude fluctuations and it exhibits ideal linear characteristics within this linear region. Correspondingly, within the CSK time slot, demodulation uses the maximum correlation peak criterion, i.e., targeting... A cyclically shifted CSK signal, from From the real-time branch correlation results corresponding to each local codeword, the codeword corresponding to the maximum envelope value is selected as the final demodulated CSK symbol. Therefore, the following is calculated: The cyclic codeword index with the largest correlation value in each instantaneous branch can be used for subsequent carrier error identification and code error identification. Since CSK modulation carries information through cyclic shifts of PRN codes, its carrier phase itself does not carry symbol data, thus eliminating phase ambiguity caused by data jumps. This characteristic allows the receiver to directly use a four-quadrant arctangent phase detector with a large linear range and high accuracy to extract carrier phase errors within the CSK time slot. The code identification function within this time slot still uses the normalized incoherent lead-hysteresis amplitude method. Given that navigation bit flipping occurs within the BPSK time slot and no data bit stripping is performed, measures are taken to avoid introducing bit polarity abrupt changes. For phase-jump interference frequency estimation, this design only uses a phase discriminator to update the PLL in the BPSK time slot, without using a frequency discriminator. In contrast, the CSK time slot carries information through code shifting, and the phase continuity of the main correlation symbol is better, making it suitable as the input of the FLL. Therefore, a frequency discriminator of the cross-product-dot-product atan2 form is used in the CSK time slot to estimate the carrier frequency error using the correlation output of two adjacent CSK time slots, thereby updating the carrier frequency channel.

[0036] Based on the carrier (phase / frequency) error and code phase error detected in different time slots, a loop filter is used to optimize the estimation. To address the tracking requirements of time-division signals in high-dynamic environments, this paper needs to handle potential carrier phase jerk (i.e., the third derivative of phase with respect to time) variations. Steady-state performance analysis shows that the fourth-order phase-locked loop has zero steady-state error when tracking a cubic phase excitation. Therefore, this design uses a third-order FLL-assisted fourth-order PLL architecture as the core of carrier tracking to ensure tracking accuracy under high-dynamic conditions.

[0037] The filtered control signals drive the carrier NCO and code NCO respectively, dynamically adjusting the phase and frequency of the local reproducible signal, ultimately achieving continuous synchronization between the received signal and the local reference signal, and completing the closed-loop update and synchronization of the tracking loop status.

[0038] II. Adaptive Kalman filter-assisted carrier tracking loop: To improve the robustness and accuracy of time-division navigation signal carrier tracking in high-dynamic environments, this paper designs an enhanced carrier tracking architecture assisted by an adaptive Kalman filter (AKF) based on novel covariance estimation. This scheme introduces a pre-adaptive Kalman filter into the traditional third-order FLL-assisted fourth-order PLL framework, forming a cascaded dual-filtering processing mechanism. The specific carrier tracking loop of the auxiliary filter is as follows: Figure 3 As shown, the core idea is to introduce an adaptive factor to adjust the system noise covariance matrix of the AKF in real time according to the principle of orthogonalized innovation sequence, enabling it to adapt to changes in external signal dynamics and noise. This preprocesses and optimizes the original error output by the carrier discriminator. The error estimate after AKF pre-filtering is then fed into the subsequent FLL-assisted PLL loop filter to achieve final carrier phase and frequency tracking. This method combines the advantages of both types of filters: the AKF leverages its optimal estimation and dynamic noise suppression capabilities to effectively improve the input signal quality; while the subsequent FLL and PLL retain their simple structure and easy parameter tuning for engineering practicality. This combined strategy improves the tracking accuracy and anti-interference capability of the system in complex dynamic environments without changing the original loop structure.

[0039] Kalman Fischer (KF) is a recursive optimal estimation algorithm based on a state-space model. Its goal is to fuse system dynamics and observation data in the sense of minimum mean square error. The core of the algorithm is a prediction-update loop: in the prediction phase, the current state and its uncertainty (error covariance) are deduced from the previous state based on the system model; in the update phase, the predicted value and the new observation value are optimally combined by calculating the Kalman gain, correcting the state estimate and quantifying its accuracy, thereby achieving continuous and optimal tracking of the system state.

[0040] The state-process model of the system is defined as follows:

[0041] in, Is the system at any time The state vector; It is the system state transition matrix, which represents the state at the previous time step. Mapping to the prior state at the current moment ; It is the control input matrix, which controls the vector. Mapped to the state space; It is process noise, following a zero-mean Gaussian distribution with a covariance of... ,Right now

[0042] The system's observation equations (measurement model) are defined as follows:

[0043] in, At any moment The observation vector; It is the observation matrix, which combines the state vector Mapped to the observation space; It is observation noise, which follows a zero-mean Gaussian distribution with a covariance of . ,Right now .noise and They are independent of each other.

[0044] Prior state estimation is based on obtaining the observations at time k. Previously, for The prediction. Directly taking the expectation of the state equation (since the noise mean is zero, its expectation is zero): This is the KF state prediction formula.

[0045] Prior observations estimated as Calculated .

[0046] The error of the prior estimate is defined as the difference between the actual state and the prior estimate:

[0047] Prior error covariance matrix Defined as:

[0048] Will Expand:

[0049] Now substitute it In the definition:

[0050] Due to posterior error With future process noise They are independent of each other, so there are overlapping terms. .therefore:

[0051] The above formula is the covariance prediction formula for KF. After obtaining new observation values Then, the posterior estimate is obtained by linearly combining the prior estimate and the new observation information:

[0052] in, This is called residual or new information. It is the Kalman gain to be determined.

[0053] The goal is to find the optimal one. This minimizes the mean squared error of the posterior estimate, i.e., minimizes the posterior error covariance. The trace. (That is, the sum of the variances of the estimation errors of all state variables) The posterior error is:

[0054] Will The expression and the observation equation Substitute:

[0055] The posterior error covariance is:

[0056] Will Substituting the expression, we get:

[0057] Similarly, due to prior error With observation noise They are independent of each other, and the expected value of their interaction term is zero. Therefore:

[0058] Now, the goal is to find the solution. smallest This is a classic optimization problem, therefore... about Take the derivative and set it to zero. Using the properties of matrix differentials, we can derive:

[0059] Simplifying the above equation, we get:

[0060]

[0061] Therefore, the optimal Kalman gain is:

[0062] To obtain the optimal gain After that, you can The expression is greatly simplified. Substituting the expression into the original After algebraic operations (expanding and combining like terms), the formula can be simplified to a more concise form with less computational complexity.

[0063] This formula is the KF covariance update formula. It only holds true when the Kalman gain is optimal.

[0064] Summarizing the above derivation results, we obtain the recursive algorithm for Kalman filtering: Prediction steps (time update):

[0065]

[0066] Update steps (measurement update):

[0067]

[0068]

[0069] This recursive loop at each time step Execute once to provide the best estimate of the system.

[0070] The AKF-assisted filtering tracking algorithm proposed in this paper introduces a pre-adaptive Kalman filter into a cascaded dual-filtering processing mechanism based on the framework of a third-order FLL assisted by a fourth-order PLL. Its core enhancement lies in the introduction of an adaptive adjustment mechanism. This mechanism can adjust the system noise covariance matrix in real time according to the dynamic characteristics of the external input signal, based on the orthogonalization innovation sequence principle. This optimizes the Kalman gain. The calculation enables it to adapt to changes in external signal dynamics and noise, thereby preprocessing and optimizing the original error output of the carrier discriminator. The error estimate after AKF pre-filtering is then fed into the subsequent FLL-assisted PLL loop filter to achieve final carrier phase and frequency tracking.

[0071] The system noise covariance matrix Introducing an adaptive adjustment factor Afterwards, the original state prediction error covariance matrix It can be reformulated as:

[0072] In an ideal scenario where the system model is accurate, the innovation sequence of the Kalman filter should be a white noise sequence that obeys the orthogonality principle. This means that the sequence itself has zero mean, and the innovation values ​​at different times in the sequence are uncorrelated, i.e.:

[0073] in, The innovation sequence represents the difference between observed data from the real world and the predictions made by the filter based on its internal model. Conversely, if the innovation sequence exhibits autocorrelation, it indicates that the filter's system model has errors or has not reached convergence, thus violating the orthogonality principle. Therefore, this paper designs an adaptive mechanism based on this principle: by calculating the statistical properties of the innovation sequence, the adaptive factor is adjusted in real time, thereby correcting the system noise covariance and ultimately driving the innovation sequence to recover its white noise characteristics, ensuring that the filter converges to the optimal estimation state. According to existing literature, for the innovation sequence to conform to the orthogonality principle, it must satisfy... ,Will Substituting the formula, we get:

[0074] For the above equation to hold true, then: ,Right now Therefore, we get:

[0075] It can be seen that when the system has no modeling error, the actual innovation covariance should be equal to the theoretical innovation covariance predicted by the model state. Based on the above formula, the expression for the adaptive adjustment factor can be explicitly obtained as follows:

[0076] Due to adaptive factor The variable is a scalar, while the innovation covariance is a matrix. Forcing element-wise equality between the two generally yields no solution. Therefore, this paper no longer requires perfect matching of the matrices on every element. Instead, from an energy perspective, it only requires that the predicted innovation covariance and the actual sample innovation covariance be consistent in terms of the population variance. Thus, by taking the trace of both sides of the matrix equation, the adaptive factor is obtained. The solution formula is as follows:

[0077] Due to the actual new information covariance Calculating the expected value is difficult, so windowing estimation is generally used as a substitute for sample estimation.

[0078] Then, substituting these values ​​into the original formula for the adaptive adjustment factor, we can obtain:

[0079] To address the system model inaccuracy caused by navigation signals under high dynamic conditions, this paper adopts a strategy of increasing the adaptive factor. This strategy effectively compensates for model uncertainty by reducing the weight of system predictions and correspondingly increasing the confidence in real-time measurements. To avoid excessive deviation from the optimal estimate, this factor must adhere to a value constraint of not less than 1 during its design, thus achieving a balance between suppressing model error and maintaining estimation stability. Therefore, the value of the adaptive factor should be:

[0080] The above summarizes the pre-filtering process for carrier tracking using AKF. This design aims to fully leverage AKF's powerful signal estimation and noise suppression capabilities to improve the overall tracking system performance. Combined with the subsequent loop filter of the FLL-assisted PLL, the signal after two stages of fine processing is used as the control variable for the carrier NCO. By precisely controlling the NCO, the frequency and phase of the local carrier are adjusted in real time, ultimately maintaining tracking synchronization with the received signal. The overall carrier tracking algorithm flowchart is shown below. Figure 4 As shown.

[0081] The high dynamic adaptability of the algorithm in a high dynamic environment was evaluated by simulation compared with that of the traditional carrier tracking algorithm. The simulation parameters for the high dynamic environment are shown in Table 1.

[0082] Table 1

[0083] Figure 5 and Figure 6 Comparing the tracking IQ demodulation data results of the traditional carrier tracking loop using a second-order FLL assisted by a third-order PLL and the proposed adaptive dual filtering method under high dynamic environments, it can be seen that when the tracking loop locks onto the signal, the difference between the carrier and code phases fluctuates almost to zero. At this point, the in-phase branch signal contains only the data signal and some noise, while the quadrature branch signal is essentially just noise. The demodulation data results show that, under high dynamic environments, the adaptive dual filtering method achieves better tracking performance than the traditional loop filter. It can maintain the power of the in-phase branch output signal near its maximum value through the loop's feedback adjustment mechanism during stable tracking, while simultaneously keeping the power of the quadrature branch output signal fluctuating around zero.

[0084] In this invention, we propose a novel carrier tracking algorithm for time-division navigation systems. This method employs a third-order FLL-assisted fourth-order PLL framework, introducing an AKF (Advanced Akine Filter) with pre-processed information covariance estimation, forming a cascaded dual-filtering processing mechanism. This optimized approach effectively combines the advantages of the AKF in signal estimation and noise suppression with the signal stabilization capabilities of the loop filter. This combined strategy, without altering the original loop structure, improves the continuous tracking accuracy and anti-interference capability of the time-division navigation system in highly dynamic environments.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method of high dynamic time-of-flight navigation signal tracking with adaptive Kalman filter assistance, characterized in that: The method comprises the following steps: S1, carrier and code stripping step: mixing the received time-division digital intermediate frequency signal with a local carrier generated by a local numerically controlled oscillator (NCO) to complete carrier stripping and obtain I and Q baseband signals; and performing correlation operation on the I and Q baseband signals and a local pseudo-random noise (PRN) code generated by a local PRN code generator to complete code stripping; S2, error discrimination step: in a binary phase shift keying (BPSK) time slot, calculating a carrier phase error by using an instant branch correlation result, and calculating a code phase error by using a leading branch and a lagging branch correlation result; in a code shift keying (CSK) time slot, adopting a maximum correlation peak criterion to determine a current CSK symbol, and calculating a carrier phase error by using an instant branch correlation result corresponding to the symbol, and calculating a code phase error by using a leading branch and a lagging branch correlation result corresponding to a symbol before and after the symbol by half a chip; S3, adaptive Kalman filter (AKF) preprocessing step: taking the carrier phase error and a frequency error obtained in S2 as observation values, and inputting the observation values into an adaptive Kalman filter for preprocessing; the adaptive Kalman filter dynamically adjusts a process noise covariance matrix by estimating statistical characteristics of a new sequence in real time, and outputs an error state estimation quantity after optimal estimation and noise suppression; S4, loop filtering and tracking step: sending the error state estimation quantity after preprocessing in S3 to a loop filter in a later stage for smoothing and prediction; the loop filter adopts a structure of a third-order frequency lock loop (FLL) assisting a fourth-order phase lock loop (PLL); a control signal after loop filter processing drives a carrier NCO and a code NCO respectively, adjusts the frequency and phase of a local reproduced carrier and the phase of a local PRN code, and completes closed-loop tracking.

2. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: The time-division digital intermediate frequency signal is a BPSK-CSK time-division multiplexing signal, wherein in a sending frame period BPSK direct spread signals and CSK signals are sent in a time slot alternation manner, starting from a zero time slot, even time slots send BPSK modulated signals, and odd time slots send CSK modulated signals.

3. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: In the error discrimination step, in a BPSK time slot, a carrier phase error is calculated by using a two-quadrant inverse tangent discriminator; and in a CSK time slot, the carrier phase error is calculated by using a four-quadrant inverse tangent discriminator.

4. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: In the error discrimination step, a code phase error is calculated by using a normalized non-coherent leading minus lagging amplitude discriminator in a BPSK time slot and a CSK time slot.

5. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: In the code stripping step, in a BPSK time slot, a local PRN code generator generates three code replica signals of a phase leading, a phase instant and a phase lagging; and in a CSK time slot, the local PRN code generator generates M groups of code replicas, each group including three code replica signals of a phase leading, a phase instant and a phase lagging, wherein M is a CSK modulation order.

6. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: The specific method by which the adaptive Kalman filter dynamically adjusts its process noise covariance matrix includes: calculating the sample covariance estimate of the innovation sequence. And according to the formula Calculate the adaptive factor ,in For the observation matrix, Here is the state transition matrix. for k The posterior error covariance matrix at time -1 To observe the noise covariance matrix, The process noise covariance matrix; then using Adjust the noise covariance matrix during the process.

7. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 6, characterized in that: sample covariance estimate of the innovation sequence The windowing estimation method is calculated by the formula where is the innovation sequence, is the window size.

8. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: The filter parameter setting of the third order FLL in the loop filter is , , where , is the bandwidth of the FLL. The filter parameter setting of the fourth order PLL is , , , where , is the bandwidth of the PLL.

9. The adaptive Kalman filter assisted high dynamic time -of-flight navigation signal tracking method according to claim 1, characterized in that: The state vector of the adaptive Kalman filter comprises a carrier phase, a carrier frequency and a carrier frequency change rate.

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