A fuzzy LQG clock fast taming method for real-time precise timing receiver

Abstract

The application discloses a fuzzy LQG clock fast taming method for real-time precise timing receivers, and relates to the technical field of GNSS precise timing. The method comprises the following steps: establishing a two-state clock difference model of a local oscillator relative to a reference time scale, estimating phase and frequency deviations by a Kalman filter, and generating a frequency adjustment amount based on a steady-state LQG control law; introducing a scheduling coefficient on the basis of the steady-state LQG reference, and improving the synchronization speed after starting, restarting or disturbance by fuzzy control. Different from empirical parameter setting, the application explores the explicit relationship between the scheduling coefficient and the capture bandwidth, determines the maximum allowed scheduling coefficient according to the physical properties of the actuator and the controlled oscillator, and projects the scheduling coefficient into a finite-dimensional fuzzy rule table. When the error enters a small error region, the controller automatically reverts to the steady-state LQG, and the steady-state performance remains unchanged. The method improves the convergence speed of the timing receiver without changing the original steady-state design, and enhances the deployment capability.

Description

Technical Field

[0001] This invention relates to the field of GNSS precision timing technology, and in particular to a method for fast discipline of fuzzy LQG clocks for real-time precision timing receivers. Background Technology

[0002] Time and frequency are fundamental physical quantities widely used in the International System of Units (SI) and require extremely high precision. GNSS real-time precision time receivers typically utilize external satellite precise clock bias, precise orbit, and observation data to estimate the phase deviation of the local receiver clock relative to a reference time scale. By controlling the frequency control terminal of the local crystal oscillator or atomic clock, the receiver's output 1PPS signal and frequency signal are made to follow the reference time scale over a long period of time.

[0003] Among existing clock discipline methods, linear quadratic Gaussian control (LQG control) is widely used because it can simultaneously handle state estimation and optimal feedback control problems. A typical LQG discipline method in a precision time receiver follows this process: First, the phase and frequency deviations of the local clock are estimated using a Kalman filter. Then, the frequency adjustment is calculated based on the estimated state using an LQR control law. Finally, the local crystal oscillator frequency is adjusted via a digital-to-analog converter (DAC).

[0004] In typical designs, LQG controllers achieve good frequency stability, but their control gain is fixed. When the receiver experiences power-on, restart, loss-of-lock recovery, or significant timing disturbances, the convergence speed of a fixed LQG controller is constrained by the steady-state design, making it difficult to balance fast acquisition with steady-state stability. Furthermore, existing parameters often rely on empirical tuning, requiring numerous repeated experiments to select suitable parameters and making it difficult to guarantee the optimality of the chosen parameters. Summary of the Invention

[0005] The purpose of this invention is to provide a fast discipline method for fuzzy LQG clocks for real-time precision timing receivers, aiming to solve or improve at least one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following solution: A fast discipline method for fuzzy LQG clocks in a real-time precision timing receiver includes: A two-state clock difference model of the local oscillator relative to a reference time scale is established, wherein the two states include phase deviation and frequency deviation; The current phase and frequency deviations are estimated using a Kalman filter based on real-time precise timing phase observations, and the current estimated state is generated. ; Determine the maximum scheduling coefficient based on the actuator's maximum linear control capability. and in the maximum scheduling coefficient Generate continuous scheduling law within range The continuous scheduling law Used to characterize the current state error and the required scheduling coefficient β The mapping relationship; The continuous scheduling law Offline projection is a fuzzy rule table; during online runtime, the current estimated state is calculated using the Kalman filter. After normalization, the fuzzy rule table is input for lookup and fuzzy inference to obtain the first... k The current scheduling coefficient of each epoch. β k ; Based on the current scheduling coefficient β k Solve the corresponding Riccati equation to obtain the feedback gain and calculate the frequency adjustment. ;in For the first k Feedback gain for each epoch; The calculated frequency adjustment is applied to the frequency control terminal of the local oscillator via a digital-to-analog converter to tame the local clock signal. When the state estimation error enters the set small error region and continues for a set number of epochs, the LQG controller is allowed to return to the steady-state LQG reference controller. To maintain steady-state performance unchanged.

[0007] Optionally, the discrete state equation and observation equation of the two-state clock difference model are respectively: In the formula, For the first k +1 epoch state vector, For the first k The state vector of each epoch. This is the frequency adjustment amount applied to the crystal oscillator frequency control terminal. For process noise, The phase observations are obtained through real-time precise timing calculations. To observe the noise, Here is the state transition matrix. For the control matrix, The observation matrix; in: In the formula, To control the sampling interval.

[0008] Optionally, the scheduling coefficient βBy changing the state weight matrix The phase state weights are used to adjust the closed-loop bandwidth. The closed-loop bandwidth With scheduling coefficient β Increases and increases, and the scheduling coefficient β Used to capture bandwidth; Wherein, the state weight matrix The expression is: In the formula, The steady-state phase frequency weighting ratio, These are the steady-state weighting coefficients.

[0009] Optionally, the scheduling coefficient β Maximum allowed value Determined by the physical constraints of the actuator, including the following steps: Determine the maximum allowable linear frequency adjustment of the actuator based on its tuning range, control voltage range, or frequency control word range. ; Based on the initial maximum state error range of the local oscillator, calculate the worst-case output of the closed-loop control under the current scheduling coefficients. ; In satisfying ≤ Under the constraints, take .

[0010] Optionally, the fuzzy rule table is generated as follows: Based on the acquisition speed requirements, the error in the current state... x Next, select the option that enables the capture time. Meets preset requirements The minimum scheduling coefficient generates a continuous scheduling law. , represented as: The continuous scheduling law After input normalization and triangular membership function fuzzification, the offline projection is an M×M fuzzy rule table R; the fuzzy rule table R is used for online operation to obtain the current scheduling coefficients based on Kalman estimated state lookup table reasoning. β k .

[0011] Optionally, the maximum phase deviation and maximum frequency deviation used for input normalization are calculated from the frequency accuracy, temperature stability, aging rate, preheating characteristics and control range indicators of the local oscillator.

[0012] Optionally, the step of causing the LQG controller to fall back to the steady-state LQG reference controller... The determination criteria are: Calculate the weighted norm of the normalized phase error and frequency error. When the weighted norm is less than a preset small error threshold and continuously exceeds a preset epoch, a backoff is triggered. After the backoff, the current scheduling coefficient... β k It is always equal to 1, and the feedback gain is fixed at the steady-state reference gain. It no longer schedules according to state changes, thus maintaining steady-state frequency stability consistent with the reference LQG design.

[0013] Optionally, the feedback gain is calculated and applied in the following way: For each candidate scheduling coefficient β The corresponding discrete algebraic Riccati equation is solved offline to obtain the feedback gain K( and closed-loop matrix And store it as a lookup table; Wherein, the closed-loop matrix Represented as: In the formula, Here is the state transition matrix. For control matrix; During online operation, the current scheduling coefficients are obtained based on the fuzzy inference. β k Obtain the corresponding feedback gain Then compare it with the current estimated state. Multiply to obtain the frequency adjustment amount and the frequency adjustment amount After passing through a digital-to-analog converter, it is applied to the voltage control terminal or frequency control word input terminal of the local oscillator.

[0014] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a fast fuzzy LQG clock discipline method for real-time precision timing receivers. The method includes establishing a two-state clock difference model of the local oscillator relative to a reference time scale, estimating the phase and frequency deviations using a Kalman filter, and generating a frequency adjustment based on a steady-state LQG control law. A scheduling coefficient is introduced above the steady-state LQG reference, and fuzzy control is used to improve the synchronization speed after power-on, restart, or disturbance. Unlike empirical parameter tuning, this invention explores the explicit relationship between the scheduling coefficient and the acquisition bandwidth, determining the maximum allowable scheduling coefficient based on the physical properties of the actuator and the controlled oscillator, and projecting the scheduling coefficient into a finite-dimensional fuzzy rule table. When the error enters the small error region, the controller automatically reverts to the steady-state LQG, maintaining stable steady-state performance. This method improves the convergence speed of the timing receiver and enhances its rapid deployment capability without changing the original steady-state design. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is an overall architecture diagram of the fuzzy LQG clock fast discipline method for real-time precision timing receivers according to the present invention; Figure 2 This is a schematic diagram of the maximum scheduling coefficient under actuator constraints in this embodiment; Figure 3 This is a schematic diagram illustrating the confirmation of the maximum scheduling coefficient under actuator constraints in this embodiment. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] The purpose of this invention is to provide a fast discipline method for fuzzy LQG clocks for real-time precision timing receivers, aiming to solve or improve at least one of the above-mentioned technical problems.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] like Figures 1-3As shown, this invention provides a fast disciplining method for fuzzy LQG clocks in real-time precision timing receivers, by introducing a scheduling coefficient based on fixed parameter LQG. The method employs online scheduling of state weights to accelerate convergence. It incorporates two core innovations: 1. Physical interpretability of parameter variations, i.e. 1. The mapping gives a clear physical meaning to the capture bandwidth; 2. The combination of fuzzy control and LQG control law, that is, the continuous capture scheduling law constrained by the actuator. The projection is a finite-dimensional fuzzy rule table with online inference, and it automatically backs down to the steady-state LQG after the error enters the small error region. This method thus significantly improves the synchronization speed of the receiver after power-on, restart, or disturbance while maintaining steady-state performance.

[0021] The overall architecture of the technical solution adopted in this invention is as follows: Figure 1 As shown in the diagram, the GNSS radio frequency front-end and baseband processing module acquires and tracks satellite signals and outputs observations; the real-time precise time synchronization (RT-PPT) calculation module outputs phase observations accordingly. The Kalman filter uses this to estimate the phase and frequency deviations of the local oscillator. The fuzzy scheduler looks up the normalized error in a table and infers the result to output the scheduling coefficients. The Riccati / LQG controller determines the feedback gain accordingly. And calculate the control quantity The control signal is converted into an analog-to-digital converter and then applied to a local oscillator (OCXO or crystal oscillator) via an actuator, ultimately outputting a 10 MHz and 1 PPS signal that continuously follows the reference time scale. Figure 1 The offline actuator constraint module on the right provides parameter support for online fuzzy clock discipline based on the initial maximum state error of the crystal oscillator and the physical constraints of the actuator.

[0022] Specifically, this invention starts from steady-state LQG design and constructs a schedulable LQG controller parameter set. The maximum startup state error is determined based on the crystal oscillator parameters, and the maximum scheduling coefficient is determined based on the maximum realizable control quantity of the actuator. Generate a continuous scheduling law based on the capture speed requirements. ;Will Projection as The invention employs a fuzzy rule table; online fuzzy scheduling LQG control is performed based on the Kalman-estimated state; and a steady-state LQG controller is restored after entering the small error region. The invention is described in detail below with reference to the system model and method flow. A schematic diagram of the normalized error projection onto the fuzzy rule table is shown below. Figure 3 As shown, Figure 3 Part (a) represents the normalized error and the capture and scheduling coefficients. The mapping relationship, Figure 3 Part (b) is the 5×5 fuzzy rule table R obtained by projection.

[0023] First, define the foundation of the model: The state of the local oscillator relative to the reference time scale is defined as a two-state vector consisting of phase deviation and frequency deviation: in For the first Phase or time deviation of each epoch For the first Frequency deviation of each epoch, This is the frequency adjustment amount applied to the crystal oscillator frequency control terminal. This is the phase observation obtained through real-time precise timing calculation. Its discrete state equation and observation equation are as follows: The state transition matrix, control matrix, and observation matrix are as follows: In the formula To control the sampling interval, For process noise, To mitigate observation noise, a Kalman filter is used to estimate the state based on precise timing observations. in To estimate the phase deviation, To estimate the frequency deviation, this estimated state serves as the input for subsequent LQG control and fuzzy scheduling. The LQR control law is: Feedback gain It is obtained from the discrete algebraic Riccati equation. The phase deviation feedback gain is used to characterize the estimated phase deviation. Adjustment amount The intensity of action, This is the frequency deviation feedback gain, used to characterize the estimated frequency deviation. right Intensity of influence; state weight matrix With control weight matrix They are respectively: in This represents the weighting ratio of the phase state to the frequency state. Represents the state weight coefficient. This indicates the cost of control.

[0024] Second, perform physical processing of the scheduling coefficients: This invention consists of a steady-state LQG reference controller (corresponding to...) Starting from =1), introduce the scheduling coefficient. ≥1, construct a set of schedulable LQG controllers with different capture strengths. The scheduled state weight matrix will then assign phase state weights according to... Scaling is defined as: For each candidate scheduling coefficient Solving the discrete algebraic Riccati equation yields the corresponding feedback gain K( ), and obtain the corresponding closed-loop matrix: Scheduling coefficient By changing the state weight matrix, the feedback gain and the closed-loop matrix can be altered. The location of the eigenvalues ​​ultimately changes the equivalent closed-loop bandwidth. ,in, Represents scheduling coefficient The corresponding closed-loop bandwidth of the capture phase. Discrete closed-loop eigenvalues. Mapping to equivalent poles in the continuous domain: The natural frequency, damping ratio, and closed-loop bandwidth are calculated based on the equivalent continuous closed-loop poles. For a second-order approximation clock-disciplined system, the closed-loop response can also be expressed in a second-order low-pass form: in: The corresponding closed-loop bandwidth can then be calculated using the following formula: In the formula, is the equivalent damping coefficient of the closed-loop system, used to characterize the damping effect of frequency deviation feedback on the closed-loop dynamic process. For the complex frequency variable in the Laplace transform, It is the equivalent phase recovery coefficient of the closed-loop system, used to characterize the effect of phase deviation feedback on the phase recovery speed.

[0025] Therefore, the scheduling coefficient It is given a clear physical meaning, that is, its essence is the closed-loop bandwidth of the capture phase. Scheduling: The larger the value, the larger the capture bandwidth, and the faster the phase error correction; when the error enters the small error region, let... =1, the closed-loop bandwidth is restored to the steady-state reference bandwidth, thus ensuring that the steady-state performance is consistent with the reference LQG.

[0026] Third, the scheduling upper limit is determined by the physical constraints of the actuator: The actuator described in this invention includes, but is not limited to, a crystal oscillator frequency control terminal, a voltage control terminal, a digital-to-analog converter output terminal, a digital frequency control word output terminal, and an internal frequency adjustment module for the receiver. Let the maximum allowable linear frequency adjustment amount of the actuator be... Its value can be determined by the tuning range, control voltage range, center control voltage, frequency pull sensitivity, and digital-to-analog converter output range specified in the crystal oscillator manual; for example, by the control voltage range and center control voltage. With tuning sensitivity Conversion: In the formula, For maximum voltage, This is the minimum voltage.

[0027] For any initial state within the receiver's maximum startup error range, the scheduling coefficient The corresponding worst-case closed-loop control output is defined as: In the formula, This is the set of initial states that may occur during receiver startup, restart, or disturbance recovery, determined by the maximum allowable phase deviation and maximum frequency deviation. The finite prediction time domain length used to evaluate the closed-loop transient control output is represented by the number of control epochs; To predict the epoch index, take . It should cover the expected capture or transient adjustment process, so that the closed-loop state has decayed to below the preset threshold at the end of the prediction time domain.

[0028] Under the constraint that the worst-case control output does not exceed the linear capability of the actuator, the maximum permissible scheduling coefficient is defined as: In the formula, This represents the worst-case output of the closed-loop control. This represents the maximum allowable linear frequency adjustment of the actuator.

[0029] Therefore, the scheduling limit It has a clear hardware source, determined by back-calculation of the actuator's maximum linear capability, rather than relying on empirical scanning or simulation parameter tuning; within this upper limit, a finite number of capture bandwidth / scheduling coefficient levels can be generated for use in fuzzy rule tables.

[0030] Fourth, fuzzification and steady-state locking of scheduling laws: Actuator constraints only limit the maximum available range of scheduling coefficients and do not directly determine the scheduling intensity to be used under different error states. Therefore, this invention generates a continuous acquisition bandwidth scheduling law within the actuator's allowable range based on acquisition speed requirements, and selects the minimum scheduling coefficient that satisfies the acquisition time requirement for the current phase and frequency deviation. To reduce real-time computation and facilitate embedded implementation, this invention uses a continuous scheduling law. After input normalization and triangular membership function fuzzification, the offline projection is an M×M fuzzy rule table R; online, the target acquisition bandwidth and online scheduling coefficient under the current state error are obtained by looking up the table based on the Kalman estimated state. Based on this, the feedback gain is obtained by solving the Riccati equation. Finally, the frequency adjustment amount is calculated: When the normalization error enters the small error region and continues for a given epoch, the controller automatically... Locked to steady-state LQG reference controller This allows for a balance between rapid acquisition and steady-state performance without altering the original steady-state design.

[0031] In summary, the present invention has the following beneficial effects: 1. The scheduling upper limit has a physical source. This invention determines the maximum allowable scheduling coefficient by utilizing the maximum linear control capability of actuators such as crystal oscillators and digital-to-analog converters. This avoids relying solely on empirical scanning or simulation parameter tuning.

[0032] 2. The normalization scale has a hardware basis. The maximum phase deviation and maximum frequency deviation are calculated from the frequency accuracy, temperature stability, aging rate, preheating characteristics and control range in the crystal oscillator manual, so that the fuzzy input normalization has a clear physical scale.

[0033] 3. The fuzzy rules are not based on manual experience tables. This invention first generates a continuous capture scheduling law constrained by the actuator. Then, it is projected into a fuzzy rule table, so the rule table is a finite-dimensional approximation of the LQG capture scheduling law constrained by the executor.

[0034] 4. Balancing fast acquisition and steady-state performance. A larger scheduling coefficient is used during periods of large errors to improve synchronization speed; during periods of small errors, it automatically reverts to the steady-state LQG controller. This maintains the original stability of the steady-state LQG without altering the original steady-state design.

[0035] 5. Easy to implement in engineering and highly versatile. Riccati gain can be solved offline and implemented by looking up tables. Online implementation only requires Kalman filtering, fuzzy inference, and matrix multiplication, making it suitable for embedded GNSS timing receivers. It is also applicable to various local oscillators such as ordinary crystal oscillators, OCXOs, TCXOs, and rubidium clocks. As long as the maximum initial state error, control range, or aging index is provided, the state error and actuator-limited scheduling upper limit can be constructed accordingly.

[0036] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0037] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver, characterized in that, include: A two-state clock difference model of the local oscillator relative to a reference time scale is established, wherein the two states include phase deviation and frequency deviation; The current phase and frequency deviations are estimated using a Kalman filter based on real-time precise timing phase observations, and the current estimated state is generated. ; Determine the maximum scheduling coefficient based on the actuator's maximum linear control capability. and in the maximum scheduling coefficient Generate continuous scheduling law within range The continuous scheduling law Used to characterize the current state error and the required scheduling coefficient β The mapping relationship; The continuous scheduling law Offline projection is a fuzzy rule table; during online runtime, the current estimated state is calculated using the Kalman filter. After normalization, the fuzzy rule table is input for lookup and fuzzy inference to obtain the first... k The current scheduling coefficient of each epoch. β k ; Based on the current scheduling coefficient β k Solve the corresponding Riccati equation to obtain the feedback gain and calculate the frequency adjustment. ;in For the first k Feedback gain for each epoch; The calculated frequency adjustment is applied to the frequency control terminal of the local oscillator via a digital-to-analog converter to tame the local clock signal. When the state estimation error enters the set small error region and continues for a set number of epochs, the LQG controller is allowed to return to the steady-state LQG reference controller. To maintain steady-state performance unchanged.

2. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 1, characterized in that, The discrete state equations and observation equations of the two-state clock difference model are as follows: In the formula, For the first k +1 epoch state vector, For the first k The state vector of each epoch. This is the frequency adjustment amount applied to the crystal oscillator frequency control terminal. For process noise, The phase observations are obtained through real-time precise timing calculations. To observe the noise, Here is the state transition matrix. For the control matrix, The observation matrix; in: In the formula, To control the sampling interval.

3. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 1, characterized in that, The scheduling coefficient β By changing the state weight matrix The phase state weights are used to adjust the closed-loop bandwidth. The closed-loop bandwidth With scheduling coefficient β Increases and increases, and the scheduling coefficient β Used to capture bandwidth; Wherein, the state weight matrix The expression is: In the formula, The steady-state phase frequency weighting ratio, These are the steady-state weighting coefficients.

4. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 1, characterized in that, The scheduling coefficient β Maximum allowed value Determined by the physical constraints of the actuator, including the following steps: Determine the maximum allowable linear frequency adjustment of the actuator based on its tuning range, control voltage range, or frequency control word range. ; Based on the initial maximum state error range of the local oscillator, calculate the worst-case output of the closed-loop control under the current scheduling coefficients. ; In satisfying ≤ Under the constraints, take .

5. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 1, characterized in that, The fuzzy rule table is generated as follows: Based on the acquisition speed requirements, the error in the current state... x Next, select the option that enables the capture time. Meets preset requirements The minimum scheduling coefficient generates a continuous scheduling law. , represented as: The continuous scheduling law After input normalization and triangular membership function fuzzification, the offline projection is an M×M fuzzy rule table R; the fuzzy rule table R is used for online operation to obtain the current scheduling coefficients based on Kalman estimated state lookup table reasoning. β k .

6. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 5, characterized in that, The maximum phase deviation and maximum frequency deviation used for input normalization are calculated from the frequency accuracy, temperature stability, aging rate, preheating characteristics and control range indicators of the local oscillator.

7. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 1, characterized in that, The LQG controller is then returned to a steady-state LQG reference controller. The determination criteria are: Calculate the weighted norm of the normalized phase error and frequency error. When the weighted norm is less than a preset small error threshold and continuously exceeds a preset epoch, a backoff is triggered. After the backoff, the current scheduling coefficient... β k It is always equal to 1, and the feedback gain is fixed at the steady-state reference gain. It no longer schedules according to state changes, thus maintaining steady-state frequency stability consistent with the reference LQG design.

8. The method for fast discipline of a fuzzy LQG clock for a real-time precision timing receiver according to claim 1, characterized in that, The method for solving and applying the feedback gain is as follows: For each candidate scheduling coefficient β The corresponding discrete algebraic Riccati equation is solved offline to obtain the feedback gain K( and closed-loop matrix And store it as a lookup table; Wherein, the closed-loop matrix Represented as: In the formula, Here is the state transition matrix. For control matrix; During online operation, the current scheduling coefficients are obtained based on the fuzzy inference. β k Obtain the corresponding feedback gain Then compare it with the current estimated state. Multiply to obtain the frequency adjustment amount and the frequency adjustment amount After passing through a digital-to-analog converter, it is applied to the voltage control terminal or frequency control word input terminal of the local oscillator.

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