Satellite navigation and timing method and device based on current model Kalman filter
By using a Kalman filter-based approach based on the current model, the problems of unsmooth and inaccurate receiver clock bias in one-way time synchronization methods are solved, thereby improving the timing accuracy and time correction accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING INST OF REMOTE SENSING EQUIP
- Filing Date
- 2022-09-20
- Publication Date
- 2026-07-07
AI Technical Summary
In the one-way time synchronization method, the receiver clock error obtained by solving the pseudorange observation equation is not smooth or accurate enough, resulting in low time synchronization accuracy and obvious clock jitter.
The method based on the current model Kalman filtering is adopted. By establishing the pseudorange observation equation, the prediction and correction process of the Kalman filtering state equation is carried out, the receiver clock error is solved, and the local time of the user receiver is corrected.
It improves time synchronization accuracy, reduces system time error, and achieves higher time correction accuracy.
Smart Images
Figure CN115616623B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of satellite navigation and timing technology, and in particular to a satellite navigation and timing method and apparatus based on the current model Kalman filter. Background Technology
[0002] Global Navigation Satellite Systems (GNSS) have become the most important timing tool due to their wide coverage, openness, and ability to serve mobile users. Satellite navigation timing methods can be divided into common-view methods and one-way timing methods. One-way timing methods receive GNSS satellite signals, process the measurements to accurately determine the deviation of the user's clock from the system time, and thus output a standard time that can be used for timing. Due to the influence of antenna position errors, ionospheric delay errors, and ephemeris errors, the timing accuracy of one-way timing methods is relatively worse than that of common-view methods. However, it does not require the transmission of uplink time comparison information, giving it irreplaceable advantages in saving terminal power, extending battery life, and reducing terminal size.
[0003] One-way time synchronization method corrects the user receiver's local time t u To obtain the Harmony of the World UTC The calculation formula is as follows:
[0004] t UTC =t u -δt u -δt UTC
[0005] Where t UTC Indicates Coordinated Universal Time; t u Indicates the local time of the user receiver; δt u =t u -t sys δt represents the offset of the user receiver's local time relative to the system time, i.e., the user receiver clock bias; UTC =t sys -t UTC t represents the offset of the system time relative to Coordinated Universal Time; sys Indicates the system time.
[0006] The offset of system time relative to Coordinated Universal Time δt UTC The calculation formula is as follows:
[0007] δt UTC =Δt LS +A0+A1(t sys -t OU )
[0008] Where Δt LSThe system time represents the integer second difference between the system time and Coordinated Universal Time; A0 and A1 represent two coefficients for calculating the intrasecond deviation between the system time and Coordinated Universal Time; t OU The reference time indicating Coordinated Universal Time.
[0009] User receiver clock bias δt u Solving this problem requires the following pseudorange observation equation:
[0010]
[0011] The superscript (n) indicates the nth visible satellite; ρ (n) Represents pseudorange observation; r (n) The distance between the satellite and the receiver is represented by δt; c represents the speed of light in a vacuum; δt represents the geometric distance between the satellite and the receiver. (n) Indicates satellite clock bias; I (n) Indicates ionospheric delay; T (n) Indicates tropospheric delay; This indicates pseudorange observation noise.
[0012] Depending on whether the user's receiver location is known, the receiver clock bias δt u The solution can be divided into the following two cases.
[0013] In the first scenario, the user receiver is stationary and the antenna position is known. In this case, the geometric distance r between the satellite and the receiver is... (n) Given a known quantity, the pseudorange observation equation only includes the receiver clock bias δt. u This is the only unknown. Therefore, the receiver can solve for the receiver clock error δt by tracking a single visible satellite and establishing a single pseudorange observation equation. u .
[0014] In the second scenario, the location of the user's receiver is unknown. In this case, the geometric distance r between the satellite and the receiver is... (n) The unknowns are the receiver's three-dimensional position coordinates and the receiver clock error δt in the pseudorange observation equation. u There are a total of 4 unknowns. Therefore, the receiver needs to track 4 or more visible satellites, obtain 4 or more pseudorange observation equations, solve them simultaneously, and then use the least squares method to solve for the receiver clock error δt. u .
[0015] The essence of one-way time synchronization is to use system time to calibrate the user receiver's local time. Because the function of the GNSS ground monitoring section includes keeping the system time synchronized with Coordinated Universal Time, the time obtained from satellite navigation timing has high long-term accuracy.
[0016] Although the aforementioned one-way time synchronization method is widely used in engineering, the receiver clock error δt at different times obtained by solving the pseudorange observation equation is still a significant issue.u Without mutual correlation or constraint, these parameters are easily affected by pseudorange observation noise, resulting in a coarse, messy, and less smooth and accurate signal. Therefore, the receiver clock error δt obtained from solving the pseudorange observation equation is directly used. u To correct the user receiver's local time t u The obtained system time t sys The large error results in the aforementioned one-way time synchronization method having problems such as low time synchronization accuracy and significant clock jitter. Summary of the Invention
[0017] (a) Technical problems to be solved
[0018] The purpose of this invention is to propose a high-precision satellite navigation timing method based on the current model Kalman filtering, in order to solve the technical problem that the receiver clock error obtained by solving the pseudorange observation equation is not smooth and accurate enough, which leads to the large error and low timing accuracy of the system time obtained by directly using the receiver clock error obtained by solving the pseudorange observation equation to correct the local time of the user receiver.
[0019] (II) Technical Solution
[0020] To address the aforementioned technical problems, this invention proposes a high-precision satellite navigation timing method based on the current model Kalman filtering, comprising the following steps:
[0021] Step 1: Establish the pseudorange observation equation and solve for the user receiver clock error;
[0022] Step 2.1: Establish the state equation based on the current model Kalman filter according to the user receiver clock error, and solve for the prior estimate of the current epoch state vector;
[0023] Step 2.2: Calculate the posterior estimate of the current epoch state vector based on the prior estimate of the current epoch state vector.
[0024] Step 2.3: Determine the filtered receiver clock error based on the posterior estimate of the current epoch state vector;
[0025] Step 3: Correct the local time of the user receiver using the filtered receiver clock error to obtain the system time.
[0026] Step 1: Using pseudorange observed by the user receiver and information such as the position of visible satellites obtained from the navigation message, establish the pseudorange observation equation and calculate the clock error of the user receiver.
[0027] The pseudorange observation equation for the k-th epoch is as follows:
[0028]
[0029] The superscript (n) indicates the nth visible satellite; Indicates pseudodistance observations; The distance between the satellite and the receiver is represented by δt; c represents the speed of light in a vacuum; δt represents the geometric distance between the satellite and the receiver. u,k Indicates the clock bias of the user receiver; Indicates satellite clock bias; Indicates ionospheric delay; Indicates tropospheric delay; This indicates pseudorange observation noise.
[0030] If the location of the user's receiver is known, the receiver clock error δt can be solved using a single pseudorange observation equation. u,k If the location of the user receiver is unknown, it is necessary to solve four or more pseudorange observation equations simultaneously and then use the least squares method to find the receiver clock error δt. u,k .
[0031] Step 2: Perform Kalman filtering on the receiver clock bias obtained in Step 1 based on the current model.
[0032] The state equation for the current Kalman filter model is as follows:
[0033]
[0034] Where x k =[δt u,k δf u,k δa u,k ] T Denotes the state vector, δf u,k and δa u,k Let A and U represent the clock drift and clock aging rate of the user receiver, respectively; A represents the state transition matrix; and U represents the input relation matrix. The Kalman filter value representing the clock aging rate of the user receiver; w k Let Q represent the process noise vector, with zero mean and variance. k Gaussian white noise.
[0035] The formula for calculating the state transition matrix A is as follows:
[0036]
[0037] The formula for calculating the input relation matrix U is as follows:
[0038]
[0039] In equations (3) and (4), T represents the sampling period; α represents the given maneuver frequency; and e represents the natural constant.
[0040] The observation equations based on the current model's Kalman filter are as follows:
[0041] y k =Cx k +v k
[0042] Where y k =δt u,k C represents the observation vector; C = [1 0 0] represents the measurement relationship matrix; v k Let R represent the measurement noise vector, with zero mean and variance. k Gaussian white noise.
[0043] In the initial epoch of the Kalman filter based on the current model, the state vector x is taken. k initial estimate And give the initial estimate of the corresponding mean square error of the state, P0.
[0044] Step 2.1: Prediction process based on the current model using Kalman filtering:
[0045] Calculate the prior estimate of the current epoch state vector:
[0046]
[0047] in This represents the prior estimate of the state vector; This represents the posterior estimate of the state vector.
[0048] Calculate the mean square error matrix of the prior estimates of the current epoch state vector:
[0049]
[0050] in P represents the mean square error matrix of the prior estimates of the state vector; k Let represent the mean square error matrix of the posterior estimate of the state vector.
[0051] The covariance matrix Q of the process noise vector k The calculation formula is as follows:
[0052]
[0053] In formula (10) The system noise variance is represented by the following formula:
[0054]
[0055] Where a max This indicates the maximum clock aging rate given.
[0056] The calculation formulas for each matrix element in equation (8) are as follows:
[0057]
[0058]
[0059]
[0060]
[0061]
[0062]
[0063] Step 2.2: Correction process based on the current model Kalman filter:
[0064] Calculate the gain matrix for the current epoch:
[0065]
[0066] Where K k Represents the gain matrix; the covariance matrix R of the measurement noise vector. k Take a constant value.
[0067] Calculate the posterior estimate of the state vector for the current epoch:
[0068]
[0069] Calculate the mean square error matrix of the posterior estimate of the current epoch state vector:
[0070]
[0071] Step 2.3: Given x k =[δt u,k δf u,k δa u,k ] T Let denot be the state vector. Then, based on the posterior estimate of the state vector of the current epoch calculated using formula (17), the filtered user receiver clock error can be solved.
[0072] Step 3: Use the filtered user receiver clock error obtained in Step 2 to correct the local time of the user receiver to obtain the system time.
[0073]
[0074] in This represents the Kalman filter value of the user receiver clock error.
[0075] Step 4: Repeat steps 1, 2, and 3. In each subsequent epoch, perform Kalman filtering on the receiver clock bias obtained from the pseudorange observation equation based on the current model, and use the filtered receiver clock bias to correct the user receiver's local time to obtain a high-precision system time.
[0076] This invention also proposes a satellite navigation timing device based on the current model Kalman filter, comprising:
[0077] The first calculation module is used to establish the pseudorange observation equation and solve for the clock error of the user receiver;
[0078] The second calculation module is used to establish the state equation based on the current model Kalman filter according to the user receiver clock error, and solve for the prior estimate of the current epoch state vector.
[0079] The third calculation module is used to calculate the posterior estimate of the current epoch state vector based on the prior estimate of the current epoch state vector.
[0080] The determination module is used to determine the filtered receiver clock error based on the posterior estimate of the current epoch state vector.
[0081] The correction module is used to correct the local time of the user receiver using the filtered receiver clock error to obtain the system time.
[0082] (III) Beneficial Effects
[0083] This invention proposes a high-precision satellite navigation timing method based on current model Kalman filtering. By using Kalman filtering based on the current model, the originally coarse and chaotic receiver clock bias becomes smoother and more accurate. This solves the technical problem that directly using the receiver clock bias obtained by solving the pseudorange observation equation to correct the system time obtained by the user receiver's local time results in large errors and low timing accuracy. This scheme effectively reduces the error of the system time obtained by correcting the user receiver's local time and improves the timing accuracy, which has important application value in the field of high-precision satellite navigation timing. Attached Figure Description
[0084] Figure 1 This is a flowchart of a satellite navigation timing method based on the current model Kalman filter according to an embodiment of the present invention.
[0085] Figure 2 This is a flowchart of a high-precision satellite navigation timing method based on the current model Kalman filter according to an embodiment of the present invention.
[0086] Figure 3 This is a comparison chart of the clock error of the user receiver before and after filtering. Detailed Implementation
[0087] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the specific embodiments described herein are merely for further explanation of the invention and do not limit the scope of protection of the invention. The invention includes, but is not limited to, the following embodiments.
[0088] Figure 1 The diagram shows a flowchart of a satellite navigation timing method based on the current model Kalman filter proposed in this invention, including the following steps:
[0089] Establish pseudorange observation equations and solve for the user receiver clock error;
[0090] Establish the state equation based on the current model Kalman filter according to the user receiver clock error, and solve for the prior estimate of the current epoch state vector;
[0091] Calculate the posterior estimate of the current epoch state vector based on the prior estimate of the current epoch state vector.
[0092] The filtered receiver clock bias is determined based on the posterior estimate of the current epoch state vector.
[0093] The system time is obtained by correcting the local time of the user receiver using the filtered receiver clock error.
[0094] This invention proposes a high-precision satellite navigation timing method based on current model Kalman filtering. By using Kalman filtering based on the current model, the originally coarse and chaotic receiver clock bias becomes smoother and more accurate. This solves the technical problem that directly using the receiver clock bias obtained by solving the pseudorange observation equation to correct the system time obtained by the user receiver's local time results in large errors and low timing accuracy. This scheme effectively reduces the error of the system time obtained by correcting the user receiver's local time and improves the timing accuracy, which has important application value in the field of high-precision satellite navigation timing.
[0095] To more clearly explain the technical solution of the present invention, the following is combined with... Figure 2 The embodiments shown provide a further detailed explanation of the technical solution of the present invention.
[0096] Step 1: Using pseudorange observed by the user receiver and information such as the position of visible satellites obtained from the navigation message, establish the pseudorange observation equation and calculate the clock error of the user receiver.
[0097] The pseudorange observation equation for the k-th epoch is as follows:
[0098]
[0099] The superscript (n) indicates the nth visible satellite; Indicates pseudodistance observations; The distance between the satellite and the receiver is represented by δt; c represents the speed of light in a vacuum; δt represents the geometric distance between the satellite and the receiver. u,k Indicates the clock bias of the user receiver; Indicates satellite clock bias; Indicates ionospheric delay; Indicates tropospheric delay; This indicates pseudorange observation noise.
[0100] If the location of the user's receiver is known, the receiver clock error δt can be solved using a single pseudorange observation equation. u,k If the location of the user receiver is unknown, it is necessary to solve four or more pseudorange observation equations simultaneously and then use the least squares method to find the receiver clock error δt. u,k .
[0101] In some embodiments provided in this application, the location of the user receiver is unknown. The receiver clock error at the 0th epoch is obtained by simultaneously solving four or more pseudorange observation equations and using the least squares method. u,0 The receiver clock difference δt at the first epoch u,1 .
[0102] Step 2: Perform Kalman filtering on the receiver clock bias obtained in Step 1 based on the current model.
[0103] The state equation for the current Kalman filter model is as follows:
[0104]
[0105] Where x k =[δt u,k δf u,k δa u,k ] T Denotes the state vector, δf u,k and δa u,k Let A and U represent the clock drift and clock aging rate of the user receiver, respectively; A represents the state transition matrix; and U represents the input relation matrix. The Kalman filter value representing the clock aging rate of the user receiver; w k Let Q represent the process noise vector, with zero mean and variance. k Gaussian white noise.
[0106] The formula for calculating the state transition matrix A is as follows:
[0107]
[0108] The formula for calculating the input relation matrix U is as follows:
[0109]
[0110] In equations (3) and (4), T represents the sampling period; α represents the given maneuver frequency; and e represents the natural constant.
[0111] The observation equations based on the current model's Kalman filter are as follows:
[0112] y k =Cx k +v k (5)
[0113] Where y k =δt u,k C represents the observation vector; C =
[100] represents the measurement relationship matrix; v k Let R represent the measurement noise vector, with zero mean and variance. k Gaussian white noise.
[0114] In the initial epoch of the Kalman filter based on the current model, the state vector x is taken. k initial estimate And give the initial estimate of the corresponding mean square error of the state, P0.
[0115] In some embodiments provided in this application, the sampling period T is 1 second, and given the corresponding maneuver frequency α, the state transition matrix A and the input relation matrix U can be calculated.
[0116] The measurement relationship matrix C = [1 0 0]. The initial estimate of the state vector x0 is taken. And the initial estimate of the corresponding mean square error of the state, P0, is given as:
[0117]
[0118] Step 2.1: Prediction process based on the current model using Kalman filtering:
[0119] Calculate the prior estimate of the current epoch state vector:
[0120]
[0121] in This represents the prior estimate of the state vector; This represents the posterior estimate of the state vector.
[0122] Calculate the mean square error matrix of the prior estimates of the current epoch state vector:
[0123]
[0124] in P represents the mean square error matrix of the prior estimates of the state vector; k Let represent the mean square error matrix of the posterior estimate of the state vector.
[0125] In some embodiments provided in this application, This is used to calculate the prior estimate of the current epoch state vector.
[0126] The covariance matrix Q of the process noise vector is calculated. k The part that does not change over time:
[0127]
[0128] The calculation formulas for each matrix element in equation (8) are as follows:
[0129]
[0130]
[0131]
[0132]
[0133]
[0134]
[0135] Given the maximum clock aging rate a max Calculate the system noise variance
[0136]
[0137] The covariance matrix Q of the process noise vector k The calculation formula is as follows:
[0138]
[0139]
[0140] Calculate the mean square error matrix of the prior estimates of the current epoch state vector:
[0141] P1 - =AP0A T +Q1
[0142]
[0143] in P represents the mean square error matrix of the prior estimates of the state vector; kLet represent the mean square error matrix of the posterior estimate of the state vector.
[0144] Step 2.2: Correction process based on the current model Kalman filter.
[0145] Calculate the gain matrix for the current epoch:
[0146]
[0147] Where K k Represents the gain matrix; the covariance matrix R of the measurement noise vector. k Take a constant value.
[0148] Calculate the posterior estimate of the state vector for the current epoch:
[0149]
[0150] Calculate the mean square error matrix of the posterior estimate of the current epoch state vector:
[0151]
[0152] In some embodiments provided in this application, the covariance matrix R of the measured noise vector is... k Take a constant value and calculate the gain matrix for the current epoch:
[0153] K1 = P1 - C T (CP1 - C T +R) -1
[0154] The observation vector y1 takes the receiver clock error δt of the first epoch. u,1 Calculate the posterior estimate of the state vector for the current epoch:
[0155]
[0156] Calculate the mean square error matrix of the posterior estimate of the current epoch state vector:
[0157] P1=(I-K1C)P1 -
[0158] Step 2.3: Given x k =[δt u,k δf u,k δa u,k ] T Let denot be the state vector. Then, based on the posterior estimate of the state vector of the current epoch calculated using formula (10), the filtered user receiver clock error can be solved.
[0159] Step 3: Use the filtered user receiver clock error obtained in Step 2 to correct the local time of the user receiver to obtain the system time.
[0160]
[0161] in This represents the Kalman filter value of the user receiver clock error.
[0162] Step 4: Repeat steps 1, 2, and 3. In each subsequent epoch, perform Kalman filtering on the receiver clock bias obtained from the pseudorange observation equation based on the current model, and use the filtered receiver clock bias to correct the user receiver's local time to obtain a high-precision system time.
[0163] Using the data from the above embodiments, a simulation was performed on the high-precision satellite navigation timing method based on the current model Kalman filtering proposed in this invention to obtain the filtered user receiver clock error, which was then compared with the unfiltered user receiver clock error to obtain the following results: Figure 3 The comparison diagram of user receiver clock bias before and after filtering is shown. It can be seen that the noise of the user receiver clock bias after filtering is significantly reduced compared to the original clock bias. This indicates that the technical solution proposed in this invention can effectively reduce the error in the system time obtained through local time correction of the user receiver, thereby improving time synchronization accuracy.
[0164] In summary, this invention proposes a high-precision satellite navigation timing method based on current model Kalman filtering. By establishing a model of user receiver clock bias, clock drift, and clock aging rate, the receiver clock biases obtained from the pseudorange observation equation at different times are correlated. Through Kalman filtering based on the current model, the originally coarse and chaotic receiver clock biases become smoother and more accurate, effectively reducing the error in the system time obtained after local time correction by the user receiver, thus improving timing accuracy. This method has significant application value in the field of high-precision satellite navigation timing.
[0165] Embodiments of the present invention also provide a satellite navigation timing device based on the current model Kalman filter, comprising:
[0166] The first calculation module is used to establish the pseudorange observation equation and solve for the clock error of the user receiver;
[0167] The second calculation module is used to establish the state equation based on the current model Kalman filter according to the user receiver clock error, and solve for the prior estimate of the current epoch state vector.
[0168] The third calculation module is used to calculate the posterior estimate of the current epoch state vector based on the prior estimate of the current epoch state vector.
[0169] The determination module is used to determine the filtered receiver clock error based on the posterior estimate of the current epoch state vector.
[0170] The correction module is used to correct the local time of the user receiver using the filtered receiver clock error to obtain the system time.
[0171] The specific execution steps of each module in the apparatus of this embodiment have been explained in detail in the embodiments of the relevant methods, and will not be repeated in this embodiment.
[0172] Embodiments of the present invention also provide a computer device, including a memory and a processor; the memory stores a computer program; the processor is used to execute the computer program stored in the memory to implement a satellite navigation timing method based on a current model Kalman filter: establishing a pseudorange observation equation and solving for the user receiver clock error; establishing a state equation based on the current model Kalman filter according to the user receiver clock error and solving for the prior estimate of the current epoch state vector; calculating the posterior estimate of the current epoch state vector according to the prior estimate of the current epoch state vector; determining the filtered receiver clock error according to the posterior estimate of the current epoch state vector; and correcting the user receiver local time using the filtered receiver clock error to obtain the system time.
[0173] Embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program can implement a satellite navigation timing method based on a current model Kalman filter: establishing a pseudorange observation equation and solving for the user receiver clock error; establishing a state equation based on the current model Kalman filter according to the user receiver clock error and solving for the prior estimate of the current epoch state vector; calculating the posterior estimate of the current epoch state vector according to the prior estimate of the current epoch state vector; determining the filtered receiver clock error according to the posterior estimate of the current epoch state vector; and correcting the user receiver local time using the filtered receiver clock error to obtain the system time.
[0174] The above-described embodiments merely illustrate a typical implementation of the present invention, and while the descriptions are quite specific and detailed, they should not be construed as limiting the scope of protection of this invention. Furthermore, it should be noted that those skilled in the art can make several non-essential improvements and adjustments without departing from the concept of the present invention, and these all fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.
Claims
1. A satellite navigation timing method based on the current model Kalman filter, comprising the following steps: Establish pseudorange observation equations and solve for the user receiver clock error; Establish the state equation based on the user receiver clock error and the current model Kalman filter, and solve for the prior estimate of the current epoch state vector; the establishment of the state equation based on the user receiver clock error and the current model Kalman filter includes the following steps: The state equation for the current Kalman filter model is: ； in Represents the state vector. and These represent the clock drift and clock aging rate of the user receiver, respectively. Represents the state transition matrix; Represents the input relation matrix; The Kalman filter value representing the clock aging rate of the user receiver; Let the process noise vector be zero, with a mean and variance of . Gaussian white noise; Wherein, the state transition matrix The calculation formula is as follows: ； Input relation matrix The calculation formula is as follows: ； In the formula Indicates the sampling period; Indicates the given maneuver frequency; Represents the natural constant; The observation equation based on the current model Kalman filter is as follows: The initial epoch is determined based on the current model's Kalman filter; where... Represents the observation vector; Represents the measurement relationship matrix; Let the measurement noise vector be zero, with a mean and variance of . Gaussian white noise; state vector The initial estimate is taken And provide an initial estimate of the corresponding mean square error of the state. ; Solving for the prior estimate of the current epoch state vector involves the following steps: Calculate the prior estimate of the current epoch state vector: ; in This represents the prior estimate of the state vector; This represents the posterior estimate of the state vector; Calculate the posterior estimate of the current epoch state vector based on the prior estimate of the current epoch state vector. The filtered receiver clock bias is determined based on the posterior estimate of the current epoch state vector. The system time is obtained by correcting the local time of the user receiver using the filtered receiver clock error.
2. The satellite navigation timing method according to claim 1, characterized in that, The specific steps for establishing the pseudorange observation equation include: No. The pseudorange observation equation for each epoch is as follows: ； superscript Indicates the first One visible satellite; Indicates pseudodistance observations; This indicates the geometric distance between the satellite and the receiver; This represents the speed of light in a vacuum. Indicates the clock bias of the user receiver; Indicates satellite clock bias; Indicates ionospheric delay; Indicates tropospheric delay; This indicates pseudorange observation noise.
3. The satellite navigation timing method according to claim 2, characterized in that, The specific steps for calculating the user receiver clock error include: If the location of the user's receiver is known, the receiver clock error can be solved using a single pseudorange observation equation. ; If the location of the user's receiver is unknown, at least four pseudorange observation equations need to be solved simultaneously, and the receiver clock error needs to be obtained using the least squares method. .
4. The satellite navigation timing method according to claim 1, characterized in that, The method also includes the following steps: Update process noise covariance matrix: ； In the formula The system noise variance is expressed by the following formula: ； in Indicates the maximum given clock aging rate; Update the mean square error matrix of the prior estimates of the current epoch state vector: ;in The mean square error matrix represents the prior estimates of the state vector; Let represent the mean square error matrix of the posterior estimate of the state vector.
5. The satellite navigation timing method according to claim 4, characterized in that, Based on the prior estimate of the current epoch state vector, the posterior estimate of the current epoch state vector is calculated, which includes the following steps: Calculate the posterior estimate of the current epoch state vector: ; In the formula This represents the gain matrix for the current epoch.
6. The satellite navigation timing method according to claim 5, characterized in that, The method also includes the following steps: Update the gain matrix for the current epoch: ;in Represents the gain matrix; the covariance matrix of the measurement noise vector. Take a constant value; Update the mean squared error matrix of the posterior estimate of the state vector: .
7. A satellite navigation timing device based on the current model Kalman filter, comprising: The first calculation module is used to establish the pseudorange observation equation and solve for the clock error of the user receiver; The second calculation module is used to establish the state equation based on the current model Kalman filter according to the user receiver clock error, and solve for the prior estimate of the current epoch state vector; specifically, the second calculation module is used to establish the state equation based on the current model Kalman filter as follows: ； in Represents the state vector. and These represent the clock drift and clock aging rate of the user receiver, respectively. Represents the state transition matrix; Represents the input relation matrix; The Kalman filter value representing the clock aging rate of the user receiver; Let the process noise vector be zero, with a mean and variance of . Gaussian white noise; Wherein, the state transition matrix The calculation formula is as follows: ； Input relation matrix The calculation formula is as follows: ； In the formula Indicates the sampling period; Indicates the given maneuver frequency; Represents the natural constant; The observation equation based on the current model Kalman filter is as follows: The initial epoch is determined based on the current model's Kalman filter; where... Represents the observation vector; Represents the measurement relationship matrix; Let the measurement noise vector be zero, with a mean and variance of . Gaussian white noise; state vector The initial estimate is taken And provide an initial estimate of the corresponding mean square error of the state. ; Solving for the prior estimate of the current epoch state vector involves the following steps: Calculate the prior estimate of the current epoch state vector: ; in This represents the prior estimate of the state vector; Represents the posterior estimate of the state vector The third calculation module is used to calculate the posterior estimate of the current epoch state vector based on the prior estimate of the current epoch state vector. The determination module is used to determine the filtered receiver clock error based on the posterior estimate of the current epoch state vector. The correction module is used to correct the local time of the user receiver using the filtered receiver clock error to obtain the system time.