Navigation signal vector tracking loop filtering method based on KF-DDF bidirectional filter

Abstract

The invention belongs to the technical field of global satellite navigation, and discloses a navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter, and the method comprises the following steps: S1, inputting an input observed quantity of a loop filter into a Kalman filter for forward filtering processing, and outputting a state estimator after one-step prediction; s2, inputting the state estimator after one-step prediction into a differential filter for reverse smooth filtering, and removing noise and interference by using a differential processing principle to obtain a state estimator after reverse filtering; and S3, carrying out weighted fusion on the state estimator and the state estimator after reverse filtering, outputting a globally optimal carrier phase error and a code phase error, obtaining a target state estimator, and through a bidirectional filtering mechanism combining forward Kalman filtering and reverse differential filtering, obtaining a target state estimator. And the signal tracking capability of the navigation system in a high dynamic environment and the robustness and anti-interference performance in a complex environment are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of global satellite navigation, and more specifically, to a navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter. Background Art

[0002] After decades of development, the Global Navigation Satellite System (GNSS) has become the most widely used navigation system in the world. Major countries have also developed their own globally controllable global navigation satellite systems to ensure the security and economic benefits of the national economy. At present, the continuous evolution of the navigation system is constantly upgraded and optimized towards the direction of high credibility, high reliability, strong robustness, and high precision. However, in the face of the increasingly complex and challenging navigation environment and diverse usage scenarios of users, traditional navigation systems are facing many severe tests. There are the following problems:

[0003] Navigation accuracy problem in harsh signal environments: In complex environments such as signal interference, short-term signal occlusion, and harsh weather conditions, traditional navigation systems often struggle to ensure their reliable operation effectively, resulting in a decline in navigation accuracy.

[0004] Signal tracking problem in high-dynamic scenarios: In high-dynamic environments, the rapid change in the signal Doppler frequency shift caused by the rapid movement of carriers (such as airplanes, unmanned aerial vehicles, and unmanned boats), combined with signal attenuation and interference in complex environments, is extremely likely to cause signal loss of lock, resulting in navigation interruption or a significant decline in accuracy.

[0005] Robustness and anti-interference performance problems of the system: Traditional navigation systems have insufficient robustness and anti-interference performance when facing signal occlusion, interference, or even spoofing attacks, and it is difficult to cope with these challenges.

[0006] In view of this, the present invention provides a navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter. Summary of the Invention

[0007] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter, aiming to improve the navigation accuracy and the stability and robustness of the system in harsh signal environments.

[0008] To achieve the above object, the present invention provides the following technical solutions: In the first aspect, the present invention provides a navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter, including the following steps:

[0009] Step S1: Send the input observation quantity of the loop filter into the Kalman filter for forward filtering processing, and output the state estimation quantity after one-step prediction;

[0010] Step S2: Use the state estimator after one-step prediction and the updated measurement noise matrix as the initial values and input them into the difference filter for backward smoothing filtering. Utilize the difference processing principle to remove noise and interference, and obtain the state estimator after backward filtering;

[0011] Step S3: Perform weighted fusion on the state estimator and the state estimator after backward filtering, output the globally optimal carrier phase error and code phase error, and obtain the target state estimator.

[0012] As a preferred technical solution of the present invention, the input observation quantities of the loop filter include carrier phase error and pseudo-code phase error.

[0013] As a preferred technical solution of the present invention, the forward filtering processing logic of the Kalman filter is as follows:

[0014] Construct a discrete state system model of the vector tracking loop filter, including:

[0015] State prediction equation: Predict the system state vector at the next moment by applying the state transition matrix to the state vector at the previous moment and superimposing the process noise;

[0016] Measurement equation: Predict the measurement vector at the next moment by multiplying the state vector at the previous moment by the measurement matrix and adding the measurement noise;

[0017] Dynamic measurement noise adjustment: Adjust the measurement noise in the forward Kalman filtering process in real time according to the carrier-to-noise ratio value of each signal tracking channel;

[0018] Update the system state through the state quantity after forward Kalman filtering prediction, obtain the filtered carrier phase error and code phase error, and output the state estimator after one-step prediction.

[0019] As a preferred technical solution of the present invention, the backward filtering processing logic of the difference filter is as follows:

[0020] Establish a discrete system model to describe the dynamic change characteristics of the system during the signal tracking process;

[0021] Introduce process noise and measurement noise, mark them as uncorrelated zero-mean Gaussian white noise of the system, and obtain the corresponding marked covariance matrix;

[0022] Predict the state quantity at the previous moment using the state transition matrix and propagate the covariance matrix; calculate the change in the state quantity by taking the difference of the state estimate to extract the dynamic characteristics of the system;

[0023] Update the system state through the state quantity after difference calculation, obtain the carrier phase error and code phase error after backward filtering, and obtain the state estimator after backward filtering.

[0024] As a preferred technical solution of the present invention, the weighted fusion processing logic of the bidirectional filter is as follows:

[0025] After completing the forward Kalman filter and the backward difference filter, the state estimate and its covariance matrix corresponding to the forward filter and the state estimate and its covariance matrix corresponding to the backward filter are obtained respectively;

[0026] The inverse matrix calculations are respectively performed using the covariance matrices of the state estimates corresponding to the forward filter and the backward filter, and their weights are calculated respectively;

[0027] The state estimates corresponding to the forward filter and the backward filter are fused in the form of weighted average to output the globally optimal carrier phase error and code phase error, and the target state estimate is obtained

[0028] Technical effects and advantages of the navigation signal vector tracking loop filtering method based on the KF-DDF bidirectional filter of the present invention:

[0029] By combining the bidirectional filtering mechanism of forward Kalman filter (KF) and backward difference filter (DDF), the present invention significantly improves the signal tracking ability of the navigation system in high-dynamic environments, the robustness in complex environments, and the anti-interference performance. Through the weighted fusion of the bidirectional filtering results, the error accumulation and lag effect of traditional single-path filtering are eliminated, and the globally optimal estimation of the carrier phase error and the code phase error is achieved, thereby improving the navigation accuracy and system stability, and is particularly suitable for the navigation requirements of high-dynamic carriers (such as airplanes, unmanned aerial vehicles, unmanned boats) and in complex environments. Description of the Drawings

[0030] Figure 1 It is a flow block diagram of the present invention.

[0031] Figure 2 It is a ship navigation experimental path diagram for verifying the method.

[0032] Figure 3 It is an enlarged view of the ship navigation experimental path for verifying the method.

[0033] Figure 4 It is an equipment installation diagram for verifying the method.

[0034] Figure 5 It is a heat map of the number of navigation satellites with normal signal reception during the verification experiment.

[0035] Figure 6 It is a result diagram of the carrier phase error of the navigation system;

[0036] Figure 7 It is a result diagram of the code phase error of the navigation system;

[0037] Figure 8 Error effect diagram of the horizontal positioning result of the navigation system;

[0038] Figure 9 Error effect diagram of the horizontal speed of the navigation system. Specific implementation mode

[0039] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0040] This embodiment proposes a navigation signal vector tracking loop filtering method based on a bidirectional filter combining forward Kalman Filtering (KF) and backward Divided Difference Filter (DDF); according to the navigation signal vector tracking loop signal processing flow of the software-defined receiver, when realizing signal tracking, the phase discriminator in the phase-locked loop outputs the carrier and code phase errors as the input observables of the loop filter.

[0041] Embodiment 1

[0042] Please refer to Figure 1 As shown, this embodiment provides a navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter, including the following steps:

[0043] Step S1: Send the input observables of the loop filter into the Kalman filter for forward filtering processing, and output the state estimate after one-step prediction, where: the state estimate includes code phase error, carrier phase error, carrier frequency error, and carrier frequency change rate error.

[0044] Specifically, the input observables of the loop filter include carrier phase error and pseudo-code phase error; the Kalman filter is abbreviated as the KF filter in this embodiment, and the KF filter predicts and updates accurate state estimates through a recursive method;

[0045] More specifically, the forward filtering processing logic of the Kalman filter is:

[0046] First, construct a discrete state system model of the vector tracking loop filter:

[0047] The state prediction equation is expressed as: By taking the state vector at the previous moment through the state transition matrix ΦKF,k / k-1 Act on and superimpose process noise Predict the system state vector at the next moment

[0048] The measurement equation is expressed as: By using the state vector at the previous moment Through the measurement matrix H KF,k Plus the measurement noise Predict the measurement vector at the next moment;

[0049] Wherein, Represents the system state vector of the i-th satellite channel in the vector tracking loop at time k, which is composed of pseudo-code phase error, carrier phase error, carrier frequency error, and carrier frequency change rate error, Φ KF Is the one-step state transition matrix of the discrete system, W KF Is the process noise vector of the system. Represents the measurement vector of the i-th satellite channel in the vector tracking loop at time k, which is composed of pseudo-code phase error and carrier phase error, H KF Is the measurement matrix of the system, V KF Is the measurement noise.

[0050]

[0051] Wherein, Δρ i (chip) is the code phase error, Δσ i (rad) is the carrier phase error, Δf i (Hz) is the carrier frequency error, Is the carrier frequency change rate error. The parameter β = f code / f carrier = 1 / 1540 represents the unit conversion between the "cycle" and "chip" of the carrier signal. T represents the data update period of the signal loop filter.

[0052]

[0053] Wherein, Represents the average value of the pseudo-code phase error, Represents the average value of the carrier phase error, and its calculation method is:

[0054]

[0055] I E ,Q E ,I P ,Q P ,I L , and Q LThey respectively represent the coherent integration numerical values of the early, prompt, and late codes of the signal tracking channels assigned to each satellite in the I and Q branches.

[0056] Next, the system adjusts the measurement noise in the forward Kalman filtering process in real time through the carrier-to-noise ratio value C / N0 of each signal tracking channel, thereby improving the signal tracking accuracy. The measurement noise calculation process is as follows:

[0057]

[0058] Wherein, and are respectively the covariance matrices output by the pseudo-code loop discriminator and the carrier loop discriminator. t is the time length of coherent integration, and d0 is the code width, which is equal to 0.5 chips.

[0059] E[W KF,k = 0 E[W KF,k (W KF,k ) T = Q KF,k

[0060] E[V KF,k = 0 E[V KF,k (V KF,k ) T = R KF,k

[0061] Generally, the system noise W KF,k and the measurement noise V KF,k are both zero-mean Gaussian white noises and show a normal distribution.

[0062] Combined with the establishment of the above system mathematical model, the update process of the forward Kalman filter in linear discrete form is as follows:

[0063]

[0064] After the forward filtering process of Kalman filtering, the state estimate obtained through one-step prediction is output as the initial state estimate value for the subsequent backward filtering.

[0065] Step S2: After completing the forward filtering process, in order to improve the accuracy and make the system more robust, the proposed method uses the state prediction result and the updated measurement noise matrix as the initial values for backward filtering estimation.

[0066] Specifically, the differential filter is abbreviated as the DDF filter; the DDF filter is used to provide an accurate system noise change matrix for the state estimator in step S1, and then through DDF filtering, the system can quickly respond to the dynamic changes of the signal loop. By the differential processing principle of the differential filter, the noise in the signal and the system state changes caused by external random interference are removed, thereby improving the accuracy of state prediction and ensuring the stability of the system.

[0067] More specifically, the forward filtering processing logic of the differential filter is as follows:

[0068] First, establish and analyze the following discrete system:

[0069]

[0070] Similar to the forward Kalman filtering process, is a 4-dimensional state vector, is the process noise vector of the system, is the process noise vector of the system. The subscript DDF indicates that the current is the reverse differential filtering process, and the superscript i indicates the current satellite channel being tracked.

[0071] In this process, the system process noise and measurement noise are both uncorrelated Gaussian white noises, and their mathematical expectations and covariance matrices can be expressed as:

[0072]

[0073]

[0074] In the calculation process, the Cholesky matrix decomposition is introduced, and the calculation formula for the covariance matrix decomposition is:

[0075]

[0076] The state prediction and state prediction covariance matrix of the filtering process are respectively expressed as:

[0077]

[0078] Among them, and are respectively:

[0079]

[0080] In the formula, represents the matrix and The j-th column, and in addition, h represents the differential step size for each step. By calculating the difference of the estimator, the change amount between differential steps is calculated, which has a good suppression effect on the non-Gaussian mean noise in the system and the large system noise in the case of short-term occlusion of the signal.

[0081] During the tracking process of the signal loop, the process noise of the system is additive noise, so the covariance matrix can be simplified as:

[0082]

[0083] Next, perform Cholesky decomposition on the covariance matrix of the measurement noise:

[0084]

[0085] Similarly, the prediction update of the observation vector and its covariance matrix is:

[0086]

[0087] Among them, and are respectively:

[0088]

[0089] and can be simplified as:

[0090]

[0091] Finally, the state update process can be expressed as:

[0092]

[0093] During the process of performing DDF backward filtering, we use the one-step updated state quantity of forward Kalman filtering and the system noise matrix adjusted by adaptive calculation to obtain higher system error sensitivity and reliability under interference conditions.

[0094] Step S3: Weightedly fuse the forward state estimator and the state estimator after backward filtering, output the globally optimal carrier phase error and code phase error, and obtain the target state estimator.

[0095] Specifically, the state estimators after bidirectional filtering are weighted and fused to output the globally optimal estimated carrier phase error and code phase error. By means of weighted fusion and averaging of the two prediction results, the system state is further corrected and optimized to obtain a globally optimal state estimation. The obtained result can eliminate the errors and lag effects in the forward filtering process, enabling the system to better capture the dynamic changes of the current system state. Especially when facing complex environments such as sudden high system noise and strong interference, the fusion of bidirectional filtering results can effectively suppress the influence of noise and improve the robustness of the system.

[0096] More specifically, the weighted fusion processing logic of the bidirectional filter is as follows:

[0097] First, a mathematical model is established by considering the results of forward and reverse filtering simultaneously, and the globally optimal estimation is obtained after data fusion. and The calculation formula is:

[0098]

[0099] Finally, the updated globally optimal solution is fed back into the carrier and pseudo-code tracking loops.

[0100] It should be noted that: the fusion of bidirectional filtering results can effectively suppress the influence of noise. Especially when facing complex environments such as sudden high system noise and strong interference, it significantly improves the robustness and dynamic response ability of the system. It solves the problems of navigation accuracy, signal tracking ability, robustness, and anti-interference performance of traditional navigation systems in complex signal environments, and is particularly suitable for the navigation requirements of high-dynamic carriers and complex environments.

[0101] Embodiment 2

[0102] Based on Embodiment 1, a specific implementation manner is provided. As Figure 2 shown, a navigation experiment path map of a ship with four bridges in occlusion is given. It moves uniformly from the starting point to the ending point during the time period from 7:41 to 7:51 on June 2, 2023 (UTC time), passing under the four bridges in sequence to verify the performance of the satellite signal vector loop proposed by the invention.

[0103] As Figure 3 shown, the specific direction of ship movement and the scenarios and occlusion distances with signal occlusion are given.

[0104] As Figure 4As shown in the figure, an experimental test platform based on the present invention is given. In the experiment, an inflatable boat 1 is selected as the carrier platform for the experimental equipment to simulate the movement and operation scenarios of the shipborne platform in the actual working environment. The core components of the experimental equipment include: an intermediate-frequency signal receiver 5 for collecting GPS intermediate-frequency signals, a navigation receiver 4 for real-time measurement and recording of positioning information, two full-band measurement antennas 2, and a computer 3 for data storage and real-time data processing. The ship motion signal corresponding to the inflatable boat 1 is obtained, and the ship motion signal is sent to the navigation receiver 4 and the signal receiver 5 through the measurement antenna 2. Different forms of ship motion signals are obtained through the navigation receiver 4 and the signal receiver 5 respectively, and the different forms of ship motion signals are processed by the computer 5 to implement the navigation signal vector tracking loop filtering method.

[0105] As Figure 5 shown, the number of navigation satellites with normal signal reception during the ship motion experiment from 7:41 to 7:51 (UTC time) on June 2, 2023 is given. It can be seen that when there is occlusion above the ship, there are different degrees of interference and noise in the satellite signals.

[0106] As Figure 6 shown, the carrier phase error of the GPS PRN5 satellite signal tracking during the ship motion from 7:41 to 7:51 (UTC time) on June 2, 2023 is given. It can be seen from the figure that the signal carrier phase error has been significantly suppressed during the experiment, indicating that the signal tracking state is good and the system runs stably.

[0107] As Figure 7 shown, the code phase error of the GPS PRN5 satellite signal tracking during the ship motion from 7:41 to 7:51 (UTC time) on June 2, 2023 is given. It can be seen from the figure that the code phase error of the satellite signal is significantly suppressed during the experiment, and the code phase error is small throughout the process, indicating that the signal tracking state is good and the signal tracking of the system is stable.

[0108] As Figure 8 and Figure 9 shown, by adopting the signal loop filtering method proposed by the present invention, the ability of the navigation system to track satellite signals and the robustness of the navigation system can be effectively improved, and high-precision navigation positioning and speed measurement can be realized, especially in the case of signal interference and environmental occlusion, the effect is obvious.

[0109] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or substitutions, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claimed rights.

[0110] Finally, the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A navigation signal vector tracking loop filtering method based on a KF-DDF bidirectional filter, characterized in that It includes the following steps: Step S1: Feed the input observation of the loop filter into the Kalman filter for forward filtering processing, and output the state estimator after one-step prediction; Step S2: Use the state estimator after one-step prediction and the updated measurement noise matrix as the initial values to input into the difference filter for reverse smoothing filtering, and utilize the difference processing principle to remove noise and interference to obtain the state estimator after reverse filtering; Step S3: Perform weighted fusion on the state estimator and the state estimator after reverse filtering, output the globally optimal carrier phase error and code phase error, and obtain the target state estimator.

2. The navigation signal vector tracking loop filtering method based on the KF-DDF bidirectional filter according to claim 1, characterized in that: The input observation of the loop filter includes the carrier phase error and the pseudo-code phase error.

3. The navigation signal vector tracking loop filtering method based on the KF-DDF bidirectional filter according to claim 2, wherein: The forward filtering processing logic of the Kalman filter is: Construct the discrete state system model of the vector tracking loop filter, including: The state prediction equation, which predicts the system state vector at the next moment by applying the state transition matrix to the state vector at the previous moment and superimposing the process noise; The measurement equation, which predicts the measurement vector at the next moment by adding the measurement noise to the state vector at the previous moment through the measurement matrix; Dynamic measurement noise adjustment, which adjusts the measurement noise in the forward Kalman filtering process in real time through the carrier-to-noise ratio value of each signal tracking channel; Update the system state through the state quantity predicted by the forward Kalman filter to obtain the filtered carrier phase error and code phase error, and output the state estimator after one-step prediction.

4. The navigation signal vector tracking loop filtering method based on the KF-DDF bidirectional filter according to claim 3, characterized in that: The reverse filtering processing logic of the difference filter is: Establish a discrete system model to describe the dynamic change characteristics of the system during the signal tracking process; Introduce the process noise and the measurement noise, mark them as uncorrelated zero-mean Gaussian white noise of the system, and obtain the corresponding marked covariance matrix; Predict the state quantity at the previous moment using the state transition matrix and propagate the covariance matrix; calculate the change of the state quantity by taking the difference of the state estimate to extract the dynamic characteristics of the system; Update the system state through the state quantity after difference calculation to obtain the carrier phase error and code phase error after reverse filtering, and obtain the state estimator after reverse filtering.

5. The navigation signal vector tracking loop filtering method based on the KF-DDF two-way filter according to claim 3, characterized in that: The weighted fusion processing logic of the bidirectional filter is: After completing the forward Kalman filtering and the reverse difference filtering, obtain the state estimate and its covariance matrix corresponding to the forward filter and the state estimate and its covariance matrix corresponding to the backward filter respectively; Perform matrix inverse calculations on the covariance matrices corresponding to the state estimates of the forward filter and the backward filter respectively, and calculate their weights respectively; Fuse the state estimates corresponding to the forward filter and the backward filter in the form of weighted average, output the globally optimal carrier phase error and code phase error, and obtain the target state estimator.

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