CN114397681B - GNSS receiver carrier tracking method based on robust prediction variable structure filtering - Google Patents

GNSS receiver carrier tracking method based on robust prediction variable structure filtering Download PDF

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CN114397681B
CN114397681B CN202111418951.7A CN202111418951A CN114397681B CN 114397681 B CN114397681 B CN 114397681B CN 202111418951 A CN202111418951 A CN 202111418951A CN 114397681 B CN114397681 B CN 114397681B
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carrier
representing
state
gnss receiver
variable structure
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CN114397681A (en
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曹璐
范广腾
王建
田世伟
马雅楠
黄昊
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National Defense Technology Innovation Institute PLA Academy of Military Science
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/25—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS
    • G01S19/256—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS relating to timing, e.g. time of week, code phase, timing offset
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/29—Acquisition or tracking or demodulation of signals transmitted by the system carrier including Doppler, related

Abstract

The invention discloses a GNSS receiver carrier tracking method based on robust prediction variable structure filtering, which comprises the following steps: generating two paths of carrier signals by using an NCO carrier generator, and sending the two paths of carrier signals to an in-phase branch correlator and a coupler; the in-phase branch correlator is used for correlating a carrier signal and an intermediate frequency signal to obtain in-phase branch data; coupling the other path of carrier signal by using a coupler; utilizing an orthogonal branch correlator to correlate the other path of coupled carrier signal and the intermediate frequency signal to obtain orthogonal branch data; based on the in-phase branch data and the orthogonal branch data, a carrier ring Kalman filter is utilized to determine a state vector comprising a carrier phase, a carrier angular frequency shift and a carrier angular frequency shift change rate in a robust prediction variable structure filtering control mode, and the state vector is sent to an NCO carrier generator. The method can realize the estimation and the transmission of the carrier tracking state vector of the receiver under the condition of considering the disturbance and the uncertainty model error existing in the system, and improve the positioning precision of the receiver.

Description

GNSS receiver carrier tracking method based on robust prediction variable structure filtering
Technical Field
The invention relates to the technical field of satellite navigation, in particular to a GNSS receiver carrier tracking method based on robust prediction variable structure filtering.
Background
A Global Navigation Satellite System (GNSS) is a space-based radio Navigation Positioning System capable of providing all-weather three-dimensional coordinates, speed and time information to a user at any place on the earth surface or in a near-earth space, the GNSS is not only an infrastructure of national security and economy, but also an important sign for embodying the status of modern big countries and national comprehensive strength, the GNSS mainly includes a Global Positioning System (GPS), a BeiDou Navigation Satellite System (BDS), a GLONASS (GLONASS) and a Galileo Navigation Satellite System (Galileo Navigation System, galileo), the basic components of the above System include a space portion (satellites, etc.), a ground control portion (master control station, injection station, monitoring station, etc.) and a user portion (receiver, navigator, etc.); at present, the satellite navigation and positioning technology basically replaces the ground-based radio navigation, the traditional geodetic survey and the astronomical survey navigation and positioning technology, and promotes the brand new development of the field of geodetic survey and navigation and positioning.
Because the GNSS has inherent disadvantages that the signal is weak and the GNSS is easily subjected to electromagnetic interference, the GNSS still has serious potential safety hazard in practical application. Specifically, due to the low transmission power and the long distance between the satellite and the earth surface, the satellite signal is weak when reaching the earth surface, usually about-160 dBW, and various intentional and unintentional interferences are near the earth surface and near the ground navigation receiver, which easily causes the ground navigation receiver to be unable to normally lock the satellite signal.
When an existing GNSS receiver receives and processes satellite signals, the GNSS receiver receives wireless signals, carries out down-conversion and sampling processing, then searches and captures GNSS visible satellites in a visual field, tracks C/A codes (pseudo-random codes) and carrier waves of the captured signals to demodulate navigation data, and demodulates self position information based on the demodulated navigation data. However, under the influence of noise, the receiver cannot accurately judge the code phase and the carrier phase of the C/a code, and for the receiver that uses carrier phase positioning and the receiver that uses carrier-assisted C/a code tracking, a carrier tracking error may affect the positioning accuracy of the receiver, cause a determination error of navigation data, and further fail to provide a positioning result. In addition, for a high dynamic receiver applied to a high-speed moving object such as an airplane, a missile and the like, the doppler shift and the frequency change rate caused by the relative motion also have great influence on the receiver tracking, for example, in the case of a high-speed fighter, if the speed of the high-speed fighter is 748m/s and the carrier frequency is 1575.42MHz, the doppler shift attached to a carrier signal can reach 3.93kHz when the two are in relative motion, and if the relative acceleration between the two is 2g, the doppler shift change rate attached to the carrier signal is 102.93Hz/s. It can be seen that the doppler shift and the change rate thereof under high dynamic conditions can seriously interfere the process of accurately aligning the carrier frequency and the phase of the local signal and the received signal by the spread spectrum receiver, resulting in an increase in the system error rate and the positioning error.
In order to solve the above problems, carrier stripping of the received signal is currently implemented by using a carrier tracking loop tracking technology; specifically, the existing carrier tracking loop tracking technology mainly includes: phase Locked Loops (PLLs), frequency Locked Loops (FLLs), and kalman filter based carrier tracking.
In order to adapt to a high dynamic environment, the loop bandwidth of the phase-locked loop and the frequency-locked loop needs to be widened to capture and track the Doppler frequency and the change of the Doppler frequency of an input signal, however, the increase of the loop bandwidth can cause the reduction of the carrier tracking sensitivity, and when the loop is in a low signal-to-noise ratio working state, the carrier tracking is also out-of-lock; moreover, when a high dynamic environment and a low signal-to-noise ratio scene are changed continuously, the phase-locked loop and the frequency-locked loop need to adjust bandwidth continuously, and the filtering state is unstable due to the fact that the bandwidth switching threshold is not easy to determine and the loop switching is frequent. Therefore, it is difficult to use a phase-locked loop or a frequency-locked loop in a high dynamic and low signal-to-noise ratio scenario simultaneously. The carrier tracking based on Kalman filtering is essentially a phase-locked loop with the optimal bandwidth gradually changed, and the carrier tracking based on Kalman filtering utilizes the optimal estimation theory of a discrete time system to adaptively adjust the gain of a filtering loop according to the noise statistical characteristic in the loop convergence process so as to complete the adjustment of the loop bandwidth; however, the kalman filter in the loop is the optimal estimation filter only when the carrier tracking based on the kalman filtering meets the condition that the system model parameters and the noise statistical characteristics are accurately known, otherwise, the optimal estimation performance is degraded, the error in the filtering equation gradually tends to zero or a certain stable value along with the increase of recursion times, but the deviation between the filtering estimation value and the actual value is larger and larger, which causes the filter to diverge. In practical application, the established dynamic model often cannot completely and accurately simulate a real physical process, and the statistical characteristics of noise may be unknown or time-varying; for this reason, applying kalman filter-based carrier tracking directly to the carrier tracking loop of GNSS signals easily leads to filter divergence.
Disclosure of Invention
In order to solve part or all technical problems in the prior art, the invention provides a GNSS receiver carrier tracking method based on robust prediction variable structure filtering.
The technical scheme of the invention is as follows:
the method is realized by utilizing a GNSS receiver carrier tracking loop based on Kalman filtering, and the GNSS receiver carrier tracking loop based on the Kalman filtering comprises the following steps: the method comprises the following steps of NCO carrier generator, coupler, in-phase branch correlator, quadrature branch correlator and carrier ring Kalman filter, and comprises the following steps:
generating two paths of carrier signals by using an NCO carrier generator, sending one path of carrier signal to an in-phase branch correlator, and sending the other path of carrier signal to a coupler;
the in-phase branch correlator is used for correlating one path of carrier signals with intermediate frequency signals corresponding to satellite signals to obtain in-phase branch data, and the in-phase branch data are sent to a carrier ring Kalman filter;
performing 90-degree orthogonal coupling on the other path of carrier signal by using a coupler, and sending the coupled other path of carrier signal to an orthogonal branch correlator;
the orthogonal branch correlator is used for correlating the other path of coupled carrier signals with intermediate frequency signals corresponding to satellite signals to obtain orthogonal branch data and sending the orthogonal branch data to the carrier ring Kalman filter;
and receiving the in-phase branch data and the orthogonal branch data by using a carrier ring Kalman filter, determining a state vector comprising a carrier phase, a carrier angular frequency shift and a carrier angular frequency shift change rate by using a robust predictive variable structure filtering control mode based on the in-phase branch data and the orthogonal branch data, and sending the state vector to an NCO carrier generator.
Further, in the GNSS receiver carrier tracking method based on the robust predictive variable structure filtering, based on the in-phase branch data and the quadrature branch data, determining a state vector including a carrier phase, a carrier angular frequency shift, and a carrier angular frequency shift change rate by using a robust predictive variable structure filtering control method includes:
constructing a novel state equation corresponding to the state vector based on the uncertainty model error of the system;
performing time-removed Taylor expansion on the observation vector to obtain a Taylor expansion item corresponding to the observation vector;
calculating and determining an estimation error of the novel state equation according to the Taylor expansion term corresponding to the observation vector;
calculating and determining the model error compensation quantity of the novel state equation according to the estimation error of the novel state equation;
correcting the novel state equation by using the model error compensation quantity to obtain an improved state equation;
and performing numerical integration on the improved state equation to determine a state vector of carrier tracking at the next moment.
Further, in the GNSS receiver carrier tracking method based on the robust prediction variable structure filtering, the novel state equation corresponding to the state vector is as follows:
x k+1 ＝f(x k )+g(x k )d k
wherein x is k+1 Representing the state vector at time k +1,x k state vector representing time k, f (x) k ) Represents the initial equation of state, g (x) k ) System matrix representing model errors, d k Representing the amount of model error compensation.
Further, in the GNSS receiver carrier tracking method based on robust prediction variable structure filtering, estimating an error includes: a priori estimation error and a posteriori estimation error.
Further, in the GNSS receiver carrier tracking method based on the robust prediction variable structure filtering, a priori estimation error is calculated and determined by using the following formula;
Figure BDA0003376166130000031
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003376166130000032
representing a priori estimation error, z k+1 Represents the observation vector at time k +1,
Figure BDA0003376166130000033
an observation vector z representing the time k k Estimate of (a), Z' (x) k ) Representing observation vector z k+1 The taylor expansion term of (1).
Further, in the GNSS receiver carrier tracking method based on the robust prediction variable structure filtering, the posterior estimation error is calculated and determined by using the following formula;
Figure BDA0003376166130000041
wherein the content of the first and second substances,
Figure BDA0003376166130000042
representing the posterior estimation error, z k The observation vector representing the time instant k,
Figure BDA0003376166130000043
denotes z k An estimate of (d).
Further, in the GNSS receiver carrier tracking method based on the robust prediction variable structure filtering, the model error compensation quantity of the novel state equation is calculated and determined by using the following formula;
Figure BDA0003376166130000044
wherein d is k The amount of model error compensation is represented,
Figure BDA0003376166130000045
a state matrix representing the amount of model error,
Figure BDA0003376166130000046
state vector x representing time k k Is determined by the estimated value of (c),
Figure BDA0003376166130000047
which is indicative of an a priori estimation error,
Figure BDA0003376166130000048
the error of the a posteriori estimation is indicated,
Figure BDA0003376166130000049
representing the estimated residual variation gradient and gamma representing a constant parameter.
Further, in the GNSS receiver carrier tracking method based on the robust predictive variable structure filtering, the improved state equation is as follows:
Figure BDA00033761661300000410
wherein x is k+1 Representing the state vector at time k +1, x k State vector representing time k, f (x) k ) Represents the initial equation of state, g (x) k ) A system matrix representing the error of the model,
Figure BDA00033761661300000411
a state matrix representing the amount of model error,
Figure BDA00033761661300000412
state vector x representing time k k Is determined by the estimated value of (c),
Figure BDA00033761661300000413
which is indicative of an a priori estimation error,
Figure BDA00033761661300000414
the error of the a posteriori estimation is indicated,
Figure BDA00033761661300000415
representing the estimated residual variation gradient, and gamma represents a constant parameter.
The technical scheme of the invention has the following main advantages:
the GNSS receiver carrier tracking method based on the robust prediction variable structure filtering can realize the estimation and the transmission of the carrier tracking state vector of the GNSS receiver under the condition of considering various disturbance and uncertainty model errors existing in the system, can improve the positioning precision of the GNSS receiver, and ensures the reliability of the positioning result.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic structural diagram of a GNSS receiver carrier tracking loop based on kalman filtering according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the specific embodiments of the present invention and the accompanying drawings. It is to be understood that the described embodiments are only some of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme provided by the embodiment of the invention is described in detail below with reference to the accompanying drawings.
An embodiment of the present invention provides a GNSS receiver carrier tracking method based on robust predictive variable structure filtering, which is implemented by using a GNSS receiver carrier tracking loop based on kalman filtering, as shown in fig. 1, where the GNSS receiver carrier tracking loop based on the kalman filtering includes: the GNSS receiver carrier tracking method based on robust prediction variable structure filtering provided by the embodiment of the invention comprises the following steps:
generating two paths of carrier signals by using an NCO carrier generator, sending one path of carrier signal to an in-phase branch correlator, and sending the other path of carrier signal to a coupler;
the in-phase branch correlator is used for correlating one path of carrier signals with intermediate frequency signals corresponding to satellite signals to obtain in-phase branch data, and the in-phase branch data are sent to a carrier ring Kalman filter;
performing 90-degree orthogonal coupling on the other path of carrier signal by using a coupler, and sending the coupled other path of carrier signal to an orthogonal branch correlator;
the orthogonal branch correlator is used for correlating the other path of coupled carrier signals with intermediate frequency signals corresponding to satellite signals to obtain orthogonal branch data and sending the orthogonal branch data to the carrier ring Kalman filter;
and receiving the in-phase branch data and the orthogonal branch data by using a carrier ring Kalman filter, determining a state vector comprising a carrier phase, a carrier angular frequency shift and a carrier angular frequency shift change rate by using a robust predictive variable structure filtering control mode based on the in-phase branch data and the orthogonal branch data, and sending the state vector to an NCO carrier generator.
The following specifically describes the steps and principles of the GNSS receiver carrier tracking method based on robust predictive variable structure filtering according to an embodiment of the present invention;
specifically, in the existing kalman filter for carrier tracking, the state vector output by the kalman filter can be expressed as:
x k ＝[θ k ω k a k ] (1)
in the formula, x k State vector representing time k, theta k 、ω k And a k Respectively representing the carrier phase, the carrier angular frequency shift and the carrier angular frequency shift change rate at the k moment;
wherein the carrier angular frequency is shifted by omega k Is determined by the acquisition result of the GNSS receiver, the carrier phase theta k And the carrier angular frequency shift rate a k Is set to 0.
Under the condition of not considering various disturbance and uncertainty model errors existing in the system, the conventional Kalman filter calculates and determines an output state vector by using an initial state equation shown in formula 2;
x k ＝Ax k-1 +w k-1 (2)
formula 2 may be specifically represented as:
Figure BDA0003376166130000061
in the formula, x k State vector, x, representing time k k-1 The state vector representing the time k-1, theta, omega and a representing the carrier phase, carrier angular frequency shift and carrier angular frequency shift rate, respectively, and a matrix
Figure BDA0003376166130000062
T coh Representing the coherent integration time, w k-1 Representing the process noise at time k-1, w k-1 ＝[w θ w ω w a ] k-1 ，w θ 、w ω And w a Respectively representing carrier phase theta, carrier angular frequency shift omega and carrierThe measurement noise of the rate of change a of the angular frequency shift of the wave.
The existing carrier tracking based on Kalman filtering is an optimal estimation filter only when the condition that system model parameters and noise statistical characteristics are accurately known is met, otherwise, the optimal estimation performance is degraded, errors in a filtering equation gradually tend to zero or a certain stable value along with the increase of recursion times, but the deviation between a filtering estimation value and an actual value is larger and larger, so that the filter is diverged.
In an embodiment of the present invention, in order to increase the application range of the carrier-loop kalman filter, enable the carrier-loop kalman filter to be applicable to any type of model error and system noise, reduce the deviation between the estimated filtering value and the actual value, and reduce the processing amount, the carrier-loop kalman filter is controlled by using a robust predictive variable structure filtering control method, and a state vector including a carrier phase, a carrier angular frequency shift, and a carrier angular frequency shift change rate is determined.
Specifically, the method for determining the state vector comprising the carrier phase, the carrier angular frequency shift and the carrier angular frequency shift change rate by using the robust predictive variable structure filtering control mode comprises the following steps:
(1) Constructing a novel state equation corresponding to the state vector based on the uncertainty model error of the system;
specifically, under the condition of considering various disturbances and uncertainty model errors existing in the system, a novel state equation corresponding to a state vector can be constructed by using an initial state equation, and the novel state equation can be expressed as:
x k+1 ＝f(x k )+g(x k )d k (4)
in the formula, x k+1 Representing the state vector at time k +1, x k State vector representing time k, f (x) k ) Represents the initial equation of state, g (x) k ) System matrix representing model errors, d k Representing the amount of model error compensation.
(2) Performing time-removing Taylor expansion on the observation vector to obtain a Taylor expansion item corresponding to the observation vector;
specifically, in the existing kalman filter for carrier tracking, an observation vector at the time k is a correlation value output by an I branch correlator and a Q branch correlator, that is, in-phase branch data and quadrature branch data;
suppose that: I.C. A k And Q k In-phase branch data and quadrature branch data respectively representing time k, z k An observation vector representing the time k, z k ＝[I k ,Q k ]The observation vector at time k can be determined using the following equation;
Figure BDA0003376166130000071
Figure BDA0003376166130000072
in the formula, N k The number of coherent accumulation points is represented,
Figure BDA0003376166130000073
representing the mean value of the phase amplitudes of the carriers within the accumulation interval, d m Representing navigation data bits, Δ φ k Representing the mean value of the phase errors of the carrier, Δ φ, in the accumulation interval k ＝φ(t)-φ NCO (t), φ (t) represents the carrier phase of the incoming intermediate frequency signal, φ NCO (t) denotes the carrier phase of the locally generated carrier signal, Δ t k Denotes the code phase error at a point in the accumulation interval, R (-) denotes the pseudo code autocorrelation function, n Ik And n Qk Representing an uncorrelated sequence of gaussian white noise.
Further, the GNSS receiver satisfies under a stable tracking condition: Δ t k =0 and R (Δ t) k ) =1, based on this, the instant branch correlation integral of the loop is normalized, and a simplified system observation equation can be obtained as follows:
z k ＝h(x k )+ν k (7)
formula 7 may be specifically represented as:
Figure BDA0003376166130000081
in the formula, z k An observation vector representing the time k, I k And Q k In-phase branch data and quadrature branch data, h (x), respectively representing time k k ) A matrix of the relationship is represented,
Figure BDA0003376166130000082
means for predicting the carrier phase at time k by using the carrier phase at time k-1, v k Which is indicative of the noise of the measurement,
Figure BDA0003376166130000083
ν I,k v and v Q,k Representing the measurement noise of the I branch and the Q branch, respectively.
Will relation matrix h (x) k ) Spread and linearized at the estimated value to obtain k times of observation matrix H (x) k ) Comprises the following steps:
Figure BDA0003376166130000084
in the formula (I), the compound is shown in the specification,
Figure BDA0003376166130000085
the state vector at time k is predicted using the observed value at time k-1.
In one embodiment of the invention, in order to determine the model error of the novel state equation, the observation vector is subjected to time-removed Taylor expansion;
specifically, the observation vector is subjected to de-temporal Taylor expansion to obtain an expansion function shown as the following formula;
z k+1 ＝z k +Z′(x k )+U(x k )d k +o(e k+1 ) (10)
in the formula, z k+1 Represents the observation vector at time k +1, z k The observation vector representing the time k, vector function Z' (x) k ) Representing observation vector z k+1 The term of the taylor expansion of (c),
Figure BDA0003376166130000086
U(x k ) A state matrix representing the amount of model error,
Figure BDA0003376166130000087
d k represents the amount of model error compensation, o (e) k+1 ) Representing an approximation error containing high order taylor expansion errors and system noise,
Figure BDA0003376166130000088
e k+1 representing after Taylor expansion z k+1 The high order error term of (2).
(3) Calculating and determining an estimation error of the novel state equation according to the Taylor expansion term corresponding to the observation vector;
in an embodiment of the present invention, the estimation error of the new state equation includes: a priori estimation error and a posteriori estimation error of state estimation at the last moment; the prior estimation error and the posterior estimation error can be calculated and determined by the following formula;
Figure BDA0003376166130000091
Figure BDA0003376166130000092
in the formula (I), the compound is shown in the specification,
Figure BDA0003376166130000093
which is indicative of an a priori estimation error,
Figure BDA0003376166130000094
denotes z k The corresponding error of the a posteriori estimation,
Figure BDA0003376166130000095
denotes z k An estimate of (d).
Based on the determined prior estimation error and the posterior estimation error, the estimated residual variation gradient can be determined by the following formula;
Figure BDA0003376166130000096
in the formula (I), the compound is shown in the specification,
Figure BDA0003376166130000097
which represents the estimation of the residual change gradient,
Figure BDA0003376166130000098
denotes z k-1 The corresponding a posteriori estimation error.
(4) Calculating and determining the model error compensation quantity of the novel state equation according to the estimation error of the novel state equation;
in an embodiment of the present invention, based on the estimation error of the new state equation determined above, the model error compensation d of the new state equation k Can be determined by calculation as follows;
Figure BDA0003376166130000099
in the formula (I), the compound is shown in the specification,
Figure BDA00033761661300000910
a state matrix representing the amount of model error,
Figure BDA00033761661300000911
state vector x representing time k k Gamma represents a constant parameter,
Figure BDA00033761661300000912
γ 1 and gamma 2 Represents the actually selected constant and satisfies
Figure BDA00033761661300000913
(5) Correcting the novel state equation by using the model error compensation quantity to obtain an improved state equation;
in one embodiment of the invention, based on the determined model error compensation quantity, a novel state equation of carrier tracking can be corrected; specifically, substituting the determined model error compensation amount into equation 4 can obtain an improved state equation:
Figure BDA00033761661300000914
(6) Performing numerical integration on the improved state equation, and determining a state vector of carrier tracking at the next moment;
further, based on the determined improved state equation of carrier tracking, the state recursion can be performed by performing numerical integration on the improved state equation by using a numerical method, so that the carrier tracking state vector at the next moment can be obtained according to the carrier tracking state vector at the previous moment, and the estimation and transmission of the stable state vector without covariance are realized.
Therefore, the GNSS receiver carrier tracking method based on the robust predictive variable structure filtering provided by the embodiment of the invention can realize the estimation and transmission of the carrier tracking state vector of the GNSS receiver under the condition of considering various disturbances and uncertainty model errors existing in the system, can improve the positioning accuracy of the GNSS receiver, and ensures the reliability of the positioning result.
It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, "front", "rear", "left", "right", "upper" and "lower" in this document are referred to the placement states shown in the drawings.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (6)

1. A GNSS receiver carrier tracking method based on robust prediction variable structure filtering is characterized in that the method is realized by utilizing a GNSS receiver carrier tracking loop based on Kalman filtering, and the GNSS receiver carrier tracking loop based on Kalman filtering comprises the following steps: the method comprises the following steps of NCO carrier generator, coupler, in-phase branch correlator, quadrature branch correlator and carrier ring Kalman filter, and comprises the following steps:
generating two paths of carrier signals by using an NCO carrier generator, sending one path of carrier signal to an in-phase branch correlator, and sending the other path of carrier signal to a coupler;
the in-phase branch correlator is used for correlating one path of carrier signals with intermediate frequency signals corresponding to satellite signals to obtain in-phase branch data, and the in-phase branch data are sent to a carrier ring Kalman filter;
performing 90-degree orthogonal coupling on the other path of carrier signal by using a coupler, and sending the coupled other path of carrier signal to an orthogonal branch correlator;
the orthogonal branch correlator is used for correlating the other path of coupled carrier signals with intermediate frequency signals corresponding to satellite signals to obtain orthogonal branch data and sending the orthogonal branch data to the carrier ring Kalman filter;
the carrier ring Kalman filter is used for receiving the in-phase branch data and the orthogonal branch data, state vectors comprising carrier phases, carrier angular frequency shifts and carrier angular frequency shift change rates are determined by a robust prediction variable structure filtering control mode based on the in-phase branch data and the orthogonal branch data, and the state vectors are sent to an NCO carrier generator;
the method for determining the state vector comprising the carrier phase, the carrier angular frequency shift and the carrier angular frequency shift change rate by using the robust predictive variable structure filtering control mode based on the in-phase branch data and the orthogonal branch data comprises the following steps: constructing a novel state equation corresponding to the state vector based on the uncertainty model error of the system; performing time-removed Taylor expansion on the observation vector to obtain a Taylor expansion item corresponding to the observation vector; calculating and determining an estimation error of the novel state equation according to the Taylor expansion term corresponding to the observation vector; calculating and determining the model error compensation quantity of the novel state equation according to the estimation error of the novel state equation; correcting the novel state equation by using the model error compensation quantity to obtain an improved state equation; performing numerical integration on the improved state equation, and determining a state vector of carrier tracking at the next moment;
the improved state equation is as follows:
Figure FDA0003958606350000011
wherein x is k+1 Representing the state vector at time k +1, x k State vector representing time k, f (x) k ) Represents the initial equation of state, g (x) k ) A system matrix representing the error of the model,
Figure FDA0003958606350000012
a state matrix representing the amount of model error,
Figure FDA0003958606350000013
state vector x representing time k k Is determined by the estimated value of (c),
Figure FDA0003958606350000014
which is indicative of an a priori estimation error,
Figure FDA0003958606350000015
the error of the a posteriori estimation is indicated,
Figure FDA0003958606350000016
representing the estimated residual variation gradient and gamma representing a constant parameter.
2. The GNSS receiver carrier tracking method based on robust predictive variable structure filtering according to claim 1, wherein the new state equation corresponding to the state vector is:
x k+1 ＝f(x k )+g(x k )d k
wherein d is k Representing the amount of model error compensation.
3. The robust predictor-variable structure filter based GNSS receiver carrier tracking method of claim 1 or 2 wherein estimating the error comprises: a priori estimation error and a posteriori estimation error.
4. The GNSS receiver carrier tracking method based on robust prediction variable structure filtering as claimed in claim 3, characterized in that the prior estimation error is calculated and determined by the following formula;
Figure FDA0003958606350000021
wherein z is k+1 Represents the observation vector at time k +1,
Figure FDA0003958606350000022
an observation vector z representing the time k k Estimate of (a), Z' (x) k ) Representing observation vector z k+1 The taylor expansion term of (1).
5. The GNSS receiver carrier tracking method based on robust prediction variable structure filtering according to claim 3, characterized in that the a posteriori estimation error is calculated and determined by the following formula;
Figure FDA0003958606350000023
wherein z is k The observation vector representing the time instant k,
Figure FDA0003958606350000024
denotes z k An estimate of (d).
6. The GNSS receiver carrier tracking method based on robust prediction variable structure filtering according to claim 2, characterized in that the model error compensation amount of the new state equation is calculated and determined by using the following formula;
Figure FDA0003958606350000025
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