CN116577814A - Vector tracking method and device suitable for time-hopping navigation signals - Google Patents
Vector tracking method and device suitable for time-hopping navigation signals Download PDFInfo
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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
- G01S19/01—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
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
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- 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
- G01S19/393—Trajectory determination or predictive tracking, e.g. Kalman filtering
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Abstract
The invention discloses a vector tracking method and a device suitable for a time-hopping navigation signal, wherein the device comprises the following steps: the device comprises a pulse control module, an integral zero clearing I & D module, a discriminator, an IUP pre-filter and a navigation filter; the navigation filter comprises a PM module, an EKF module and an LOS mapping module; vector tracking is used for processing a pseudo-satellite time hopping navigation signal, and Kalman channel pre-filtering based on an irregular updating period IUP and navigation filtering based on error observational quantity prediction PM are designed according to the pseudo-satellite time hopping navigation signal; and then, completing the line-of-sight projection and channel feedback correction by utilizing the line-of-sight LOS mapping, and realizing vector tracking applicable to time-hopping navigation signals. The invention improves the loop tracking precision and stability of the time-hopping navigation signal vector tracking loop and the positioning and speed measuring precision of the receiver through the navigation filtering after the channel pre-filtering and the observed quantity synchronization of the irregular updating.
Description
Technical Field
The invention belongs to the technical field of radio navigation, and particularly relates to a vector tracking method and device suitable for time-hopping navigation signals.
Background
Pseudolite positioning systems are capable of providing continuous and reliable positioning services to users in urban canyons, surface mines, and environments where global navigation satellite systems (Global Navigation Satellite System, GNSS) are limited. In order to be compatible with the GNSS to a certain extent, the pseudolite positioning system often adopts a signal system similar to the GNSS, namely, a pseudo-random code is used for directly sequence spreading the signals, so that code division multiple access multiplexing is realized. However, the distance difference between the user and each pseudolite base station is sometimes very large in the coverage area of the pseudolite positioning system, so that the problem of serious near-far effect is caused. The near-far effect cannot be effectively restrained only by the relevant gain brought by the spread spectrum code, so that the time hopping pulse modulation technology with lower implementation cost is generally adopted to improve the performance of the system for resisting the near-far effect.
Time-hopping pulse modulation divides a signal into three levels of frames, subframes, and slots, each frame containing N f Subframes, each subframe containing N s Time slots, where N f N depends on the length of the pseudo-random time hopping sequence s Then it depends on the pulse signal duty cycle. The pseudo-random time hopping sequence determines the transmitting time slot of each pseudo-satellite in each subframe, ensures that each pseudo-satellite transmits time hopping pulse signals at an approximate random interval, and maintains the original frequency spectrum characteristic of the signals to the greatest extent, thereby avoiding the problem of signal false locking caused by periodic frequency spectrum movement. Meanwhile, the time-hopping pulse modulation enables only one pseudolite to transmit signals in each time slot, and cross-correlation interference caused by other pseudolites in the system is restrained.
Like GNSS signals, pseudolite time-hopping navigation signals may also be tracked using vector loops. The vector tracking loop (Vector Tracking Loop, VTL) concentrates the observables of all channels into one navigation filter for processing, and the information of different channels mutually assist, so that compared with a scalar tracking mode, the dynamic tracking performance of the receiver can be improved, and the signal tracking continuity is improved. However, the conventional vector tracking method aims at continuous signals, and for a pseudo satellite positioning system adopting time hopping pulse modulation, signals are discontinuous, pulse intervals have pseudo random characteristics, and effective time slots of all pseudo satellites are not overlapped, so that the problems of increased errors of tracking loop discriminators and asynchronous output time of all tracking channel discriminators are caused, and further, the signal tracking performance and the receiver positioning performance are reduced. Therefore, it is difficult to achieve accurate and reliable vector tracking of pseudolite time-hopping navigation signals in the prior art.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a vector tracking method suitable for time-hopping navigation signals, which improves the loop tracking precision, stability and receiver positioning and speed measuring precision of a pseudo-satellite time-hopping navigation signal vector tracking loop through irregularly updated channel pre-filtering and navigation filtering after observed quantity synchronization.
The method of the invention comprises, on the one hand, a Kalman channel pre-filtering method based on irregular update periods (Irregular Update Periods, IUP): and adjusting the updating period according to the pulse interval of the pseudo-satellite time hopping navigation signal to obtain the baseband signal tracking error estimated value. Another aspect includes a navigation filtering method based on error observance prediction (Predicted Measurements, PM): and extrapolating tracking errors estimated by different channel prefilters to the same moment to obtain synchronous navigation filtering observables, then obtaining a navigation error estimated value, and then completing Line-of-Sight (LOS) projection and channel feedback correction.
The technical scheme of the invention is as follows:
the invention provides a vector tracking method suitable for time hopping navigation signals, which applies vector tracking in the processing of pseudo-satellite time hopping navigation signals and provides a Kalman channel pre-filtering method based on IUP and a navigation filtering method based on PM according to the characteristics of the pseudo-satellite time hopping navigation signals, and mainly comprises the following steps:
the first step, a channel prefilter is designed, and in a vector tracking architecture, the channel prefilter carries out filtering processing on in-phase and quadrature path integral values of a baseband signal, so that the effects of estimating and smoothing tracking errors are achieved, and meanwhile, an output result of the channel prefilter provides an input observed quantity for a subsequent navigation filter.
First, a system model of the channel prefilter is built. According to the linear system theory, the equivalent discretization model of the Kalman filtering continuous time system equation is as follows:
Δx k，1 ＝F k|k-1，1 ·Δx k-1，1 +Γ k，1 W k，1
wherein ,Δxk，1 Is a state vector in an IUP-based channel pre-filter; subscript '1' denotes the channel prefilter and subscript k denotes the epoch number of the loop update; f (F) k|k-1，1 Representing a state transition matrix Γ k，1 Driving the matrix for discrete process noise, w k，1 Is a discrete process noise vector. The invention designs the state vector delta x in the IUP-based channel prefilter k，1 Can be expressed as:
Δx k，1 ＝[Δτ k ，Δφ k ，Δf k ，Δα k ] T
wherein ,Δτk Representing code phase error, delta phi k Representing carrier phase error, Δf k and Δαk The carrier doppler error and the carrier doppler change rate error are represented respectively. The superscript T denotes a transpose.
If the update period of the navigation signal tracking loop when the pseudo satellite is marked to jump is T k The state transition matrix of the IUP channel prefilter proposed by the present invention can be expressed as:
wherein ,f code representing the spread spectrum code rate, f c Is the carrier frequency.
In a conventional channel pre-filter for GNSS applications, the period T is updated k Normally constant coherent integration time T cor In the present invention, however, the pre-filtering time update period T is used to more accurately estimate the error state information of the pseudo-satellite time-hopping navigation signal tracking k Will vary with the pulse interval. Accordingly, the process noise covariance matrix of the IUP channel prefilter also changes with each epoch update period, denoted as:
wherein ,Qk，1 A process noise covariance matrix for the IUP channel prefilter; e [. Cndot.]Representing computational mathematical expectations; q (Q) code 、Q b 、Q d 、Q Los Process noise covariance matrices related to code phase, receiver clock frequency, and line of sight (LOS) acceleration jitter, respectively; q τ 、q b 、q d 、q α Process noise power spectral densities for code phase, receiver clock frequency, and line-of-sight acceleration, respectively; omega rf Is the carrier circular frequency; c is the speed of light.
According to the IUP channel prefilter system state equation, the channel error state information estimated by the previous epoch is utilized to carry out prior estimation, so as to obtain the channel error state of the current epoch and covariance thereof, which are expressed as:
wherein ,a posterior estimate representing the state quantity of the k-1 th epoch channel error,/and>representing a priori estimates of the state quantity of the k-th epoch channel error, P k-1，1 A posteriori estimated covariance representing k-1 epoch channel error state quantity, P k|k-1，1 Representing the k epoch a priori estimated covariance matrix.
Then, establishing a channel prefilter observation model;
the observed quantity of the channel prefilter is the code phase error output by the discriminatorError with carrier phase>Thus, the observation vector z k，1 The method comprises the following steps:
wherein ,for average code phase error +.>Is the average carrier phase error.
The observation equation for the channel pre-filter can be constructed as:
z k，1 ＝H 1 Δx k，1 +v k，1
wherein ,H1 To observe the matrix, v k，1 Is w is equal to k，1 Irrelevant zero-mean Gaussian white noise with noise covariance matrixdiag[·]Representing diagonal elements of the matrix. The observed noise variance of the phase detector output is expressed as:
wherein ,C/N0 T is the carrier to noise ratio s Representing the slot length, i.e. the single pulse integration time. Observed quantity z k，1 And an error state quantity Deltax k，1 The relationship between can be modeled as follows:
thus, a constant observation matrix H can be obtained k，1 The method comprises the following steps:
the IUP channel pre-filtering gain K can be calculated according to the observation model k，1 And the posterior estimation of the channel prefilter error state quantity and the covariance thereof is completed:
P k，1 ＝(I 4×4 -K k，1 H k，1 )P k|k-1，1
second, a navigation filter is designed, including an error observance Prediction (PM) module, an extended Kalman filter (Extended Kalman Filter, EKF) module, and an LOS mapping module.
First, the PM module completes channel error observables prediction. In order to solve the problem of asynchronous observed quantity input by the navigation filter, according to one embodiment of the invention, a PM module is added in the navigation filter, and a mathematical model is described as follows:
wherein ,λc ＝c/f code and λr ＝c/f c Representing the pseudo code length and carrier wavelength respectively, and />Representing pseudo-range and pseudo-range rate errors, respectively, +.>And the difference between the sampling time of the navigation filter and the completion posterior estimation time of each channel pre-filter is represented. The output of the channel prefilter in the first step is utilized to obtain the pseudo-range and pseudo-range rate after synchronization according to the mathematical modelError observables.
Then, the PVT error state of the EKF module in the navigation filter is updated in time;
position, velocity and time (PVT) error state vectors in the EKF are as follows:
wherein Δx, Δy, Δz andthe positioning and velocity measurement errors of the receiver under the XYZ rectangular coordinate system are respectively represented, the delta b and delta d represent the clock error and Zhong Piao error of the receiver, the subscript '2' refers to the EKF, and the subscript k refers to the kth navigation filter update epoch. The system state vector can be described as a first order gaussian-markov process whose discrete system state equations are as follows:
Δx k，2 ＝F k|k-1，2 ·Δx k-1，2 +Γ k，2 W k，2
wherein ,Γk，2 w k，2 As process noise, its covariance matrix is Q k，2 ，F k|k-1，2 Is an EKF state transition matrix. According to one embodiment, the update interval of the EKF is equal to the sub-frame period T of the pseudolite time-hopping navigation signal f I.e. F k|k-1，2 Can be expressed as:
wherein ,I3×3 Representing a three-order unit array, T f ＝N s T s Representing the subframe period, N s F for the number of slots in each subframe t Can be expressed as:
according to the EKF system state equation, the time update process can be expressed as:
then, the PVT error state is observed and updated;
based on the observed quantity predicted value calculated by the PM module, the observed vector of the EKF can be expressed as:
the pseudo-range equation for the ith pseudolite time-hopped navigation signal may be modeled as follows:
wherein ,representing corrected pseudoranges b k Representing receiver clock error, < >>Representing pseudo-range noise->For the observation vector length of the ith pseudolite base station at the receiver, namely:
wherein ,xi 、y i 、z i Representing the ith pseudolitePosition of base station, x k 、y k 、z k Representing the receiver position of the kth epoch. Since the location of pseudolite base stations is typically fixed, the EKF does not update the location of the base station every epoch. Linearizing the pseudo-range equation using a first-order taylor expansion to obtain a pseudo-range errorThe following are provided:
record unit observation vector and />Respectively represent unit observation vector +.>Components in the X-axis, Y-axis and Z-axis directions, namely:
then likewise, the pseudo-range rate errorCan be expressed as:
the observation equation for EKF can be established as follows:
z k，2 ＝H k，2 ·Δx k，2 +v k，2
wherein ,vk，2 For observing noise, the covariance matrix is R k，2 . Observing a transfer matrix H k，2 The method comprises the following steps:
based on the established EKF observation model, the EKF gain K can be calculated k，2 Posterior estimation of the state quantity and covariance of the state quantity and the EKF error, thereby finishing EKF observation updating:
P k，2 ＝(I 8×8 -K k，1 H k，2 )P k|k-1，2
finally, the LOS mapping module is utilized to complete the line-of-sight projection and channel feedback correction, so that the vector tracking suitable for the pseudo-satellite time hopping navigation signal is realized;
the purpose of the LOS mapping is to convert the receiver navigation error state vector estimated by the EKF into the code phase and carrier doppler error amounts for each channel and feed back to the numerically controlled oscillator (Numerically Controlled Oscillator, NCO). The feedback correction amount of each channel NCO is calculated by:
wherein , and />Pseudo-range estimates and pseudo-range observations for the kth EKF filtered epoch, +.> and />The estimated and observed values of the pseudo-range rate for the kth EKF filtered epoch, respectively.
The invention also provides a vector tracking device suitable for time-hopping navigation signals, which mainly comprises: a pulse control module, an integral clear (I & D) module, a discriminator, an IUP pre-filter, and a navigation filter. The navigation filter in turn includes a PM module, an EKF module, and an LOS mapping module.
The pulse control module is used for calculating the time interval of two adjacent effective time slots according to the locally repeated pseudo-random time hopping sequence;
the integral zero clearing (I & D) module is used for integrating the pseudolite signals in the effective time slot, so that noise of a silent time slot and the interference of other pseudolite time-hopping navigation signals are avoided;
the discriminator is used for outputting carrier phase error and code phase error;
the IUP pre-filter is used for carrying out Kalman filtering estimation according to the carrier phase error and the code phase error result and outputting an error state quantity;
the PM module is used for extrapolating the error observed quantity to the same moment and is used as the input observed quantity of the EKF module to reduce the noise of the input observed quantity of each channel;
the EKF module is used for carrying out fusion filtering on all channel observables;
the LOS mapping module is used for projecting estimated position and velocity correction amounts onto the line of sight, and the generated feedback amounts are used for adjusting the doppler and code phase values of each channel.
Compared with the prior art, the invention has the beneficial technical effects that:
the Kalman filter is adopted in the channel pre-filtering, and the updating period is adjusted according to the pulse interval of the pseudo-satellite time-hopping navigation signal, so that the problem that the traditional phase-locked loop cannot timely correct the phase error caused by the updating period of the time-varying loop is avoided, and the carrier wave and code tracking precision of the pseudo-satellite time-hopping navigation signal is improved.
Aiming at the problem that the time of the posterior estimation of each channel prefilter is not synchronous, the invention extrapolates the tracking errors estimated by different channel prefilters to the same moment, thereby obtaining synchronous navigation filtering observables, avoiding the performance degradation of the navigation filter, and improving the stability of the vector tracking loop and the positioning and speed measuring precision of the receiver.
Drawings
Fig. 1 shows a single pulse integration pattern and time-hopping pulse time interval of a pseudolite time-hopping navigation signal.
Fig. 2 shows the relationship between the observed sampling moments of each channel input to the navigation filter of the present invention.
Fig. 3 shows a block flow diagram of a method of time-hopped navigation signal vector tracking in accordance with one embodiment of the present invention.
Detailed Description
The objects, technical solutions and advantages of the present invention will become more apparent by the following detailed description of the present invention with reference to the accompanying drawings. It should be understood that the description is only illustrative and is not intended to limit the scope of the invention.
The invention provides a vector tracking method suitable for a time-hopping navigation signal, which comprises the following steps:
firstly, modeling an intermediate frequency signal in a pseudo satellite positioning system;
in a pseudolite positioning system, a time hopping signal transmitted by a pseudolite base station is transmitted for a certain distance, then received by a receiving antenna of a receiver, and is changed into an intermediate frequency signal after being processed by a low noise amplifier, down-conversion, filtering and the like, and the mathematical model of the intermediate frequency signal is as follows:
wherein ,Srx (t) is a received intermediate frequency signal; n (N) BS Representing the number of pseudolite base stations; t represents time; superscript i denotes the ith pseudolite base station signal, a i For receiving signal amplitude τ i Representing propagation delay of pseudolite time-hopping navigation signal, D i (t-τ i ) PN for navigation of text data i Representing pseudo-random code, f IF Represents the intermediate frequency (if) frequency,indicating doppler shift due to receiver motion and clock drift,/->For initial carrier phase offset, H i (t-τ i ) Representing a pseudo-random time hopping sequence, n (t) is gaussian white noise.
Step two, acquiring a pseudo satellite time hopping navigation signal reproduced locally by a receiver;
the ith pseudolite time hopping navigation signal reproduced locally by the receiver can be expressed as follows:
wherein ,a pseudo-satellite time hopping navigation signal representing local reproduction; />Representing the frequency of local reproduction, +.> and />Representing locally estimated Doppler frequency values and code phases, respectivelyDelay (I)>For locally reproduced pseudo code, +.>Is a locally recurring pseudo-random time hopping sequence.
Thirdly, mixing the received signal with a locally reproduced pseudo satellite time hopping navigation signal to obtain a baseband signal;
in the tracking stage of the pseudo-satellite time-hopping navigation signal, the pulse control module can be used for starting a tracking channel only when an effective pulse signal arrives, so that noise of a silence time slot and interference of other pseudo-satellite signals are avoided being introduced during integration, and the loss of signal-to-noise ratio is reduced as much as possible. The baseband signal after mixing the received signal with the local reproduction signal is as follows:
wherein ,representing baseband signal +.> When the receiver is in a steady tracking state, the local reproduction frequency f rep Near the frequency of the received signal, i.eTherefore, these two frequency quantities in the baseband signal satisfy: Δf i ≈0，/> Is a high-frequency component, and can be filtered after integration and filtration; and Δf i The low frequency component is an error amount which needs to be emphasized in the tracking process, and the purpose is to make the frequency error tend to zero as much as possible so as to improve the precision and stability of carrier tracking. When the loop is stably tracked, it can be considered +.>The in-phase and quadrature branches of the baseband signal can be expressed as:
wherein ,i i (t) represents an in-phase branch, q i And (t) represents an orthogonal branch. Subscript X represents the locally recurring Early (E), immediate (P), or Late (Late, L) code phase. d, d X Represents the code phase of the X-way and has d E ＝d、d P ＝0、d L = -d, d represents the correlator interval, typically half chip length. The first term in square brackets is the low frequency signal component and the second term is the high frequency signal component.
Fourth, obtaining normalized coherent integration results output by an integration-zero clearing module;
after the mixing is completed to obtain a baseband signal, the receiver correlates the local E, P, L three pseudo codes with the baseband signal, and completes the single pulse integration-zero clearing operation of the signal in an effective time slot under the control of a pulse signal generator, thereby obtaining a normalized coherent integration result. Fig. 1 illustrates a single pulse integration scheme and time-hopping pulse time interval of a pseudolite time-hopping navigation signal. Since the tracking loop is only activeWhen the pulse time slot arrives, single pulse coherent integration is carried out, and the coherent integration time is the duration T of one pulse time slot s Therefore, the normalized coherent integration result of the same-phase branch of the P paths is as follows:
wherein ,representing code phase estimation error,/->Indicating the end time of the active pulse slot during the kth loop update, i.e. +.>For sub-frame period, N s For the number of time slots in each subframe, k represents the number of epoch updated by the loop, which is equivalent to the fact that the current effective pulse is in the kth subframe; />Representing the i-th pseudolite base station in the k-th subframe>The signal is transmitted in time slots. Phase error->Gain factor->Since coherent integration is only performed in an effective time slot, the modulated data information bit Di (t) does not change according to the characteristics of the pseudolite time hopping navigation signal. R (delta tau) i ) The autocorrelation function representing the pseudo code is at δτ i The value at (single pulse time T s Identical to the pseudo code period).
Similarly, the normalized coherent integration result of the orthogonal branch of the P-path is:
thus, the coherent integration results of the leading and lagging paths can be obtained as follows:
fifthly, obtaining the output of the carrier phase and code phase discriminator by using the coherent integration result;
according to the instant road integral result and />The carrier phase discriminator results in:
the above shows that the output of the phase detector is approximately the average phase error between the received signal and the local reproduction signal in the active slot, andis subjected to Deltaf i 、T s and />Influence. The amount of change in the phase detector output of adjacent epochs during each tracking period can be expressed as:
wherein ,
the time interval between the last active pulse slot and the current active pulse slot is represented, as shown in fig. 1, and is determined by a pseudo-random sequence. Whereas for GNSS continuous signals +.>Is generally constant as a coherent integration time T cor . Similarly, according to the integration results of the advance path and the retard path, the output of the code phase discriminator adopting the normalized advance-minus-retard amplitude method is as follows: />
wherein ,
due to code phase errorsAnd is also mainly caused by relative motion, so there is a correspondence with carrier doppler,the following can also be described:
wherein ,f code representing the spread spectrum code rate, f c Is the carrier frequency. Similarly, the amount of change in the output of the adjacent epoch code phase discriminator is:
the loop update period is fixed while tracking the GNSS continuous signal, and thereforeAlso constant, conventional tracking loops are able to accurately estimate and correct frequency errors. While in tracking the pseudolite time-hopping navigation signal +.>Along with->Changes in (a) and (b)>And the same is true. If the tracking loop ignores->The frequency error will not be accurately estimated, resulting in degradation of the loop tracking performance.
Sixthly, completing Kalman channel prefiltering based on irregular updating period;
GNSS signal carrier tracking usually adopts a Phase Lock Loop (PLL) based on wiener filtering, and the filtering parameters are fixed, but when the navigation signal is tracked when pseudo satellite is jumped, the PLL cannot correct the Phase error caused by the time-varying Loop update period in time, so that the performance of carrier tracking and code tracking is reduced. The Kalman filtering utilizes a system dynamic model and a statistical model to estimate signal parameters so as to minimize the mean square error of a tracking filter, has the advantages of dynamically adjusting an updating period and a gain, and is more suitable for being used as a channel prefilter for pseudo-satellite time hopping navigation signal vector tracking. In order to solve the problem, the invention provides a Kalman channel prefilter method based on irregular updating period, which is realized by an IUP channel prefilter:
first, a channel prefilter waveform time update is performed. According to the linear system theory, the equivalent discretization model of the Kalman filtering continuous time system equation is as follows:
Δx k，1 ＝F k|k-1，1 ·Δx k-1，1 +Γ k，1 w k，1
state vector deltax in IUP channel prefilter k，1 Can be expressed as:
Δx k，1 ＝[Δτ k ，Δφ k ，Δf k ，Δα k ] T
if the update period of the navigation signal tracking loop is marked as pseudo satellite time hoppingThe state transition matrix of the channel prefilter can be expressed as: />
The above indicates F k|k-1 Is changed with the update epoch, so that the error status information can be estimated more accurately. The process noise covariance matrix of the channel pre-filter can be expressed as:
according to a state equation of the channel prefilter system, the channel error state information estimated by the previous epoch is utilized to carry out prior estimation, and the channel error state and covariance of the current epoch are obtained as follows:
then, the channel prefilter state measurement is updated. The observed quantity of the channel prefilter is the code phase error output by the discriminator in the fifth stepError with carrier phase>Thus, the observation vector z k，1 The method comprises the following steps:
the observation equation for the channel pre-filter can be constructed as:
z k，1 ＝H 1 Δx k，1 +v k，1
observed quantity z k，1 And an error state quantity Deltax k，1 The relationship between can be modeled as follows:
thus, a constant observation matrix H can be obtained k，1 The method comprises the following steps:
calculating IUP channel pre-filtering gain K according to the measurement model k，1 And the posterior estimation of the channel prefilter error state quantity and the covariance thereof is completed:
P k，1 ＝(I 4×4 -K k，1 H k，1 )P k|k-1，1
seventhly, completing navigation filtering based on error observational quantity prediction;
in the vector tracking loop, the navigation filter takes the tracking error amount of each channel as an input observed amount, and the observed amount needs to be sampled at the same time, so that the fusion filter can obtain more accurate NCO feedback correction amount. For the pseudo-satellite time-hopping navigation signal, the posterior estimation of the pre-filter can only reflect the tracking error before the end of the current effective pulse time slot; and the time for each tracking channel prefilter to finish the posterior estimation is asynchronous because the effective time slots of each time-hopping signal pseudo-random change are not overlapped.
Fig. 2 illustrates the relationship between the observed amount sampling times of each channel input to the navigation filter. The position indicated by the dashed arrow in the figure is the sampling instant of the navigation filter, while the position indicated by the solid arrow represents the error estimation instant of the respective tracking channel, and the grey shading represents the time-varying time difference between the two instants. If the posterior error estimated value of each channel pre-filter is directly used as the observed quantity of the navigation filter, the tracking error of the gray shade part cannot be reflected, and the performance of the navigation filter in the traditional VTL algorithm is degraded, so that the VTL algorithm needs to be designed according to the pseudo-random pulse characteristics of the pseudo-satellite time-hopping navigation signals.
Aiming at the problem, the invention provides a navigation filtering method based on error observance prediction, which is realized by a navigation filter and comprises a PM module, an EKF module and an LOS mapping module:
first, the PM module completes channel error observables prediction. In order to solve the problem of asynchronous observance quantity input by the navigation filter, according to one embodiment of the invention, an observance quantity prediction module is added in the navigation filter, and a mathematical model is described as follows:
/>
and utilizing the output of the prefilter in the sixth step, the synchronized pseudo-range and pseudo-range rate error observed quantity can be obtained according to the mathematical model.
Then, PVT error state time update of the EKF module in the navigation filter is carried out. The position, velocity and time error state vectors in the EKF are as follows:
the system state vector can be described as a first order gaussian-markov process whose discrete system state equations are as follows:
Δx k，2 ＝F k|k-1，2 ·Δx k-1，2 +Γ k，2 w k，2
according to one embodiment, the update interval of the EKF is equal to the sub-frame period of the pseudolite time-hopping navigation signal, F k|k-1，2 Can be expressed as:
according to the EKF system state equation, the time update process can be expressed as:
next, PVT error state observation update is performed. Based on the observed quantity predicted value calculated by the PM module, the observed vector of the EKF can be expressed as:
the observation equation for EKF can be established as follows:
z k，2 ＝H k，2 ·Δx k，2 +v k，2
wherein ,vk，2 For observing noise, the covariance matrix is R k，2 . Observing a transfer matrix H k，2 The method comprises the following steps:
according to the established EKF observation modelThe EKF gain K can be calculated k，2 Posterior estimation of the state quantity and covariance of the state quantity and the EKF error, thereby finishing EKF observation updating:
/>
P k，2 ＝(I 8×8 -K k，1 H k，2 )P k|k-1，2
and finally, completing the line-of-sight projection and channel feedback correction by using an LOS mapping module. The purpose of the LOS mapping is to convert the receiver navigation error state vector estimated by the EKF into the code phase and carrier doppler error amounts of each channel and feed back to the NCO. The feedback correction amount of each channel NCO is calculated by:
in summary, a block diagram of a system structure implemented by the time-hopping navigation signal vector tracking method according to an embodiment of the present invention is shown in fig. 3, and the pseudo-satellite time-hopping navigation signal vector tracking system mainly includes: pulse control module, integral zero clearing (I)&D) A module, a discriminator, an IUP pre-filter and a navigation filter. The navigation filter further comprises a PM module, an EKF module and an LOS mapping module. As shown in fig. 3, the pulse control module is based on a locally recurring pseudo-random time hopping sequence H i (t) calculating the time interval between two adjacent active time slotsIntegral zero clearing (I)&D) The module performs pseudolite signal processing in effective time slotLine integration, avoiding noise introduced into silent time slots and interference of other pseudo satellite time hopping navigation signals; the discriminator outputs carrier phase error->Error of code phase>IUP prefilter is based on-> and />Carrying out Kalman filtering estimation on the result and outputting an error state quantity; the PM module extrapolates the error observables to the same moment and is used as the input observables of the EKF module, so that the noise of the input observables of each channel is reduced; the EKF module performs fusion filtering on observed quantities of all channels; the LOS mapping module projects the estimated position and velocity corrections onto the line of sight, and the resulting feedback amounts are used to adjust the doppler and code phase values for each channel.
It should be understood that the above-described embodiments of the present invention are merely illustrative of or explanation of the principles of the present invention and are in no way to be construed as limiting of the present invention, and therefore any modifications, equivalent substitutions, improvements, etc. made without departing from the scope of the invention are intended to be included in the scope of the present invention. Furthermore, the appended claims are intended to cover all such changes and modifications that fall within the scope and boundary of the appended claims or the equivalents of such scope and boundary.
Claims (10)
1. A vector tracking method suitable for time hopping navigation signals is characterized in that vector tracking is used for processing pseudo-satellite time hopping navigation signals, and Kalman channel prefiltering based on irregular update period IUP and navigation filtering based on error observance prediction PM are designed according to the pseudo-satellite time hopping navigation signals; then, line-of-sight projection and channel feedback correction are completed by utilizing line-of-sight LOS mapping, so that vector tracking applicable to pseudo-satellite time hopping navigation signals is realized; the method comprises the following steps:
firstly, designing a channel prefilter;
the in-phase and quadrature path integral values of the baseband signals are filtered through the channel prefilter, the in-phase and quadrature path integral values are used for estimating and smoothing tracking errors in vector tracking, and meanwhile, an output result of the channel prefilter provides input observables for the navigation filter; comprising the following steps:
11 A system model of the channel prefilter is established; the equivalent discretized model of the Kalman filter continuous time system equation is expressed as:
Δx k,1 ＝F k|k-1,1 ·Δx k-1,1 +Γ k,1 w k,1
wherein ,Δxk,1 Is a state vector in an IUP-based channel pre-filter; subscript '1' denotes the channel prefilter and subscript k denotes the epoch number of the loop update; f (F) k|k-1,1 Representing a state transition matrix Γ k,1 Driving the matrix for discrete process noise, w k,1 Is a discrete process noise vector;
12 Establishing a channel prefilter observation model;
the observed quantity of the channel prefilter is the code phase error output by the discriminatorError with carrier phase>Observation vector z k,1 Expressed as:
wherein ,for average code phase error +.>For average carrier phase error, superscript T represents transpose;
an observation equation of the channel prefilter is constructed, expressed as:
z k,1 ＝H 1 Δx k,1 +v k,1
wherein ,H1 To observe the matrix, v k,1 Is w is equal to k,1 An irrelevant zero-mean gaussian white noise; noise covariance matrixdiag[·]Diagonal elements representing a matrix;
the observed noise variance of the phase detector output is expressed as:
wherein ,C/N0 T is the carrier to noise ratio s Representing the slot length, i.e., the single pulse integration time;
observed quantity z k,1 And an error state quantity Deltax k,1 The relationship between the two is modeled as follows:
obtaining a constant observation matrix H k,1 Expressed as:
calculating IUP channel prefilter gain K according to observation model k,1 And complete a posterior estimation of the channel pre-filter error state quantity and covariance, expressed as:
P k,1 ＝(I 4×4 -K k,1 H k,1 )P k|k-1,1
secondly, designing a navigation filter, wherein the navigation filter comprises an error observance prediction PM module, an extended Kalman filter EKF module and an LOS mapping module; comprising the following steps:
21 The PM module is used for completing channel error observed quantity prediction;
the model of the PM module is expressed as:
wherein ,λc ＝c/f code and λr ＝c/f c Representing the pseudo code length and carrier wavelength respectively, and />Representing pseudo-range and pseudo-range rate errors, respectivelyDifference (S)>Representing the difference between the sampling time of the navigation filter and the completion posterior estimation time of each channel pre-filter;
the output of the channel prefilter in the first step is utilized, so that the synchronized pseudo range and pseudo range rate error observed quantity can be obtained according to the mathematical model;
22 Time updating the PVT error state of the EKF module in the navigation filter;
the position, velocity and time PVT error state vectors in the EKF are expressed as:
wherein Δx, Δy, Δz andrespectively representing the positioning and speed measurement errors of the receiver under an XYZ rectangular coordinate system, wherein Deltab and Deltad respectively represent the clock error and Zhong Piao error of the receiver, the subscript '2' refers to EKF, and the subscript k refers to the kth navigation filter update epoch; the discrete system state equation for the system state vector is expressed as follows:
Δx k,2 ＝F k|k-1,2 ·Δx k-1,2 +Γ k,2 w k,2
wherein ,Γk,2 w k,2 As process noise, its covariance matrix is Q k,2 ，F k|k-1,2 Is an EKF state transition matrix;
the time update procedure is expressed as:
23 Performing observation and update of PVT error states;
according to the observed quantity predicted value calculated by the PM module, the observed vector of the EKF is expressed as:
the pseudo range equation for the ith pseudolite time hopping navigation signal is modeled as follows:
wherein ,representing corrected pseudoranges b k Representing receiver clock error, < >>Representing pseudo-range noise->The length of the observation vector at the receiver for the ith pseudolite base station;
linearizing the pseudo-range equation using a first-order taylor expansion to obtain a pseudo-range errorExpressed as:
record unit observation vector and />Respectively represent unit observation vector +.>Components in the X-axis, Y-axis and Z-axis directions, namely:
pseudo range rate errorExpressed as:
an observation equation of EKF was established, expressed as:
z k,2 ＝H k,2 ·Δx k,2 +v k,2
wherein ,vk,2 For observing noise, the covariance matrix is R k,2 The method comprises the steps of carrying out a first treatment on the surface of the The observation transfer matrix is H k,2 ；
Calculating EKF gain K according to the established EKF observation model k,2 Posterior estimation of the state quantity and covariance of the state quantity and the EKF error, so that EKF observation updating is completed; expressed as:
P k,2 ＝(I 8×8 -K k,1 H k,2 )P k|k-1,2
24 The LOS mapping module is used for completing line-of-sight projection and channel feedback correction, and vector tracking applicable to time-hopping navigation signals is realized.
2. The method for vector tracking for a time-hopped navigational signal according to claim 1 wherein the state vector Δx in the IUP based channel prefilter k,1 Expressed as:
Δx k,1 ＝[Δτ k ,Δφ k ,Δf k ,Δα k ] T
wherein ,Δτk Representing code phase error, delta phi k Representing carrier phase error, Δf k and Δαk Respectively representing carrier Doppler error and carrier Doppler change rate error; the superscript T denotes a transpose.
3. The vector tracking method for a time-hopped navigational signal according to claim 2 wherein the state transition matrix of the IUP channel prefilter is expressed as:
wherein ,f code representing the spread spectrum code rate, f c Is the carrier frequency; t (T) k And (3) tracking the update period of the loop for the pseudo-satellite time hopping navigation signal.
4. A method for vector tracking for time-lapse navigation signals as claimed in claim 3, wherein the pre-filter time is updated by a period T k As the pulse interval changes; the process noise covariance matrix of the IUP channel prefilter also changes with each epoch update period, denoted as:
wherein ,Qk,1 A process noise covariance matrix for the IUP channel prefilter; e [. Cndot.]Representing computational mathematical expectations; q (Q) code 、Q b 、Q d 、Q LOS Process noise covariance matrices related to code phase, receiver clock frequency, and line-of-sight acceleration jitter, respectively; q τ 、q b 、q d 、q α Process noise power spectral densities for code phase, receiver clock frequency, and line-of-sight acceleration, respectively; omega rf Is the carrier circular frequency; c is the speed of light.
5. The method for vector tracking for a time-lapse navigation signal according to claim 4, wherein the channel error state information estimated by the previous epoch is used for a priori estimation according to the IUP channel prefilter system state equation to obtain the channel error state of the current epoch and covariance thereof, expressed as:
wherein ,a posterior estimate representing the state quantity of the k-1 th epoch channel error,/and>representing a priori estimates of the state quantity of the k-th epoch channel error, P k-1,1 A posteriori estimated covariance representing k-1 epoch channel error state quantity, P k|k-1,1 Representing the k epoch a priori estimated covariance matrix.
6. The method of vector tracking for a time-hopped navigational signal according to claim 1 wherein in step 22) the update interval of the EKF is equal to the sub-frame period T of the pseudolite time-hopped navigational signal f I.e. F k|k-1,2 Expressed as:
wherein ,I3×3 Representing a three-order unit array, T f ＝N s T s Representing the subframe period, N s F for the number of slots in each subframe t Expressed as:
7. the method for vector tracking for a time-lapse navigation signal as claimed in claim 6, wherein in step 23), the length of the observation vector of the ith pseudolite base station at the receiverExpressed as:
wherein ,xi 、y i 、z i Representing the position of the ith pseudolite base station, x k 、y k 、z k Representing the receiver position of the kth epoch.
8. The method for vector tracking for a time-lapse navigation signal as claimed in claim 7, wherein the observation transition matrix H k,2 Expressed as:
calculating EKF gain K according to the established EKF observation model k,2 Posterior estimation of the state quantity and covariance of the state quantity and the EKF error, so that EKF observation updating is completed; expressed as:
P k,2 ＝(I 8×8 -K k,1 H k,2 )P k|k-1,2 。
9. the method for vector tracking of time-lapse navigation signals according to claim 8, wherein in step 24), the receiver navigation error state vector estimated by EKF is converted into the code phase and carrier doppler error values of each channel through LOS mapping and fed back to the numerically controlled oscillator NCO; the feedback correction amount of each channel NCO is calculated by:
wherein , and />Pseudo-range estimates and pseudo-range observations for the kth EKF filtered epoch, +.> and />The estimated and observed values of the pseudo-range rate for the kth EKF filtered epoch, respectively.
10. An apparatus implemented using the vector tracking method for time-lapse navigation signals of claim 1, comprising: the device comprises a pulse control module, an integral zero clearing I & D module, a discriminator, an IUP pre-filter and a navigation filter; the navigation filter comprises a PM module, an EKF module and an LOS mapping module;
the pulse control module is used for calculating the time interval of two adjacent effective time slots according to the locally repeated pseudo-random time hopping sequence; the integral zero clearing I & D module is used for integrating pseudolite signals in an effective time slot, so that noise of a silent time slot and interference of other pseudolite time-hopping navigation signals are avoided; the discriminator is used for outputting carrier phase error and code phase error;
the IUP pre-filter is used for carrying out Kalman filtering estimation according to the carrier phase error and the code phase error result and outputting an error state quantity;
the PM module is used for extrapolating the error observed quantity to the same moment and is used as the input observed quantity of the EKF module to reduce the noise of the input observed quantity of each channel; the EKF module is used for carrying out fusion filtering on all channel observables; the LOS mapping module is used for projecting estimated position and velocity correction amounts onto the line of sight, and the generated feedback amounts are used for adjusting the doppler and code phase values of each channel.
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| CN116819576B (en) * | 2023-08-31 | 2023-11-10 | 中国科学院空天信息创新研究院 | Pseudo satellite time hopping signal tracking method based on time hopping pattern gating or parameter tracing |
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