CN111444663A - Kalman tracking loop design method, Kalman tracking loop and aerospace vehicle - Google Patents

Kalman tracking loop design method, Kalman tracking loop and aerospace vehicle Download PDF

Info

Publication number
CN111444663A
CN111444663A CN202010165702.0A CN202010165702A CN111444663A CN 111444663 A CN111444663 A CN 111444663A CN 202010165702 A CN202010165702 A CN 202010165702A CN 111444663 A CN111444663 A CN 111444663A
Authority
CN
China
Prior art keywords
plasma sheath
kalman
amplitude attenuation
phase
phase shift
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010165702.0A
Other languages
Chinese (zh)
Other versions
CN111444663B (en
Inventor
石磊
包为民
吕跃广
袁淑容
李小平
刘彦明
姚博
魏海亮
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN202010165702.0A priority Critical patent/CN111444663B/en
Publication of CN111444663A publication Critical patent/CN111444663A/en
Application granted granted Critical
Publication of CN111444663B publication Critical patent/CN111444663B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Radio Relay Systems (AREA)
  • Plasma Technology (AREA)

Abstract

The invention belongs to the technical field of aerospace craft measurement and control communication, and discloses a Kalman tracking loop design method, a Kalman tracking loop and an aerospace craft.A time-varying plasma sheath model is established and the amplitude attenuation and the phase shift of a received signal under a plasma sheath are calculated; establishing an autoregressive model of amplitude attenuation and calculating the statistical characteristic of phase shift; designing a state equation and an observation equation of a Kalman filter; designing a novel Kalman tracking loop of the hypersonic aircraft; analyzing the amplitude attenuation and the phase shift of a received signal under a plasma sheath channel, calculating an autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift, and designing a Kalman filter suitable for the plasma sheath channel; and considering the amplitude attenuation of the received signal under the action of the plasma sheath in the design of a tracking loop, and establishing a Kalman filter for simultaneously tracking the amplitude attenuation and the phase of the received signal. The method provides a new idea for the stable signal tracking of the hypersonic aircraft.

Description

Kalman tracking loop design method, Kalman tracking loop and aerospace vehicle
Technical Field
The invention belongs to the technical field of measurement and control communication of aerospace vehicles, and particularly relates to a Kalman tracking loop design method, a Kalman tracking loop and an aerospace vehicle, in particular to a novel Kalman tracking loop design method for a hypersonic aircraft.
Background
At present, due to the characteristics of high flying speed and large maneuvering range of a hypersonic aerocraft in a near space, a receiver receiving signal has large Doppler frequency shift and high-order derivatives. In addition, when the hypersonic aircraft penetrates the atmosphere, a plasma sheath covering the surface of the aircraft can absorb, reflect and scatter electromagnetic waves, and electromagnetic signals can generate severe amplitude attenuation and phase shift after passing through the plasma sheath. Therefore, the design of the carrier tracking loop of the hypersonic aircraft is challenged by multiple factors such as large dynamic Doppler frequency offset, severe amplitude attenuation and phase shift.
The first method does not consider the influence of amplitude noise of a received signal, the bandwidth of the loop filter is a constant value, the large dynamic Doppler requires that the bandwidth of the loop filter is large, the low signal-to-noise ratio requires that the bandwidth of the loop filter is small, the contradiction between a large broadband and high precision cannot be balanced, and the carrier tracking capability of the traditional phase-locked loop is sharply reduced under the conditions of high dynamic low signal-to-noise ratio and serious plasma sheath amplitude attenuation.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) the existing tracking loop has the defects that the loop bandwidth is required to be larger due to large dynamic Doppler and smaller loop bandwidth is required due to low signal-to-noise ratio under the dual severe conditions of large dynamic Doppler and a plasma sheath channel.
(2) The traditional tracking loop uses the fixed value of the bandwidth of a loop filter, and can not balance the contradiction between large bandwidth and high precision.
(3) The traditional tracking loop works in a scene that the signal amplitude attenuation can be generally ignored or is a fixed value, the received signal amplitude attenuation of the hypersonic aircraft has fast time-varying property, and the traditional tracking loop is very easy to lose lock under the hypersonic scene due to the influence of the time-varying amplitude attenuation.
The difficulty in solving the above problems and defects is:
the hypersonic aircraft receive signal is severely amplitude attenuated by the plasma sheath effect. In the traditional tracking loop, the amplitude attenuation of the received signal is ignored in the tracking process, and the influence of large dynamic Doppler frequency offset and Doppler acceleration on the received signal can only be overcome. In a hypersonic environment, the amplitude attenuation of the received signal can cause the phase-locked loop to lose lock and cannot be ignored. How to consider the amplitude attenuation of the received signal in the loop design is a difficult point of realizing carrier stable tracking of the phase-locked loop under the plasma sheath.
The significance of solving the problems and the defects is as follows:
the invention provides a Kalman tracking loop design method, realizes the steady tracking of a received signal in a hypersonic environment, and provides a new idea for designing a receiver tracking loop with serious amplitude attenuation.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a Kalman tracking loop design method, a Kalman tracking loop and a space vehicle.
The Kalman tracking loop design method is realized by establishing a time-varying plasma sheath model and calculating the amplitude attenuation and phase shift of a received signal under a plasma sheath; establishing an autoregressive model of amplitude attenuation and statistical characteristics of phase shift; designing a state equation and an observation equation of a Kalman filter; designing a novel Kalman tracking loop of the hypersonic aircraft; analyzing the amplitude attenuation and the phase shift of a received signal under a plasma sheath channel, calculating an autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift, and designing a Kalman filter suitable for the plasma sheath channel; and considering the amplitude attenuation of the received signal under the action of the plasma sheath in the design of a tracking loop, and establishing a Kalman filter for simultaneously tracking the amplitude attenuation and the phase of the received signal.
Further, the kalman tracking loop design method includes:
in the first step, a time-varying plasma sheath electron density model is established to solve the amplitude attenuation r (t) of a received signaln) And phase shift
Figure BDA0002407378310000031
Determining an electron density model Ne (z) for a time-invariant plasma sheath channel using a double Gaussian modelm) (ii) a Or determining the electron density model Ne (z) of the time-invariant plasma sheath channel at different flight heights from measured data in RAM-Cm) (ii) a Time-varying plasma sheath electron density model Ne (z) is established by adding time-varying jitter delta on the basis of time-invariant electron channelm,tn) The amplitude attenuation r (t) after the signal passes through the plasma sheath is calculated according to the theory of electromagnetic wave transmission in uniform plasman) And phase shift
Figure BDA0002407378310000032
Second step, buildingMean-value-removed autoregressive model r' (t) for immediately receiving signal amplitude attenuationn) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift
Figure BDA0002407378310000033
Sum variance
Figure BDA0002407378310000034
Inputting the amplitude attenuation r (t) of the simulated received signaln) And phase shift
Figure BDA0002407378310000035
Solving by using L evison-Durbin algorithm to obtain one-time iteration coefficient α of autoregressive model2,1Coefficient of second iteration α2,2And the iterative noise variance σνObtaining an autoregressive model of the amplitude attenuation of the received signal, and calculating the mean value thereof by using the input phase shift
Figure BDA0002407378310000036
Sum variance
Figure BDA0002407378310000037
Thirdly, designing a Kalman filter and inputting phase noise upsilon generated by a tracking loop circuit1,nDoppler frequency noise v2,nDoppler acceleration noise v3,nThe covariance matrix Q of the received signal, the covariance matrix R of the observed noise at the output end of the phase discriminator, and the integration time T of the receiversCoefficient α for one iteration of an autoregressive model with mean value removed from received signal amplitude attenuation2,1Coefficient of second iteration α2,2And the iterative noise variance σνAmplitude decay mean (r (t)n) Average of received signal phase shifts)
Figure BDA0002407378310000038
Sum variance
Figure BDA0002407378310000039
State equation X for a Kalman filter for designing state variables including amplitude attenuation and phase of a received signaln＝AXn-1+BYn-1+Wn-1And observation equation Zn＝HnXn+Vn；
Fourthly, inputting a state equation of the Kalman filter: xn＝AXn-1+BYn-1+Wn-1And the observation equation: zn＝HnXn+VnActual observed value Z of phase discriminator outputnInitial value X of the observation vector0Initial value P of covariance matrix of observation vector0Initial phase θ of local oscillatorvcoAnd Doppler frequency offset w after coarse acquisitiondLoop update time TsAnd realizing a Kalman filter tracking loop under a plasma sheath channel according to the tracking step of the Kalman filter loop.
Further, the first time-varying plasma sheath channel-down amplitude attenuation and phase shift calculation setup includes:
(1) calculating the specific distribution of plasma sheath electron density at fixed times along the aircraft surface, using NASA's RAM-C measured data or a double Gaussian distribution:
Figure BDA0002407378310000041
the thickness of the sheath of the surface plasma is Z and the plasma sheath is layered into M during the flight of the input hypersonic aerocraft, wherein the thickness of each layer is dmPeak electron density ne,maxThe first Gaussian function influencing parameter σ1And a second Gaussian function influence parameter σ2Taking the value as a constant value, zTIs the plasma sheath thickness, zBFor boundary layer thickness, an electron density model Ne (z) of the time invariant plasma sheath channel is determinedm)；
(2) Calculating the electron density distribution of the time-varying plasma sheath yields a non-stationary colored noise n (t) with a standard deviation of 1n) Adding a jitter factor delta of the electron density on the basis of the time-invariant plasma sheath, and establishing a time-variant plasma sheath electron density distribution as follows:
Ne(zm,tn)＝Ne(zm)*[1+Δ*n(tn)]；
(3) calculating the amplitude attenuation coefficient and the phase shift coefficient of each layer: according to the electromagnetic wave propagation theory in the uniform plasma, inputting0Is the absolute dielectric constant in vacuum, meCalculating the characteristic frequency of the time-varying plasma according to the mass of free electrons and the number of charges of free electrons
Figure BDA0002407378310000042
Collision frequency v of input plasmaenThe angular frequency ω of the incident electromagnetic wave, the speed of light c, the signal amplitude attenuation coefficient for each layer, and the phase shift coefficient:
Figure BDA0002407378310000043
Figure BDA0002407378310000044
(4) the amplitude attenuation and phase shift of the signal across the entire plasma sheath are calculated as:
Figure BDA0002407378310000051
Figure BDA0002407378310000052
further, the second step establishes an autoregressive model r' (t) with the received signal amplitude attenuation and the mean value removedn) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift
Figure BDA0002407378310000053
Sum variance
Figure BDA0002407378310000054
Comprises the following steps:
(1) the resulting amplitude attenuation is de-averaged: solving for mean (r (t) of signal amplitude attenuationn) The signal amplitude after the mean value is removed is attenuated to r' (t)n)＝r(tn)-mean(r(tn) Mean-removed data r' (t)n) Using an autoregressive model as:
r′(tn)＝α2,1r(tn-1)+α2,2r(tn-2)+v(n)；
solving one-iteration coefficient α by using L evison-Durbin algorithm2,1Coefficient of second iteration α2,2Variance is σνWhite gaussian noise v (n);
(2) calculating the statistical properties of the phase shift: inputting simulation result of phase shift, the phase shift obeys Gaussian distribution function, and solving the mean value of the input phase shift according to the statistical characteristics of the Gaussian distribution function
Figure BDA0002407378310000055
Sum variance
Figure BDA0002407378310000056
Further, the third step of Kalman filter design includes:
(1) determining the sum local oscillator true phase difference Δ θ of the input signal at time nnExpression (c): true phase difference Δ θ from the previous time instantn-1Doppler frequency ω d at the previous timen-1Doppler acceleration wan-1Phase noise generated by plasma sheath channel
Figure BDA0002407378310000057
Noise v generated by the circuit1,nThen the true phase difference delta theta between the received signal and the local oscillator at time nnExpressed as:
Figure BDA0002407378310000058
(2) determining a state equation of the Kalman filter: obtaining a Kalman filter state equation for simultaneously tracking amplitude attenuation and carrier phase according to an autoregressive model and a kinetic equation as follows:
Figure BDA0002407378310000061
(3) determining an observation equation of a Kalman filter: observed variable ZnIs output U of the phase discriminator0(tn)i、U0(tn)qPlus observation noise, expressed as:
Figure BDA0002407378310000062
expressing the observation equation in linear form, i.e. the output h (X) of the phase detectorn) And (6) linearization is carried out.
Further, the output U of the phase discriminator0(tn)i、U0(tn)q：
1) Considering the speed and computational complexity of the phase detector, the output of the phase detector without filtering is represented as:
θe(tn)＝y(tn)×UVCO；
wherein y (t)n) For receiving signals, UVCOA carrier signal generated for a local oscillator;
2) will thetae(tn) The expression after passing through the low pass filter is taken as the final output of the phase detector:
Figure BDA0002407378310000063
further, the observation equation linearization implementation method comprises the following steps:
linearizing the observation vector ZnIs composed of
Figure BDA0002407378310000064
Is represented by Zn＝HnXn+VnSolving for HnThe method comprises the following steps:
Figure BDA0002407378310000065
obtaining:
Figure BDA0002407378310000066
further, the implementation of the tracking of the fourth Kalman filtering loop includes:
(1) pre-estimation with last moment state vector optimal value
Figure BDA0002407378310000067
(2) Pre-estimation error variance
Figure BDA0002407378310000068
(3) Kalman filter gain calculation
Figure BDA0002407378310000071
(4) Optimal state vector
Figure BDA0002407378310000072
(5) Updating the error variance Pn＝[1-KnHn]Pn,n-1；
(6) Updating the oscillation frequency w of a local oscillatorvco,n＝wd+ωdn-1And an initial phase thetavco,n＝Δθn-1
Another objective of the present invention is to provide a Kalman tracking loop obtained by the Kalman tracking loop design method, where the Kalman tracking loop includes a phase discriminator, a Kalman filter, and a local oscillator; a Kalman filter that takes into account the amplitude decay of the signal after passing through the plasma sheath.
Another object of the invention is to provide an aerospace vehicle incorporating the kalman tracking loop.
By combining all the technical schemes, the invention has the advantages and positive effects that: the method comprises the steps of establishing a time-varying plasma sheath model and calculating amplitude attenuation and phase shift of a received signal under a plasma sheath; establishing an autoregressive model of amplitude attenuation to calculate the statistical characteristic of phase shift; designing a state equation and an observation equation of the Kalman filter on the basis; and designing a novel Kalman tracking loop of the hypersonic aircraft. The method avoids the problem of lock losing caused by neglecting amplitude attenuation in the plasma sheath tracking of the traditional phase-locked loop, and provides a new idea for the stable signal tracking of the hypersonic aircraft. Aiming at the requirement of rapid measurement and control tracking of a high-speed aircraft, the invention simultaneously considers the amplitude attenuation and phase shift of a received signal and large dynamic Doppler frequency offset under the condition of a complex channel and designs a novel tracking loop based on Kalman filtering.
The invention analyzes the amplitude attenuation and the phase shift of the received signal under the plasma sheath channel, calculates the autoregressive model of the amplitude attenuation and the statistical characteristic of the phase shift, designs the Kalman filter suitable for the plasma sheath channel, and realizes the novel Kalman filter loop design under the plasma sheath channel of the hypersonic aircraft.
According to the invention, the amplitude attenuation of the received signal under the action of the plasma sheath is considered in the design of the tracking loop, and the Kalman filter for simultaneously tracking the amplitude attenuation and the phase of the received signal is established, so that the problem of loop lock loss caused by serious amplitude attenuation of the received signal is avoided; the Kalman filter is used for replacing a traditional loop filter, the bandwidth is not fixed but adjusted to an optimal value in real time in the working process, and the problem of bandwidth design conflict caused by large dynamic Doppler and low signal-to-noise ratio in the traditional loop filter is solved. The amplitude attenuation and the phase shift of the received signal of the hypersonic aircraft and related parameters can be stored on the receiver in advance, and the tracking loop only stores the value at the previous moment in work, so the algorithm has good real-time property.
Drawings
Fig. 1 is a flowchart of a kalman tracking loop design method according to an embodiment of the present invention.
Fig. 2 is a block diagram of a Kalman tracking loop provided by an embodiment of the present invention.
FIG. 3 is a diagram of a time-varying plasma density stratification model provided by an embodiment of the present invention.
Fig. 4 is a graph of amplitude attenuation under a plasma sheath provided by an embodiment of the present invention.
Fig. 5 is a phase shift diagram under a plasma sheath provided by an embodiment of the present invention.
Fig. 6 is a graph of phase tracking results of Kalman tracking loops in example 1 to example 7 according to an embodiment of the present invention.
FIG. 7 is a graph of the phase tracking results of a Kalman tracking loop at 71km for flight of an aircraft provided by an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a Kalman tracking loop design method, a Kalman tracking loop and a space vehicle, and the invention is described in detail by combining the attached drawings.
As shown in fig. 1, the kalman tracking loop design method provided by the embodiment of the present invention includes the following steps:
s101: determining a time-varying plasma model to calculate amplitude attenuation and phase shift of a received signal;
s102: calculating the statistical properties of the autoregressive model and the phase shift after the mean value of the amplitude attenuation is removed;
s103: designing a Kalman filter of which the state variable and the observation variable simultaneously consider amplitude attenuation and phase;
s104: a plasma-sheathed Kalman filter tracking loop is designed.
The technical solution of the present invention is further described with reference to the following specific examples.
Example 1
The existing tracking loop design aims at the application scenario that the signal amplitude attenuation can be ignored, the received signal amplitude attenuation under the plasma sheath channel of the hypersonic aircraft is serious, and at the moment, the traditional tracking loop is easy to lose lock. The method is used for carrying out simulation analysis on the amplitude attenuation and the phase shift of the signal under the time-varying plasma to obtain an autoregressive model of the amplitude attenuation and a statistical characteristic of the phase shift, and on the basis, a Kalman filter considering the amplitude attenuation and the phase shift of the signal is designed at the same time.
The novel Kalman tracking loop design method under the plasma sheath channel of the hypersonic aircraft comprises the following steps:
in the first step, a time-varying plasma sheath electron density model is established and the amplitude attenuation r (t) of the received signal is solvedn) And phase shift
Figure BDA0002407378310000091
Determining an electron density model Ne (z) for a time-invariant plasma sheath channel using a double Gaussian modelm). Or determining the electron density model Ne (z) of the time-invariant plasma sheath channel at different flight heights from measured data in RAM-Cm). Time-varying plasma sheath electron density model Ne (z) is established by adding time-varying jitter delta on the basis of time-invariant electron channelm,tn). The amplitude attenuation r (t) of the signal after passing through the plasma sheath is calculated according to the theory of electromagnetic wave transmission in uniform plasman) And phase shift
Figure BDA0002407378310000092
Figure BDA0002407378310000093
Figure BDA0002407378310000094
According to the invention, by establishing a time-varying plasma sheath electron density distribution model, the amplitude attenuation and the phase shift of a received signal after passing through a plasma sheath are calculated, so that an amplitude attenuation autoregressive model is established subsequently, and the statistical characteristic of the phase shift is calculated.
Secondly, establishing an autoregressive model r' (t) with the amplitude attenuation of the received signal and the mean value removedn) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift
Figure BDA0002407378310000095
Sum variance
Figure BDA0002407378310000096
Inputting the amplitude attenuation r (t) of the simulated received signaln) And phase shift
Figure BDA0002407378310000097
Solving the coefficient of one iteration α of the autoregressive model using the L evison-Durbin algorithm2,1Coefficient of second iteration α2,2And the iterative noise variance σνAnd obtaining an amplitude attenuation autoregressive model after the mean value is removed:
r′(tn)＝α2,1r(tn-1)+α2,2r(tn-2)+v(n)；
computing mean values using input phase shifts
Figure BDA0002407378310000101
Sum variance
Figure BDA0002407378310000102
The invention establishes a corresponding autoregressive model aiming at the amplitude attenuation of the signal, and expresses the amplitude attenuation without the mean value as a second-order iteration mode, so that the simultaneous consideration of the amplitude attenuation and the phase into a state variable becomes possible when a Kalman filter state equation is designed. And calculating the statistical characteristic of the signal phase shift under the influence of the plasma sheath, and providing a basis for designing a Kalman filter.
Thirdly, designing a Kalman filter: phase noise v generated by an input tracking loop circuit1,nDoppler frequency noise v2,nDoppler acceleration noise v3,nThe covariance matrix Q of the received signal, the covariance matrix R of the observed noise at the output end of the phase discriminator, and the integration time T of the receiversAmplitude attenuation removal of received signalCoefficient of one iteration α of autoregressive model of mean2,1Coefficient of second iteration α2,2And the iterative noise variance σνAmplitude decay mean (r (t)n) Average of received signal phase shifts)
Figure BDA0002407378310000103
Sum variance
Figure BDA0002407378310000104
State equation X for a Kalman filter for designing state variables including amplitude attenuation and phase of a received signaln＝AXn-1+BYn-1+Wn-1And observation equation Zn＝HnXn+Vn. Wherein the equation of state is specifically represented as:
Figure BDA0002407378310000105
the observation equation is specifically expressed as:
Figure BDA0002407378310000106
according to the method, by analyzing the characteristics of amplitude attenuation and phase shift of the received signal under the plasma sheath channel, a state equation and an observation equation of which the state variables and the observation variables simultaneously comprise the amplitude attenuation and the phase shift of the signal are designed, so that the Kalman filter considers the influence of the amplitude attenuation, and a mathematical model is more consistent with the real state during signal tracking.
And step four, realizing a novel Kalman tracking loop: inputting a state equation of a Kalman filter: xn＝AXn-1+BYn-1+Wn-1And the observation equation: zn＝HnXn+VnActual observed quantity Z of phase detector outputnInitial value X of the observation vector0Initial value P of covariance matrix of observation vector0Initial phase θ of local oscillatorvcoAnd Doppler frequency offset w after coarse acquisitiondLoop update time TsIn a Kalman filtering loopThe tracking step realizes the novel Kalman loop tracking of the hypersonic aircraft:
1) pre-estimation with last moment state vector optimal value
Figure BDA0002407378310000111
2) Pre-estimation error variance
Figure BDA0002407378310000112
3) Kalman filter gain calculation
Figure BDA0002407378310000113
4) Optimal state vector
Figure BDA0002407378310000114
5) Updating the error variance Pn＝[1-KnHn]Pn,n-1；
6) Updating the oscillation frequency w of the generated signal of the local oscillatorvco,n＝wd+ωdn-1And an initial phase thetavco,n＝Δθn-1。
The invention provides an overall design idea of a novel Kalman tracking loop of a hypersonic aircraft, and the structure of the tracking loop is shown in figure 2. The phase detector consists of a phase discriminator, a Kalman filter and a local oscillator. Amplitude attenuation of the signal passing through the plasma sheath is considered in Kalman filter design, so that a mathematical model of a tracking loop is more consistent with a real tracking condition, and stable tracking of a signal carrier can be realized under the condition of serious amplitude attenuation.
Example 2
The method for designing the novel Kalman tracking loop of the hypersonic aircraft is the same as that in embodiment 1, and the amplitude attenuation r (t) of the signal after passing through a plasma sheath is calculatedn) And phase shift
Figure BDA0002407378310000115
The method comprises the following steps:
in a first step, a time-varying plasma sheath electron density distribution is established as shown in fig. 3: the electron density distribution ne (z) as a function of the plasma sheath thickness for a fixed time instant can be expressed as:
Figure BDA0002407378310000121
wherein n ise,maxRepresents the dynamic plasma sheath maximum electron density; z is a radical ofBIs the boundary layer position; z is a radical ofTIs the plasma sheath thickness; sigma1、σ2The coefficient of variation of the electron density of the plasma sheath is shown, and from data collected by the RAM-C engineering of NASA, it is known that the influence of the plasma sheath on the received signal is the worst when the flying height of the aircraft is 30km, and n is the loweste,max＝7.7×1018m-3，zT＝15cm，zB＝5cm，σ1＝1，σ20.5. After obtaining ne (z) at a fixed time, the time-varying model of the plasma electron density can be expressed as:
Ne(z,t)＝Ne(z)*[1+Δ*n(t)]；
wherein, Delta is the relative shaking intensity of electrons in the plasma, the value is generally between 0 and 20 percent, the value in the patent is 10 percent, and n (t) is the non-stationary colored noise with the standard deviation of 1.
Second, calculating the characteristic frequency omega of the time-varying plasma sheathp(zm,tn): input Ne(zm,tn) Represents tnAt time point m, the electron density of the plasma layer, the number of free electron charges e, is 1.6 × 10-19C, absolute dielectric constant in vacuum0＝8.854×10-12F/m, free electron mass me＝9.1×10-31And (kg). Time-varying characteristic frequency omega of plasma sheathp(zm,tn) Specifically, it can be expressed as:
Figure BDA0002407378310000122
thirdly, countingComputing amplitude attenuation coefficients α (z) for each layer after layeringm,tn) And phase shift β (z)m,tn): characteristic frequency omega of input time-varying plasma sheathp(zm,tn) The collision frequency v of the plasmaenAt 5GHz, the angular frequency ω of the incident electromagnetic wave is 2 pi × 30 × 109rad/s, light speed c 3 × 108m/s. According to the theory of electromagnetic wave propagation in uniform plasma, tnAmplitude attenuation coefficient α (z) of the mth layer at time instantm,tn) And phase shift β (z)m,tn) The expression is as follows:
Figure BDA0002407378310000123
Figure BDA0002407378310000124
the fourth step, calculate the amplitude attenuation r (t) of the signal under the plasma sheath channeln) And phase shift
Figure BDA0002407378310000131
Amplitude attenuation coefficient for each layer of the input plasma sheath α (z)m,tn) And phase shift β (z)m,tn). Overall amplitude decay r (t) of signal after passing through plasman) And phase shift
Figure BDA0002407378310000132
Expressed as:
Figure BDA0002407378310000133
Figure BDA0002407378310000134
the amplitude attenuation in the plasma sheath channel was simulated as shown in figure 4. The phase shift is shown in fig. 5.
Example 3
Novel Karl of hypersonic aerocraftA design method of a Mantracking loop. In the same manner as in example 1-example 2, an autoregressive model r' (t) with the amplitude attenuation of the received signal and the mean value removed was establishedn) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift
Figure BDA0002407378310000135
Sum variance
Figure BDA0002407378310000136
The method comprises the following steps:
in a first step, the amplitude of the signal obtained is attenuated by r (t)n) Mean value is removed to obtain r' (t)n)：
r′(tn)＝r(tn)-mean(r(tn))；
Second, the mean value-removed data r' (t) is processedn) Establishing an autoregressive model: using a second order autoregressive model:
r′(tn)＝α2,1r(tn-1)+α2,2r(tn-2)+v(n)；
where v (n) is the obedience variance σνGaussian distribution of (a)ν、α2,1、α2,2Are all parameters to be solved, and r' (t) obtained in the first step is inputn) And solving by using an L evison-Durbin algorithm to obtain parameter results:
Figure BDA0002407378310000137
third, the statistical properties of the phase shift induced by the plasma sheath are calculated: the existing research shows that the statistical characteristic of the phase shift under the plasma sheath channel presents Gaussian distribution, and the input phase shift
Figure BDA0002407378310000138
Calculating an average of phase shifts in a worst flight environment
Figure BDA0002407378310000139
Variance (variance)
Figure BDA00024073783100001310
Comprises the following steps:
Figure BDA0002407378310000141
example 4
The method for designing the novel Kalman tracking loop of the hypersonic aircraft is the same as that in embodiment 1-embodiment 3, and the state equation for calculating and designing the Kalman filter comprises the following steps:
first, a receiving end signal model y (t) is establishedn) Comprises the following steps:
Figure BDA0002407378310000142
wherein r (t)n) Is the amplitude attenuation produced by the plasma sheath; a is the amplitude of the original signal, and the value is 1 in the patent for simplifying the operation; carrier phase
Figure BDA0002407378310000143
Including phase due to residual doppler frequency offset and doppler acceleration after coarse acquisition, phase noise and initial phase affected by the plasma sheath;
Figure BDA0002407378310000144
the noise generated by the receiver obeys a mean of 0 and a variance of
Figure BDA0002407378310000145
A gaussian distribution of (a). Namely, it is
Figure BDA0002407378310000146
Second, calculating phase discriminator output U0(tn) Considering the real-time and algorithm complexity of the tracking loop, the phase detector of the conventional P LL tracking loop generally uses the result of the multiplication of the local oscillation signal and the received signal and the passing of the result through a low-pass filter as the output of the phase detectorVCOAnd a received signal y (t)n) Result of multiplication thetae(tn) Expressed as:
θe(tn)＝y(tn)×UVCO；
including low frequency components and high frequency components, wille(tn) The in-phase and quadrature components of the phase detector output after passing through the low pass filter can be expressed as follows, where Δ θnGenerating a true phase difference for the received signal and the local oscillator:
Figure BDA0002407378310000147
third, estimating the phase difference delta theta between the received signal and the local oscillator generated signaln: inputting the optimal phase difference delta theta estimated by a Kalman filtering tracking loop at the last momentn-1At TsDoppler frequency ω d over a time periodn-1Doppler acceleration wan-1And phase noise due to plasma
Figure BDA0002407378310000148
Noise v generated by the circuit1,nΔ θ at that timenIt can be estimated that:
Figure BDA0002407378310000151
fourthly, designing a state equation X of the Kalman filtern＝AXn-1+BYn-1+Wn-1: unlike a conventional Kalman filter tracking loop, the state variables in its state equation also include the phase information Δ θ of the signalnAnd amplitude attenuation information r' (t)n). Combined r' (t)n)＝α2,1r(tn-1)+α2,2r(tn-2) + v (n) amplitude decay autoregressive model after mean removal, formula
Figure BDA0002407378310000152
Expressed phase difference estimation method, kinetic equation. Defining the state variable as [ Delta theta ]nωdnwanr′ r′n-1]TThen the state equation X of the novel Kalman filtern＝AXn-1+BYn-1+Wn-1Expressed as:
Figure BDA0002407378310000153
example 5
The design method of the novel Kalman tracking loop of the hypersonic aircraft is the same as the embodiment 1-embodiment 4, and the observation equation Z of the Kalman filter is calculated and designedn＝HnXn+VnThe method comprises the following steps:
first, determining an observed variable: observed variable ZnIs the same phase output U of the phase discriminator0(tn)i、U0(tn)qPlus observation noise ni,n、nq,nExpressed as:
Figure BDA0002407378310000154
secondly, establishing an observation equation: linearized representation of an observed variable as a state variable XnAnd an observation matrix HnForm of multiplication, typically solving for HnThe method comprises
Figure BDA0002407378310000155
Obtaining:
Figure BDA0002407378310000156
the specific expression form of the observation equation is as follows:
Figure BDA0002407378310000161
example 6
The method for designing the novel Kalman tracking loop of the hypersonic aircraft is the same as that in the embodiment 1-embodiment 5, and the steps for calculating the novel Kalman tracking loop of the hypersonic aircraft are as follows:
first, pre-estimating by using the optimal value of the state vector at the last moment
Figure BDA0002407378310000162
Wherein Y isn-1The value of the water-soluble organic acid is 1,
Figure BDA0002407378310000163
initial value X of state variable of input tracking loop0＝[0 ωd0wa000]TWhere ω d is0The Doppler frequency offset value after the coarse capture is 3KHz and wa0The initial Doppler acceleration value is 800 KHz. A. then,n-1For the state variables to be constant in this patent:
Figure BDA0002407378310000164
wherein T iss＝8.3×10-7。
Second, pre-estimating error variance
Figure BDA00024073783100001610
Wherein A isn,n-1Inputting initial expression as in step 6.1)
Figure BDA0002407378310000165
Figure BDA0002407378310000166
Wherein
Figure BDA0002407378310000167
Variance of phase shift under influence of plasma sheath
Figure BDA0002407378310000168
σνFor a variable σ in an autoregressive modelν＝0.005，σ1,n、σ2,n、σ3,nRespectively taking the variances of phase noise, Doppler frequency offset noise and Doppler acceleration noise caused by the circuitThe values are 0.1, 0.3, respectively.
Thirdly, Kalman filter gain calculation
Figure BDA0002407378310000169
Wherein HnFor the observation matrix, the specific expression is:
Figure BDA0002407378310000171
where mean (r (n)) is the mean of the amplitude attenuation caused by the plasma sheath, mean (r (t)n) 0.2186. R is observation noise
Figure BDA0002407378310000172
The covariance matrix of (a) is specifically expressed as:
Figure BDA0002407378310000173
wherein
Figure BDA0002407378310000174
The signal-to-noise ratio of the receiver is 0dB, TsIs the correlation time.
Step four, solving the optimal state vector
Figure BDA0002407378310000175
Wherein ZnFor actual values of observed variables, h (X)n) Is the theoretical output value of the phase detector. The specific expression is as follows:
Figure BDA0002407378310000176
the fifth step, update the error variance Pn＝[1-KnHn]Pn,n-1。
Sixthly, updating the oscillation frequency w of the generated signal of the local oscillatorvco,n＝ωdn-1And an initial phase thetavco,n＝Δθn-1。
The seventh step is to use TsAnd in order to update the time, repeating the first step to the sixth step to realize a novel Kalman filtering carrier tracking loop under the plasma sheath channel.
The technical effects of the present invention will be described in detail with reference to simulations.
1. Simulation conditions are as follows:
the thickness of the plasma sheath is 15cm, the average thickness is 150 parts, and the collision frequency v inside the plasmaenAt 5GHz, the angular frequency ω of the incident electromagnetic wave is 2 pi × 30 × 109rad/s, Doppler frequency offset of a receiving end is 3KHz, Doppler acceleration is 800KHz/s, and integration time T of a receiversIs 8 × 10-7s, the signal-to-noise ratio of the receiving end is 0 dB.
2. Simulation results and analysis:
fig. 6 is a diagram of the tracking result of the hypersonic aircraft novel kalman tracking loop in embodiment 1 to embodiment 7 on the carrier phase of the received signal, which is to perform real-time tracking under the condition that the environment of the aircraft has the worst influence on the received signal, and it can be seen from fig. 6 that the novel kalman tracking loop of the present invention can realize the stationary tracking of the carrier phase.
The invention discloses a design scheme of a novel Kalman tracking loop of a hypersonic aircraft, which mainly solves the problem of lock losing of the traditional phase-locked loop tracking loop caused by amplitude attenuation of a received signal under a plasma sheath channel. The realization process is as follows: establishing a time-varying plasma sheath model and calculating amplitude attenuation and phase shift of a received signal under a plasma sheath; establishing an autoregressive model of amplitude attenuation and statistical characteristics of phase shift; designing a state equation and an observation equation of the Kalman filter on the basis; and designing a novel Kalman tracking loop of the hypersonic aircraft. The method avoids the problem of lock losing caused by neglecting amplitude attenuation in the plasma sheath tracking of the traditional phase-locked loop, and provides a new idea for the stable signal tracking of the hypersonic aircraft.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A Kalman tracking loop design method is characterized in that the Kalman tracking loop design method establishes a time-varying plasma sheath model and calculates amplitude attenuation and phase shift of a received signal under a plasma sheath; establishing an autoregressive model of amplitude attenuation and statistical characteristics of phase shift; designing a state equation and an observation equation of a Kalman filter; designing a novel Kalman tracking loop of the hypersonic aircraft; analyzing the amplitude attenuation and the phase shift of a received signal under a plasma sheath channel, calculating an autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift, and designing a Kalman filter suitable for the plasma sheath channel; and considering the amplitude attenuation of the received signal under the action of the plasma sheath in the design of a tracking loop, and establishing a Kalman filter for simultaneously tracking the amplitude attenuation and the phase of the received signal.
2. The kalman tracking loop design method according to claim 1, wherein the kalman tracking loop design method comprises:
in the first step, a time-varying plasma sheath electron density model is established to solve the amplitude attenuation r (t) of a received signaln) And phase shift
Figure FDA0002407378300000017
Determining an electron density model Ne (z) for a time-invariant plasma sheath channel using a double Gaussian modelm) (ii) a Or determined not to be in the RAM-C measured dataElectron density model Ne (z) of time-invariant plasma sheath channel at fly heightm) (ii) a Time-varying plasma sheath electron density model Ne (z) is established by adding time-varying jitter delta on the basis of time-invariant electron channelm,tn) The amplitude attenuation r (t) after the signal passes through the plasma sheath is calculated according to the theory of electromagnetic wave transmission in uniform plasman) And phase shift
Figure FDA0002407378300000011
Secondly, establishing an autoregressive model r' (t) with the amplitude attenuation of the received signal and the mean value removedn) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift
Figure FDA0002407378300000012
Sum variance
Figure FDA0002407378300000013
Inputting the amplitude attenuation r (t) of the simulated received signaln) And phase shift
Figure FDA0002407378300000014
Solving by using L evison-Durbin algorithm to obtain one-time iteration coefficient α of autoregressive model2,1Coefficient of second iteration α2,2And the iterative noise variance σνObtaining an autoregressive model of the amplitude attenuation of the received signal, and calculating the mean value thereof by using the input phase shift
Figure FDA0002407378300000015
Sum variance
Figure FDA0002407378300000016
Thirdly, designing a Kalman filter and inputting phase noise upsilon generated by a tracking loop circuit1,nDoppler frequency noise v2,nDoppler acceleration noise v3,nThe covariance matrix Q of the received signal, the covariance matrix R of the observed noise at the output of the phase discriminator, and the integration time of the receiverTsCoefficient α of one iteration of an autoregressive model with mean value removed by signal amplitude attenuation2,1Coefficient of second iteration α2,2And the iterative noise variance σνAmplitude decay mean (r (t)n) Average of received signal phase shifts)
Figure FDA0002407378300000021
Sum variance
Figure FDA0002407378300000022
State equation X for a Kalman filter for designing state variables including amplitude attenuation and phase of a received signaln＝AXn-1+BYn-1+Wn-1And observation equation Zn＝HnXn+Vn；
Fourthly, inputting a state equation of the Kalman filter: xn＝AXn-1+BYn-1+Wn-1And the observation equation: zn＝HnXn+VnActual observed value Z of phase discriminator outputnInitial value X of the observation vector0Initial value P of covariance matrix of observation vector0Initial phase θ of local oscillatorvcoAnd Doppler frequency offset w after coarse acquisitiondLoop update time TsAnd realizing a Kalman filter tracking loop under a plasma sheath channel according to the tracking step of the Kalman filter loop.
3. The method of kalman tracking loop design according to claim 2, wherein the first step of time varying plasma sheath channel amplitude attenuation and phase shift calculation setup includes:
(1) calculating the specific distribution of plasma sheath electron density at fixed times along the aircraft surface, using NASA's RAM-C measured data or a double Gaussian distribution:
Figure FDA0002407378300000023
input high ultrasoundThe thickness of the surface plasma sheath is Z and the plasma sheath is layered into M during the flying process of the fast aircraft, wherein the thickness of each layer is dmPeak electron density ne,maxThe first Gaussian function influencing parameter σ1And a second Gaussian function influence parameter σ2Taking the value as a constant value, zTIs the plasma sheath thickness, zBFor boundary layer thickness, an electron density model Ne (z) of the time invariant plasma sheath channel is determinedm)；
(2) Calculating the electron density distribution of the time-varying plasma sheath to produce a non-stationary colored noise n (t) with a standard deviation of 1n) Adding a jitter factor delta of the electron density on the basis of the time-invariant plasma sheath, and establishing a time-variant plasma sheath electron density distribution as follows:
Ne(zm,tn)＝Ne(zm)*[1+Δ*n(tn)]；
(3) calculating the amplitude attenuation coefficient and the phase shift coefficient of each layer: according to the electromagnetic wave propagation theory in the uniform plasma, inputting0Is the absolute dielectric constant in vacuum, meCalculating the characteristic frequency of the time-varying plasma according to the mass of free electrons and the number of charges of free electrons
Figure FDA0002407378300000024
Collision frequency v of input plasmaenThe angular frequency ω of the incident electromagnetic wave, the speed of light c, the signal amplitude attenuation coefficient for each layer, and the phase shift coefficient:
Figure FDA0002407378300000031
Figure FDA0002407378300000032
(4) the amplitude attenuation and phase shift of the signal across the entire plasma sheath were calculated:
Figure FDA0002407378300000033
Figure FDA0002407378300000034
4. the method of Kalman tracking loop design of claim 2 wherein the second step builds an autoregressive model r' (t) with the received signal amplitude attenuated and mean removedn) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift
Figure FDA0002407378300000035
Sum variance
Figure FDA0002407378300000036
Comprises the following steps:
(1) the resulting amplitude attenuation is de-averaged: solving the mean of the signal to mean (r (t)n) The averaged signal is subtracted r' (t)n)＝r(tn)-mean(r(tn) Mean-removed data r' (t)n) Using an autoregressive model as:
r′(tn)＝α2,1r(tn-1)+α2,2r(tn-2)+v(n)；
solving one-iteration coefficient α by using L evison-Durbin algorithm2,1Coefficient of second iteration α2,2Variance is σνWhite gaussian noise v (n);
(2) calculating the statistical properties of the phase shift: inputting simulation result of phase shift, the phase shift obeys Gaussian distribution function, and solving the mean value of the input phase shift according to the statistical characteristics of the Gaussian distribution function
Figure FDA0002407378300000037
Sum variance
Figure FDA0002407378300000038
5. The Kalman tracking loop design method of claim 2, wherein the third step of Kalman filter design includes:
(1) determining the sum local oscillator true phase difference Δ θ of the input signal at time nnExpression (c): true phase difference Δ θ from the previous time instantn-1Doppler frequency ω d at the previous timen-1Doppler acceleration wan-1Phase noise generated by plasma sheath channel
Figure FDA0002407378300000041
Noise v generated by the circuit1,nThen the true phase difference delta theta between the received signal and the local oscillator at time nnExpressed as:
Figure FDA0002407378300000042
(2) determining a state equation of the Kalman filter: obtaining a Kalman filter state equation for simultaneously tracking amplitude attenuation and carrier phase according to an autoregressive model and a kinetic equation as follows:
Figure FDA0002407378300000043
(3) determining an observation equation of a Kalman filter: observed variable ZnIs output U of the phase discriminator0(tn)i、U0(tn)qPlus observation noise, expressed as:
Figure FDA0002407378300000044
expressing the observation equation in linear form, i.e. the output h (X) of the phase detectorn) And (6) linearization is carried out.
6. The Kalman tracking loop design method of claim 5, wherein the output of the phase detector, U0(tn)i、U0(tn)q：
(1) Considering the operation speed and the calculation complexity of the phase detector, the output of the phase detector which is not subjected to filtering processing is represented as follows:
θe(tn)＝y(tn)×UVCO；
wherein y (t)n) For receiving signals, UVCOA carrier signal generated for a local oscillator;
(2) will thetae(tn) The result after passing through the low pass filter is taken as the final output of the phase detector:
Figure FDA0002407378300000045
7. the Kalman tracking loop design method of claim 5, wherein the observation equation linearization implementation method comprises:
linearization: will observe vector ZnIs composed of
Figure FDA0002407378300000051
Is represented by Zn＝HnXn+VnSolving for HnThe method comprises the following steps:
Figure FDA0002407378300000052
obtaining:
Figure FDA0002407378300000053
8. the Kalman tracking loop design method of claim 2, wherein the fourth step of the implementation of tracking of the Kalman filtering loop comprises:
(1) pre-estimation with last moment state vector optimal value
Figure FDA0002407378300000054
(2) Pre-estimation error variance
Figure FDA0002407378300000055
(3) Kalman filter gain calculation
Figure FDA0002407378300000056
(4) Optimal state vector
Figure FDA0002407378300000057
(5) Updating the error variance Pn＝[1-KnHn]Pn,n-1；
(6) Updating the oscillation frequency w of a local oscillatorvco,n＝wd+ωdn-1And an initial phase thetavco,n＝Δθn-1。
9. A Kalman tracking loop obtained by the Kalman tracking loop design method according to any one of claims 1 to 8, wherein the Kalman tracking loop includes a phase discriminator, a Kalman filter, and a local oscillator; the amplitude of the signal after passing through the plasma sheath is attenuated into a Kalman filter.
10. An aerospace vehicle carrying the kalman tracking loop of claim 9.
CN202010165702.0A 2020-03-11 2020-03-11 Kalman tracking loop design method, kalman tracking loop and aerospace vehicle Active CN111444663B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010165702.0A CN111444663B (en) 2020-03-11 2020-03-11 Kalman tracking loop design method, kalman tracking loop and aerospace vehicle

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010165702.0A CN111444663B (en) 2020-03-11 2020-03-11 Kalman tracking loop design method, kalman tracking loop and aerospace vehicle

Publications (2)

Publication Number Publication Date
CN111444663A true CN111444663A (en) 2020-07-24
CN111444663B CN111444663B (en) 2023-05-12

Family

ID=71650574

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010165702.0A Active CN111444663B (en) 2020-03-11 2020-03-11 Kalman tracking loop design method, kalman tracking loop and aerospace vehicle

Country Status (1)

Country Link
CN (1) CN111444663B (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112638022A (en) * 2020-12-19 2021-04-09 西安电子科技大学 Electron collision frequency diagnosis method, system, medium, device, terminal and application
CN112737659A (en) * 2020-12-03 2021-04-30 西安电子科技大学 Remote measuring channel incoherent large-scale SIMO processing method, system and application
CN115941021A (en) * 2022-10-24 2023-04-07 西安电子科技大学 LDPC-BICM-ID system based on power modulation under hypersonic aircraft telemetering SIMO channel

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018014602A1 (en) * 2016-07-19 2018-01-25 东南大学 Volume kalman filtering method suitable for high-dimensional gnss/ins deep coupling
CN110531393A (en) * 2019-07-27 2019-12-03 金华航大北斗应用技术有限公司 Weak signal tracking based on adaptive Kalman filter

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018014602A1 (en) * 2016-07-19 2018-01-25 东南大学 Volume kalman filtering method suitable for high-dimensional gnss/ins deep coupling
CN110531393A (en) * 2019-07-27 2019-12-03 金华航大北斗应用技术有限公司 Weak signal tracking based on adaptive Kalman filter

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
丛丽;岳崧;李瑾;金天;: "INS控制量辅助GNSS卡尔曼跟踪环路方法" *
沈飞;李荣冰;刘建业;韩志凤;周颖;: "基于卡尔曼滤波的北斗接收机高灵敏度跟踪算法研究" *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112737659A (en) * 2020-12-03 2021-04-30 西安电子科技大学 Remote measuring channel incoherent large-scale SIMO processing method, system and application
CN112737659B (en) * 2020-12-03 2022-04-08 西安电子科技大学 Remote measuring channel incoherent large-scale SIMO processing method, system and application
CN112638022A (en) * 2020-12-19 2021-04-09 西安电子科技大学 Electron collision frequency diagnosis method, system, medium, device, terminal and application
CN115941021A (en) * 2022-10-24 2023-04-07 西安电子科技大学 LDPC-BICM-ID system based on power modulation under hypersonic aircraft telemetering SIMO channel

Also Published As

Publication number Publication date
CN111444663B (en) 2023-05-12

Similar Documents

Publication Publication Date Title
CN111444663A (en) Kalman tracking loop design method, Kalman tracking loop and aerospace vehicle
CN109977914B (en) Self-adaptive noise reduction method based on VMD
CN111596290B (en) Radar target tracking method based on maximum correlation entropy extended Kalman filtering
RU189247U1 (en) SIMULATOR OF REFLECTED RADAR SIGNALS
Meller Cheap cancellation of strong echoes for digital passive and noise radars
CN102394593B (en) Integrated least-mean-square (LMS) adaptive filter and method
CN110780274B (en) Improved L for scanning radar1Regularization azimuth super-resolution imaging method
CN113064134B (en) Laser radar echo processing method based on improved fuzzy neural network filtering
CN110492866B (en) Kalman filtering method for moving target
CN115792839A (en) High-frequency vibration compensation method for SAR platform under terahertz waveband
CN114167359A (en) Adaptive correlation filtering method, system and storage medium for weak and small targets
Orguner et al. Particle filtering with propagation delayed measurements
Shkolnikov et al. Simulation study of the homing interceptor guidance loop with sliding mode observers versus kalman filter
Yadaiah et al. Fuzzy Kalman Filter based trajectory estmation
RezazadehReyhani et al. An analog adaptive notch filter based on the noise cancellation principle
CN112583381B (en) Self-adaptive filtering method based on deviation compensation auxiliary variable
Dong et al. Mono-pulse radar angle estimation algorithm under low signal-to-noise ratio
CN108270705B (en) Demodulation device and demodulation method for frequency modulation signal
Steinbring et al. Semi-analytic progressive Gaussian filtering
Zhuoya et al. FPGA Implementation of Variable Step Power Inversion Array for BeiDou Receiver
Wu et al. Joint analysis of system delay window and target echo error for active cancellation of LFM signal
Wang et al. Design and Implementation of DSLMS Algorithm Based Photoelectric Detection of Weak Signals
Kadirkamanathan et al. Maximum-likelihood estimation of delta-domain model parameters from noisy output signals
Lin et al. Detection of Ground Maneuvering Target Based on Range Frequency Reversal Transform and Searching Lv's Distribution
Zhou et al. Unscented Kalman-Bucy filtering for nonlinear continuous-time systems with multiple delayed measurements

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant