CN105704071A - Information-sequence-based adaptive fading extended kalman particle filter (AFEKPF) doppler frequency shift estimation method - Google Patents
Information-sequence-based adaptive fading extended kalman particle filter (AFEKPF) doppler frequency shift estimation method Download PDFInfo
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Abstract
The invention discloses an information-sequence-based adaptive fading extended kalman particle filter (AFEKPF) doppler frequency shift estimation method. The method mainly comprises the steps of: firstly, receiving signal parameters by means of an antenna receiver, and defining a sampled signal by adopting a vector table method; secondly, regarding a carrier phase of the sampled signal as a state variable of a particle filter equation, and carrying out dynamic unfolding to obtain a state transition matrix of a system and a covariance matrix of a noise interference vector; estimating a state vector by using adaptive fading kalman with fading particles to obtain optimal filter estimation; and generating an importance density function through AFEKPF, updating posteriori distribution continuously through gaussian approximation to achieve recursive estimation, and completing AFEKPF (adaptive fading extended kalman particle filter).
Description
Technical field
The present invention relates to a kind of Doppler frequency estimation algorithm, particularly relate to a kind of self adaptation based on information sequence and fade the Doppler frequency shift estimation method of spreading kalman particle filter。Relate to Patent classificating number H04 electrical communication technology H04B and transmit the parts of the H04B1/00 transmission system being not included in single group of H04B3/00 to H04B13/00；The parts H04B1/69 spread spectrum H04B1/707 of the transmission system being not feature differentiation with the transmission medium used utilizes direct sequence to modulate。
Background technology
At present, a lot of scholars propose multiple algorithm for estimating for Doppler frequency shift, and these methods are difficult to the Doppler frequency estimation being applicable under high dynamic environment。Under high dynamic environment, Doppler frequency estimation being studied, provide foundation for Doppler shift compensation, the confidentiality of communication system can be effectively improved, reducing the bit error rate, thus improving the communication capacity of system。In Doppler frequency shift estimation method; formula expresses complexity; calculating process is loaded down with trivial details, often nonlinear function to be estimated is carried out the linearization process of local, and dynamically descending Doppler frequency estimation system to there is system for height can not the problem that easily changes in time of accurate modeling or model error。
Summary of the invention
The present invention is directed to the proposition of problem above, the Doppler frequency shift estimation method of spreading kalman particle filter and a kind of self adaptation based on information sequence developed fades, comprise the steps:
Consider that expanded Kalman filtration algorithm is based on the computing of matrix-vector, employing vector representation energy better adopting said method, therefore the signal parameter that employing aerial receiver receives；Adopt vector table legal justice sampled signal；Obtain the observation of signal and the initial value of algorithm state variable。And obtain these two marks being also signals collecting and terminating；
So signal matrix vectorization can be considered from the speed of motion, acceleration, three aspects of acceleration, improve estimated accuracy。
Using the carrier phase of the sampled signal state variable as particle filter equation, after carrying out dynamically launching, obtain the state-transition matrix of system and the covariance matrix of noise jamming vector；Use and obtain optimal filter estimate with the Kalman's estimation to state vector that fades of the self adaptation of fading factor；
Produce the importance density function by AFEKF, verify after being constantly updated by Gaussian approximation that distribution realizes recurrence estimation, complete AFEKPF (adaptivefadingextendedkalmanparticlefilter) particle filter。
As preferred embodiment, based on vector representation, sampled signal is defined as:
Wherein, n (k)T=[nI(k)nQ(k)] zero-mean gaussian vector, lower Table I, Q refer to homophase and orthogonal component and the mean square error σ of noise2=N0/2Ts, TsFor the sampling period, it is equal to the renewal interval of carrier tracking loop；A is the amplitude receiving signal, and θ is the sampling period is TsSignal carrier phase；The input signal-to-noise ratio of corresponding receiver is
Further, to state vectorEstimation procedure as follows:
Prediction one step of state equation calculates:
Prediction one step of predictive equation calculates:
The calculating of optimum spreading kalman gain:
One step of predictive equation updates:
The calculating that optimal filter is estimated:
Wherein, R=σ2I。For h (xk) the linearizing factor。
Further, fading factor is the scale factor in formula (14)
The criterion judging filtering divergence in filtering is:
In formula: γ is reserve factor (γ > 1),Obtained by measuring value；Most stringent of convergence criterion is met, namely when γ=1The real information covariance matrix estimated is
The employing estimation technique of windowing is determinedIt is similar to Sage filtering
Fade the spreading kalman Doppler frequency estimation to high-speed aircraft communication system to meet self adaptation, formula (26) modified:
Wherein, v0Information of forecasting vector during for k=0；
Historical information is not averaged by modified rear formula (27), and directly adopts the estimated information of current time, reflection current time system model error that more can be sensitive than formula (26)。Then fading factorCan be estimated as:
Further, AFEKF algorithm is used as follows posterior density to be similar in each moment:
In formula,State estimation for the k moment；P is the estimate variance in k moment。In particle filter algorithm, it is possible to AFEKF, each particle is updated, using the approximate posterior density that finally obtains as the importance density function, namely
Then from importance density, produce new particle, carry out after right value update particle collection resampling；Effective resampling can effectively suppress sample degeneracy phenomenon；
IfThen carry out resampling, by original cum rights sampleThe power sample such as it is mapped asThus completing AFEKPF filtering。
Accompanying drawing explanation
Technical scheme for clearer explanation embodiments of the invention or prior art, introduce the accompanying drawing used required in embodiment or description of the prior art is done one simply below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the premise not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings。
Fig. 1 is the Doppler frequency shift schematic diagram of high-speed aircraft communication system
Fig. 2 is the graph of a relation of the RMS frequency displacement estimation difference of different filtering algorithm and SNR
Fig. 3 is different filtering method frequency tracking error schematic diagrams
Fig. 4 is the algorithm flow chart of the present invention
Detailed description of the invention
For making the purpose of embodiments of the invention, technical scheme and advantage clearly, below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear complete description:
As Figure 1-Figure 4:
Fade the Doppler frequency shift estimation method of spreading kalman particle filter based on the self adaptation of information sequence, comprises the steps:
First, carrying out signals collecting due to the existence of the relative velocity of the Transmitting and Receiving End of signal, it causes the signal generation Doppler frequency shift that receiving terminal is received。So they relations are as follows:
Wherein, fdT () is Doppler frequency；F is carrier frequency；C is the light velocity；VdT () claims doppler velocity；In order to calculate maximum Doppler frequency shift, it is assumed here that communication angle cos α=1 between communications carrier, namely it is radially communication between them。
The speed trajectory of visible receiver is multiplied by a factor can obtain corresponding Doppler frequency shift track。
In order to express the change of Doppler frequency, suppose that its all of k rank rate of change all exists in this patent, then Doppler frequency process can be expressed as t0Neighbouring Taylor series expansion form:
Wherein,
At t0Observation interval carrier phase represented when launching near=0 is:
Wherein, parameter f0For Doppler frequency (unit: Hz)；F1For its single order rate of change (unit: Hz/s)；F2For its second order rate of change (unit: Hz/s2)。ω0,ω1,ω2For angular frequency, relevant with the rate of change of the dynamic speed of actual receiver, acceleration and acceleration respectively, available vector method is expressed as ω=[ω0,ω1,ω2]T。
Adopt the interval carrier phase of observation to adopt vector method to be conducive to applying to spreading kalman method, be conducive to the simulation calculating of hereafter Kalman's aspect。
Reception antenna received signal on communications carrier is modulated by the dynamic parameter (namely receiver is relative to the relative velocity of transmitter, acceleration and acceleration) of receiver, and be subject to zero-mean, steadily, the interference of narrowband Gaussian noise,
Receiver dynamically receives signal parameter, adopts the representation of vector, and sampled signal can be defined as:
Wherein, n (k)T=[nI(k)nQ(k)] zero-mean gaussian vector, lower Table I, Q refer to homophase and orthogonal component and the mean square error σ of noise2=N0/2Ts, TsFor the sampling period, it is equal to the renewal interval of carrier tracking loop；A is the amplitude receiving signal, owing to AFEKPF is not usually required to the value estimating A。For convenience of calculation, it is assumed here that it is unit value。θ is the sampling period is TsSignal carrier phase。The input signal-to-noise ratio of corresponding receiver is
Secondly, the AFEKF (adaptivefadingextendedkalmanfilter) of particle updates
Doppler frequency process is represented as the form of Taylor series expansion, in like manner, θ (k) can be considered the method adopting aforementioned Taylor series, sampled by the integral function of frequency locus and obtain, here θ (k) represents the carrier phase of the sampled signal that the sampling period is TS and between the area of observation coverage, carrier phase is same physical quantities before, and carrier phase refers to the measured value of the carrier signal phase that the phase place at the satellite-signal accepting reception produces relative to receiver。Angular frequency is carrier phase application in spreading kalman。Indication acceleration is relative acceleration, corresponding to corresponding angular frequency。, each rank rate of change respectively ω of note θ (k)0(k), ω1(k), ω2The state variable x (k) of k particle filter equation that () forms。
θ (k)=lTX (k), lT=[1,0 ..., 0] (5)
xT(k)=[θ (k), ω0(k),ω1(k),ω2(k)](6)
The all-order derivative Taylor series expansion of signal phase difference will be estimated:
ω1(k+1)=ω1(k)+Tsω2(k)+ξ3(k)(8)
ω2(k+1)=ω2(k)+ξ4(k)(9)
Wherein, νiK () is called dynamic model noise, it describes model above and is subject to the impact of some interference。
State-transition matrix by the above known system of formula:
For the white Gauss noise process that power spectral density is q, the covariance matrix of noise jamming vector ξ (k) can be obtained:
Fade spreading kalman to state vector by self adaptationState vector is the same with state variable。State-transition matrix is a parameter in state variable, and its estimation procedure is as follows:
Prediction one step of state equation calculates:
Prediction one step of predictive equation calculates:
The calculating of optimum spreading kalman gain:
One step of predictive equation updates:
The calculating that optimal filter is estimated:
Wherein, R=σ2I。For h (xk) the linearizing factor。
Formula 13-20 is that whole self adaptation fades the process of spreading kalman, and this is the process of a reciprocation cycle, and formula 18 is the result circulated each time。
Again, the choosing of fading factor
Formula (14) the mesoscale factorIt is called fading factor, generally takesThis means that filtering algorithm now is bigger to the weighting weight of information than basic EKF method, namelyReduce the impact on estimated value of the outmoded measuring value。
In EKF, tkThe information sequence in moment observation vector r (k) is (17) formula, push away its covariance matrix is:
Formula (17) is information sequence, can be derived from information sequence covariance matrix and is:
When gain battle arrayDuring for optimum gain battle array, information sequence is white noise sequence, and the auto-correlation function of information sequence is
Formula (15) and formula (17) are brought into formula (22) obtain
By above formula it can be seen that work as gain battle arrayDuring for optimum gain battle array, information sequence keeps orthogonal everywhere, it is combined with spreading kalman algorithm, strengthens the performance of spreading kalman。
In actual applications, can there is model error in system model, causes information covariance matrix and the theoretical value of realityDifferent, may not necessarily the auto-correlation function value of guarantee information sequence be so zero。
Based on this, real-time and adjust gain battle array by fading factorMakeObtaining minimum, namely information sequence can keep weak autocorrelation。
The criterion judging filtering divergence in filtering is[9]
In formula: γ is reserve factor (γ > 1),Obtained by measuring value。Formula (22) left side is information sequence actual estimated error in actual applications, and the right is relevant with the mark of the covariance matrix of information sequence, describes the information of theoretical prediction error。Most stringent of convergence criterion is met, namely when γ=1The real information covariance matrix estimated is
The employing estimation technique of windowing is determinedIt is similar to Sage filtering
Fade the spreading kalman Doppler frequency estimation to high-speed aircraft communication system to meet self adaptation, formula (26) modified:
Wherein, v0Information of forecasting vector during for k=0。
Historical information is not averaged by modified rear formula (27), and directly adopts the estimated information of current time, reflection current time system model error that more can be sensitive than formula (26)。Then fading factorCan be estimated as
Information sequence estimation differenceIncrease cause error covariance matrixIncrease time, fading factor valueCan increase accordingly, it is possible to a greater extent effective information is extracted from information sequence, strengthen the weak autocorrelation of information sequence, improve algorithm suggestion distribution and estimate robustness and the estimated accuracy of parameter。
4th, self adaptation fades spreading kalman particle filter model
AFEKPF algorithm is on the basis of particle filter, application AFEKF takes into full account that the measuring value of current time can obtain better the importance density function, prior distribution can be made to move towards high likelihood score region so that AFEKPF can reach good Doppler frequency estimation effect。
In particle filter, utilizeExpression system posterior probability density function p (x0:k|z1:k) particle assembly,Being corresponding weights isParticle collection, wherein, x0:k={ xj, j=0 ..., k} is the state set in 0 to k moment。
Weights are normalized toThen the Posterior probability distribution of k moment system mode can be weighted to discretely:
Wherein, weights are selected by importance sampling。If particle collectionCan by importance density function q (x0:k|z1:k) obtain, then weights are
If q is (x0:k|z1:k)=q (xk|x0:k-1,z1:k)q(x0:k-1|z1:k-1) then can be obtained importance weight formula by formula (30) and be
If q is (xk|x0:k-1,z1:k)=q (xk|xk-1,zk),
Then the importance density function only relies upon xk-1And zk, representing the value in K moment is only that the value in moment is relevant with eve, must not be affected by initial value。So assume to contribute to reducing the preceding value impact on current predicted value, strengthen precision of prediction。
When calculating, it is only necessary to storage particleWithout being concerned about particle collectionWith past measuring value z1:k-1。Revised weights are
By weightsNormalization, namely
AFEKPF algorithm produces the importance density function by AFEKF, AFEKF is in conjunction with up-to-date measuring value, constantly update Posterior distrbutionp by Gaussian approximation and realize recurrence estimation, say, that posterior density was similar in each moment by AFEKF as follows:
In formula,State estimation for the k moment；P is the estimate variance in k moment。In particle filter algorithm, it is possible to AFEKF, each particle is updated, using the approximate posterior density that finally obtains as the importance density function, namely
Then producing new particle from importance density, carry out after right value update particle collection resampling, effective resampling can effectively suppress sample degeneracy phenomenon。IfThen carry out resampling, by original cum rights sampleThe power sample such as it is mapped asThus completing AFEKPF filtering。
5th, Doppler frequency estimation simulation analysis。
The specific embodiment of the present invention is described in detail below in conjunction with technical scheme and accompanying drawing。
Accompanying drawing 2 is the graph of a relation of the RMS frequency displacement estimation difference of different filtering algorithm and SNR。Assume that the process noise of system and observation noise are all obey zero-mean gaussian distribution,
Original state,
Initial variance, observation frequency has carried out 20 Monte-Carlo Simulation experiments, and particle number is 100。AFEKF, EKPF, AFEKPF filtering performance is compared by Fig. 2 respectively。Under equal conditions, PF algorithm estimated accuracy in nonlinear system has obvious advantage than EKF algorithm, and EKF is improve particle filter estimated accuracy as suggestion distribution by EKPF algorithm, and therefore, the estimated accuracy of EKPF algorithm is apparently higher than AFEKF algorithm。The EKF AFEKF improved is distributed by AFEKPF algorithm as suggestion so that the importance probability density of particle filter is closer to real posterior probability density, and in estimated accuracy, AFEKPF algorithm has good raising than EKPF algorithm。
Accompanying drawing 3 is the frequency tracking error of AFEKF, EKPF, AFEKPF。For vehicular communication system frequency shift tracking, in AFEKPF algorithm, to have the odds ratio AFEKF algorithm estimation difference suitable in strongly non-linear system little for particle filter。AFEKF is distributed as the suggestion of particle filter by AFEKPF algorithm, EKF adds the fading factor based on information sequence, utilize current observation data, reduce the impact of outmoded measured value, effectively raise the robustness of estimation。As can be seen here, proposed can quickly restraining using the spreading kalman that fades of the self adaptation based on information sequence as the AFEKPF algorithm of suggestion distribution, stability is strong, and estimation difference is little。
Embodiment,
(1) initialization is first filtered。Initialize k=0, samplingNamely according to p (X0) profile samples obtainsPerform (2)。
(2) filtering is as follows:
Step1: carry out particle renewal with AFEKF。
Step2: weight computing: samplingCalculate weightsWeights normalization obtains:
Step3: resampling: ifThen carry out resampling, by original cum rights sampleThe power sample such as it is mapped as
Step4: output state is estimated: make k=k+1, returns Step1 and carries out recurrence calculation。
The above; it is only the present invention preferably detailed description of the invention; but protection scope of the present invention is not limited thereto; any those familiar with the art is in the technical scope that the invention discloses; it is equal to replacement according to technical scheme and inventive concept thereof or is changed, all should be encompassed within protection scope of the present invention。
Claims (5)
1. the self adaptation based on information sequence fades the Doppler frequency shift estimation method of spreading kalman particle filter, it is characterised in that have following steps:
The signal parameter that aerial receiver receives；Adopt vector table legal justice sampled signal；
Using the carrier phase of the sampled signal state variable as particle filter equation, after carrying out dynamically launching, obtain the state-transition matrix of system and the covariance matrix of noise jamming vector；Use and obtain optimal filter estimate with the Kalman's estimation to state vector that fades of the self adaptation of fading factor；
Produce the importance density function by AFEKF, verify after being constantly updated by Gaussian approximation that distribution realizes recurrence estimation, complete AFEKPF (adaptivefadingextendedkalmanparticlefilter) particle filter。
2. the self adaptation based on information sequence according to claim 1 fades the Doppler frequency shift estimation method of spreading kalman particle filter, is further characterized in that sampled signal is defined as based on vector representation:
Wherein, n (k)T=[nI(k)nQ(k)] zero-mean gaussian vector, lower Table I, Q refer to homophase and orthogonal component and the mean square error σ of noise2=N0/2Ts, TsFor the sampling period, it is equal to the renewal interval of carrier tracking loop；A is the amplitude receiving signal, and θ is the sampling period is TsSignal carrier phase；The input signal-to-noise ratio of corresponding receiver is
3. the self adaptation based on information sequence according to claim 2 fade spreading kalman example filtering Doppler frequency shift estimation method, be further characterized in that: to state vectorEstimation procedure as follows:
Prediction one step of state equation calculates:
Prediction one step of predictive equation calculates:
The calculating of optimum spreading kalman gain:
One step of predictive equation updates:
The calculating that optimal filter is estimated:
Wherein, R=σ2I。For h (xk) the linearizing factor。
4. the self adaptation based on information sequence according to claim 3 fade spreading kalman example filtering Doppler frequency shift estimation method, be further characterized in that: fading factor is the scale factor in formula (14)
The criterion judging filtering divergence in filtering is:
In formula: γ is reserve factor (γ > 1),Obtained by measuring value；Most stringent of convergence criterion is met, namely when γ=1The real information covariance matrix estimated is
The employing estimation technique of windowing is determinedIt is similar to Sage filtering
Fade the spreading kalman Doppler frequency estimation to high-speed aircraft communication system to meet self adaptation, formula (26) modified:
Wherein, v0Information of forecasting vector during for k=0；
Historical information is not averaged by modified rear formula (27), and directly adopts the estimated information of current time, reflection current time system model error that more can be sensitive than formula (26)。Then fading factorCan be estimated as:
5. the self adaptation based on information sequence according to claim 4 fade spreading kalman example filtering Doppler frequency shift estimation method, be further characterized in that:
AFEKF algorithm is used as follows posterior density to be similar in each moment:
In formula,State estimation for the k moment；P is the estimate variance in k moment。In particle filter algorithm, it is possible to AFEKF, each particle is updated, using the approximate posterior density that finally obtains as the importance density function, namely
Then from importance density, produce new particle, carry out after right value update particle collection resampling；Effective resampling can effectively suppress sample degeneracy phenomenon；
IfThen carry out resampling, by original cum rights sampleThe power sample such as it is mapped asThus completing AFEKPF filtering。
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Application publication date: 20160622 |