CN105954713A - Time delay estimation method based on TDOA observed quantity localization algorithm - Google Patents

Abstract

The invention relates to a time delay estimation method based on TDOA observed quantity localization algorithm. The method comprises the following steps: receiving the signal transmitted from a base station by a receiving end; performing correlation calculation to the received signal; performing correlation calculation again to the correlation signal obtained in the previous step; and performing Hilbert transformation and envelope calculation to the correlation signal obtained by correlation operations again to obtain the time delay difference between the receiving end and different base stations. According to the invention, the signals received from different base stations undergo correlation calculations and afterwards, the obtained correlation signals are correlated again. With this, a remarkable noise reduction effect is achieved with improved robustness to noise. Further in the method, according to the principle of Hilbert transformation, correlation function envelope is solved. Through the utilization of the characteristics of the envelope signal that its phases are not affected by noise during a transmission process to analyze the envelope signal so as to obtain a time delay difference, estimation errors for time delay difference can be reduced while the localization precision is increased.

Description

A kind of delay time estimation method based on TDOA observed quantity location algorithm

Technical field

The present invention relates to the indoor navigation location technology of a kind of wireless sensor network, see based on TDOA particularly to one The delay time estimation method of measurement and positioning algorithm.

Background technology

Time delay is estimated to have a wide range of applications in the fields such as communication, radar and navigator fix, along with data signal processes The development of method is perfect, and substantial amounts of Time Delay Estimation Algorithms is suggested, wherein generalized correlation method, generalized phase spectrometry and adaptive Answering method is the most frequently used three kind methods.

The feature that generalized correlation method has easily realization, amount of calculation is little, but the method requires signal and noise, noise and makes an uproar Between sound orthogonal, variable time delay is estimated and the estimation difference of unstable signal is big, depend on input signal and noise Statistics priori, the optimal estimation on realization theory can only be approximated.

Generalized phase spectrometry is that the time domain of generalized correlation method being estimated, being transformed into frequency domain estimates, same rely on input signal and The priori of noise.

Adaptive method can adjust inherent parameters in an iterative process, and then estimates the dynamic and time delay of time-varying, but When filter order height, calculate that quantitative change is big, convergence rate slows down, it is seen that the method be by sacrifice calculate speed reduce right Signal and the dependence of noise statistics priori.

Chen Xiao is " adaptive based on LMS equal within 2015, being published in " commander controls and emulation " the 3rd paper of the 69-74 page of phase Time Delay Estimation Algorithms relevant with the secondary of Hilbert difference should be filtered ", it is proposed that a kind of time delay based on adaptive method is estimated Method, the method utilizes that sef-adapting filter is less to the priori demand of signal and noise, have and be automatically adjusted self ginseng The ability of number, first carries out front-end filtering process to signal, then the signal after processing carries out secondary and is correlated with, and finally utilizes Xi Er Correlation peak is sharpened by Bert differential technique, it is possible to obtain more accurate time delay estimated result.Asking of the existence of the method Topic is, when filter order is relatively low, estimation precision is low；When filter order is higher, calculating quantitative change is big, convergence rate slows down.

Summary of the invention

For the above-mentioned problems in the prior art, the present invention proposes a kind of based on TDOA (Time difference Of Arrival, the time of advent is poor) delay time estimation method of observed quantity location algorithm.The method utilizes wireless network to carry out data Transmitting-receiving, is correspondingly improved it based on TDOA observed quantity theory of algorithm, improve algorithm to the robustness of noise and Indoor position accuracy.

For achieving the above object, the present invention adopts the following technical scheme that:

A kind of delay time estimation method based on TDOA observed quantity location algorithm, comprises the following steps:

Step 1, receiving terminal receives the signal of Base Transmitter.The i.e. i-th of signal of the i-th base station received receives signal x_i(t) be:

x_i(t)=A_is(t-t_i)+n_i(t)

Wherein: s (t) is signal source signal, t_iThe time delay that signal relative signal source signal produces, A is received for i-th_iIt is I the gain receiving signal, n_iT () is the noise signal that i-th receives in signal, s (t-t_i) and n_iT () is separate, the most not Relevant, i=1,2 ..., m, m are base station number.

Step 2, the docking collection of letters number carries out related operation.

Step 3, the coherent signal obtaining step 2 carries out related operation again.

Step 4, the coherent signal obtaining step 3 carries out Hilbert transform and envelope calculates, and obtains receiving terminal to not Delay inequality with base station.

Further, step 2 uses Fourier transform to carry out related operation at frequency domain, and method is as follows:

Step 2.1, the docking collection of letters number carries out Fourier transform.I-th receives the Fourier transform X of signal_i(k) be:

$X_i\left(k\right)=\underset{n=0}{\overset{N-1}{\Σ}}{x}_i\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

Wherein: x_i[n] is x_iThe discrete sampling sequence of (t), i=1,2 ..., m, k=0 ..., N-1, N are discrete periodic, i.e. The discrete signal point number that in locating periodically T, receiving terminal receives, and N takes even number, and (purpose makes in Hilbert transform below N/2 is integer).

Step 2.2, asks coherent signal i.e. to receive signal and carries out the Fourier transform of the signal after related operation.I-th connects The autocorrelation signal of the collection of letters number and i-th receive signalBecome with the Fourier of the cross-correlated signal that jth receives signal ChangeIt is respectively as follows:

$R_{ii}^{\left(1\right)}\left(k\right)=X_i\left(k\right){X_i}^{*}\left(k\right)$

$R_{ij}^{\left(1\right)}\left(k\right)=X_i\left(k\right){X_j}^{*}\left(k\right)$

Wherein: j=1,2 ..., m, j ≠ i, conjugation is sought in " * " expression.

Step 2.3, Fourier transform of negating obtains the coherent signal of time domain.I-th receives the autocorrelation signal of signalAnd i-th receives the cross-correlated signal of signal and jth reception signalIt is respectively as follows:

$r_{ii}^{\left(1\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ii}^{\left(1\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

$r_{ij}^{\left(1\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ij}^{\left(1\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Wherein :-(N-1)≤n≤(N-1).

Further, step 3 related operation again uses Fourier transform to carry out at frequency domain, obtains the relevant letter of time domain NumberFor:

$r_{ij}^{\left(2\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ij}^{\left(2\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Wherein:

$R_{ij}^{\left(2\right)}\left(k\right)=R_{ij}^{\left(1\right)}\left(k\right)R_{ii}^{\left(1\right)}\left(k\right)$

$R_{ij}^{\left(1\right)}\left(k\right)=\underset{n=0}{\overset{N-1}{\Σ}}{r}_{ij}^{\left(1\right)}\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

$R_{ij}^{\left(1\right)}\left(k\right)=\underset{k=0}{\overset{N-1}{\Σ}}{r}_{ii}^{\left(1\right)}\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

Further, the method for step 4 calculation delay difference is as follows:

Step 4.1, the coherent signal obtaining step 3 carries out Hilbert transform, and method is as follows:

Order:

$Z_{ij}\left(k\right)=\left\{\begin{array}{cc}{R}_{ij}^{\left(2\right)}\left(k\right),& k=0\\ 2R_{ij}^{\left(2\right)}\left(k\right),& k=1,2,...,\frac{N}{2}-1\\ 0,& k=\frac{N}{2},\frac{N}{2}+1,...,N-1\end{array}\right.$

Z_ijThe inverse fourier transform z of (k)_ij[n] is:

$z_{ij}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{Z}_{ij}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Hilbert transformFor:

${\hat{r}}_{ij}^{\left(2\right)}\[n\]=-j(z_{ij}\[n\]-r_{ij}^{\left(2\right)}\[n\])$

Step 4.2, calculates the envelope function of coherent signal, and formula is as follows:

${\mathrm{EN}}_{ij}\[n\]=r_{ij}^{\left(2\right)}\[n\]+j{\hat{r}}_{ij}^{\left(2\right)}\[n\]$

$e_{ij}\[n\]=|{\mathrm{EN}}_{ij}\[n\]|=\sqrt{{(r_{ij}^{\left(2\right)}\[n\])}^2+{({\hat{r}}_{ij}^{\left(2\right)}\[n\])}^2}$

${\mathrm{\θ}}_{ij}\[n\]=\arctan \frac{{\hat{r}}_{ij}^{\left(2\right)}\[n\]}{r_{ij}^{\left(2\right)}\[n\]}$

Wherein: EN_ij[n] isEnvelope function, e_ij[n] and θ_ij[n] is respectively envelope range value and phase place.

Step 4.3, calculates the delay inequality between receiving terminal and different base station, and formula is as follows:

${\mathrm{\Δt}}_{ij}\[n\]=\frac{e_{ij}\[n\]-N}{F_s}$

Wherein: Δ t_ij[n] is the delay inequality of the signal of the i-th base station that receives of receiving terminal and jth base station, and Fs is base Stand and send the frequency of signal to receiving terminal.

Further, receiving terminal is equal to receiving terminal to the delay inequality of base station and amassing of the light velocity to the range difference of base station.

Preferably, base station number m=4.

Compared with prior art, the method have the advantages that

The signal of the present invention different base station to receiving carries out related operation, then to the coherent signal obtained phase again Closing, noise reduction is notable, improves the robustness to noise；Principle solving correlation envelope according to Hilbert transform, Utilize the characteristic that envelope signal phase place in transmitting procedure is the most affected by noise, be analyzed trying to achieve delay inequality to envelope signal, Reduce delay inequality estimation error, improve positioning precision.

Accompanying drawing explanation

Fig. 1 is the flow chart of the method for the invention.

Detailed description of the invention

The present invention will be further described with embodiment below in conjunction with the accompanying drawings.

A kind of delay time estimation method based on TDOA observed quantity location algorithm, flow chart is as it is shown in figure 1, include following step Rapid:

Step 1, receiving terminal receives the signal of Base Transmitter.The i.e. i-th of signal of the i-th base station received receives signal x_i(t) be:

x_i(t)=A_is(t-t_i)+n_i(t)

In formula, s (t) is signal source signal, t_iThe time delay that signal relative signal source signal produces, A is received for i-th_iIt is I the gain receiving signal, n_iT () is the noise signal that i-th receives in signal, s (t-t_i) and n_iT () is separate, the most not Relevant, i=1,2 ..., m, m are base station number.

Step 2, the docking collection of letters number carries out related operation.

The basic thought of related operation is the similarity investigating two signals.I.e. believe owing to receiving the useful signal in signal Number source signal component is separate with the noise signal being mixed into, orthogonal, therefore carries out useful signal component after related operation Strengthening, noise signal component can substantially reduce.

Step 3, the coherent signal obtaining step 2 carries out related operation again.

Coherent signal carries out a related operation again, and its result is inevitable occurs a peak value at shift value, enters simultaneously One step reduces effect of noise, improves the algorithm robustness to noise.

Step 4, the coherent signal obtaining step 3 carries out Hilbert transform and envelope calculates, and obtains receiving terminal to not Delay inequality with base station.

Step 2 uses Fourier transform to carry out related operation at frequency domain, and method is as follows:

Step 2.1, the docking collection of letters number carries out Fourier transform.I-th receives the Fourier transform X of signal_i(k) be:

$X_i\left(k\right)=\underset{n=0}{\overset{N-1}{\Σ}}{x}_i\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

Wherein: x_i[n] is x_iThe discrete sampling sequence of (t), i=1,2 ..., m, k=0 ..., N-1, N are discrete periodic, i.e. The discrete signal point number that in locating periodically T, receiving terminal receives.

Step 2.2, seeks the Fourier transform of coherent signal.I-th receives autocorrelation signal and the i-th reception letter of signal NumberThe Fourier transform of the cross-correlated signal of signal is received with jthIt is respectively as follows:

$R_{ii}^{\left(1\right)}\left(k\right)=X_i\left(k\right){X_i}^{*}\left(k\right)$

$R_{ij}^{\left(1\right)}\left(k\right)=X_i\left(k\right){X_j}^{*}\left(k\right)$

Wherein: j=1,2 ..., m, j ≠ i, conjugation is sought in " * " expression.

Step 2.3, Fourier transform of negating obtains the coherent signal of time domain.I-th receives the autocorrelation signal of signalAnd i-th receives the cross-correlated signal of signal and jth reception signalIt is respectively as follows:

$r_{ii}^{\left(1\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ii}^{\left(1\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

$r_{ij}^{\left(1\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ij}^{\left(1\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Wherein :-(N-1)≤n≤(N-1).

Step 3 related operation again uses Fourier transform to carry out at frequency domain, the coherent signal of the time domain obtained For:

$r_{ij}^{\left(2\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ij}^{\left(2\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Wherein:

$R_{ij}^{\left(2\right)}\left(k\right)=R_{ij}^{\left(1\right)}\left(k\right)R_{ii}^{\left(1\right)}\left(k\right)$

$R_{ij}^{\left(1\right)}\left(k\right)=\underset{k=0}{\overset{N-1}{\Σ}}{r}_{ij}^{\left(1\right)}\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

$R_{ii}^{\left(1\right)}\left(k\right)=\underset{k=0}{\overset{N-1}{\Σ}}{r}_{ii}^{\left(1\right)}\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

The method of step 4 calculation delay difference is as follows:

Step 4.1, the coherent signal obtaining step 3 carries out Hilbert transform, and method is as follows:

Order:

$Z_{ij}\left(k\right)=\left\{\begin{array}{cc}{R}_{ij}^{\left(2\right)}\left(k\right),& k=0\\ 2R_{ij}^{\left(2\right)}\left(k\right),& k=1,2,\mathrm{...},\frac{N}{2}-1\\ 0,& k=\frac{N}{2},\frac{N}{2}+1,\mathrm{...},N-1\end{array}\right.$

Z_ijThe inverse fourier transform z of (k)_ij[n] is:

$z_{ij}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{Z}_{ij}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Hilbert transformFor:

${\hat{r}}_{ij}^{\left(2\right)}\[n\]=-j(z_{ij}\[n\]-r_{ij}^{\left(2\right)}\[n\])$

Step 4.2, calculates the envelope function of coherent signal, and formula is as follows:

${\mathrm{EN}}_{ij}\[n\]=r_{ij}^{\left(2\right)}\[n\]+j{\hat{r}}_{ij}^{\left(2\right)}\[n\]$

$e_{ij}\[n\]=|{\mathrm{EN}}_{ij}\[n\]|=\sqrt{{(r_{ij}^{\left(2\right)}\[n\])}^2+{({\hat{r}}_{ij}^{\left(2\right)}\[n\])}^2}$

${\mathrm{\θ}}_{ij}\[n\]=\arctan \frac{{\hat{r}}_{ij}^{\left(2\right)}\[n\]}{r_{ij}^{\left(2\right)}\[n\]}$

Wherein: EN_ij[n] isEnvelope function, e_ij[n] and θ_ij[n] is respectively envelope range value and phase place.

Step 4.3, calculates the delay inequality between receiving terminal and different base station, and formula is as follows:

${\mathrm{\Δt}}_{ij}\[n\]=\frac{e_{ij}\[n\]-N}{F_s}$

Wherein: Δ t_ij[n] is the delay inequality of the signal of the i-th base station that receives of receiving terminal and jth base station, F_sFor base Stand and send the frequency of signal to receiving terminal.The receiving terminal obtained according to step 4, to the delay inequality of different base station, can calculate reception End is to the range difference of base station.Receiving terminal is equal to receiving terminal to the delay inequality of base station and amassing of the light velocity to the range difference of base station.

Preferably, base station number m=4.

The invention is not restricted to above-mentioned embodiment, those skilled in the art made to above-mentioned embodiment any aobvious and The improvement being clear to or change, all without beyond the design of the present invention and the protection domain of claims.

Claims (6)

1. a delay time estimation method based on TDOA observed quantity location algorithm, it is characterised in that comprise the following steps:

Step 1, receiving terminal receives the signal of Base Transmitter；The i.e. i-th of signal of the i-th base station received receives signal x_i(t) For:

x_i(t)=A_is(t-t_i)+n_i(t)

In formula, s (t) is signal source signal, t_iThe time delay that signal relative signal source signal produces, A is received for i-th_iFor i-th Receive the gain of signal, n_iT () is the noise signal that i-th receives in signal, s (t-t_i) and n_iT () is separate, the most not phase Close, i=1,2 ..., m, m are base station number；

Step 2, the docking collection of letters number carries out related operation；

Step 3, the coherent signal obtaining step 2 carries out related operation again；

Step 4, the coherent signal obtaining step 3 carries out Hilbert transform and envelope calculates, and obtains receiving terminal to different bases The delay inequality stood.

Delay time estimation method based on TDOA observed quantity location algorithm the most according to claim 1, it is characterised in that step 2 use Fourier transform to carry out related operation at frequency domain, and method is as follows:

Step 2.1, the docking collection of letters number carries out Fourier transform；I-th receives the Fourier transform X of signal_i(k) be:

$X_i\left(k\right)=\underset{n=0}{\overset{N-1}{\Σ}}{x}_i\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

In formula, x_i[n] is x_iThe discrete sampling sequence of (t), i=1,2 ..., m, k=0 ..., N-1, N are discrete periodic, i.e. position The discrete signal point number that in cycle T, receiving terminal receives, and N is even number；

Step 2.2, asks coherent signal i.e. to receive signal and carries out the Fourier transform of the signal after related operation；I-th receives letter Number autocorrelation signalAnd i-th receives the Fourier transform that signal receives the cross-correlated signal of signal with jthIt is respectively as follows:

$R_{ii}^{\left(1\right)}\left(k\right)=X_i\left(k\right)X_i^{*}\left(k\right)$

$R_{ij}^{\left(1\right)}\left(k\right)=X_i\left(k\right)X_j^{*}\left(k\right)$

Wherein: j=1,2 ..., m, j ≠ i, conjugation is sought in " * " expression；

Step 2.3, Fourier transform of negating obtains the coherent signal of time domain；I-th receives the autocorrelation signal of signalAnd I-th receives the cross-correlated signal of signal and jth reception signalIt is respectively as follows:

$r_{ii}^{\left(1\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ii}^{\left(1\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

$r_{ij}^{\left(1\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ij}^{\left(1\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Wherein :-(N-1)≤n≤(N-1).

Delay time estimation method based on TDOA observed quantity location algorithm the most according to claim 2, it is characterised in that step 3 again related operation use Fourier transform carry out at frequency domain, obtain the coherent signal of time domainFor:

$r_{ij}^{\left(2\right)}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{R}_{ij}^{\left(2\right)}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Wherein:

$R_{ij}^{\left(2\right)}\left(k\right)=R_{ij}^{\left(1\right)}\left(k\right)R_{ii}^{\left(1\right)}\left(k\right)$

$R_{ij}^{\left(1\right)}\left(k\right)=\underset{n=0}{\overset{N-1}{\Σ}}{r}_{ij}^{\left(1\right)}\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}$

$R_{ii}^{\left(1\right)}\left(k\right)=\underset{k=0}{\overset{N-1}{\Σ}}{r}_{ii}^{\left(1\right)}\[n\]e^{-j\frac{2\mathrm{\π}}{N}kn}.$

Delay time estimation method based on TDOA observed quantity location algorithm the most according to claim 3, it is characterised in that step The method of 4 calculation delay differences is as follows:

Step 4.1, the coherent signal obtaining step 3 carries out Hilbert transform, and method is as follows:

Order:

$Z_{ij}\left(k\right)=\left\{\begin{array}{cc}{R}_{ij}^{\left(2\right)}\left(k\right),& k=0\\ 2R_{ij}^{\left(2\right)}\left(k\right),& k=1,2,...,\frac{N}{2}-1\\ 0,& k=\frac{N}{2},\frac{N}{2}+1,...,N-1\end{array}\right.$

Z_ijThe inverse fourier transform z of (k)_ij[n] is:

$z_{ij}\[n\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{Z}_{ij}\left(k\right)e^{j\frac{2\mathrm{\π}}{N}kn}$

Hilbert transformFor:

${\hat{r}}_{ij}^{\left(2\right)}\[n\]=-j(z_{ij}\[n\]-r_{ij}^{\left(2\right)}\[n\])$

Step 4.2, calculates the envelope function of coherent signal, and formula is as follows:

${\mathrm{EN}}_{ij}\[n\]=r_{ij}^{\left(2\right)}\[n\]+j{\hat{r}}_{ij}^{\left(2\right)}\[n\]$

$e_{ij}\[n\]=|{\mathrm{EN}}_{ij}\[n\]|=\sqrt{{(r_{ij}^{\left(2\right)}\[n\])}^2+{({\hat{r}}_{ij}^{\left(2\right)}\[n\])}^2}$

${\mathrm{\θ}}_{ij}\[n\]=\arctan \frac{{\hat{r}}_{ij}^{\left(2\right)}\[n\]}{r_{ij}^{\left(2\right)}\[n\]}$

Wherein: EN_ij[n] isEnvelope function, e_ij[n] and θ_ij[n] is respectively envelope range value and phase place；

Step 4.3, calculates the delay inequality between receiving terminal and different base station, and formula is as follows:

${\mathrm{\Δt}}_{ij}\[n\]=\frac{e_{ij}\[n\]-N}{F_s}$

Wherein: Δ t_ij[n] is the delay inequality of the signal of the i-th base station that receives of receiving terminal and jth base station, F_sFor base station to Receiving terminal sends the frequency of signal.

Delay time estimation method based on TDOA observed quantity location algorithm the most according to claim 1, it is characterised in that receive End is equal to receiving terminal to the delay inequality of base station and amassing of the light velocity to the range difference of base station.

6., according to the delay time estimation method based on TDOA observed quantity location algorithm described in Claims 1 to 5 any one, it is special Levy and be, base station number m=4.