CN103874192A - Pseudo code ranging time delay estimation method - Google Patents

Abstract

The invention provides a pseudo code ranging time delay estimation method. The method comprises that: a receiving end samples the received baseband signal so that a sampling signal is obtained, and digital matching filtering is performed on the sampling signal so that a digital filtering signal is obtained; a first extreme value point of the digital filtering signal is searched and acquired; and estimation values of coefficients a, b and c of Taylor series near the position of the first extreme value point are defined, the extreme value point is selected to be the center, and least square estimation is performed on the coefficients a, b and c by 2m+1 sample value points of extreme value points of distance of two sides within a code element period of being not greater than 1/4 so that the estimation values (img file='DDA00002566275600011. TIF' wi='157' he='58 /) are obtained, and signal arrival estimation time (img file='DDA00002566275600012. TIF' wi='61' he='58 /) is obtained. Complexity of exiting methods is reduced by the method. Meanwhile, non-ideal factors in channels are considered so that the delay estimation method is wider in range of application.

Description

A kind of time delay estimation method of pseudo-random code ranging

Technical field

The present invention relates to radio distance-measuring and field of locating technology, particularly a kind of time delay estimation method of digital pseudo-random code ranging.

Background technology

Radio distance-measuring technology mainly contains Doppler ranging method at present, pseudo-random code ranging method, and carrier wave telemetry etc.Wherein, pseudo-random code ranging can be divided into unidirectional range finding and bidirectional ranging, no matter be which kind of metering system, all need time of arrival (toa) to estimate, mainly contain several as follows according to the signal receiving to estimating (being that time delay is estimated) method the time of advent:

Maximum Likelihood Estimation Method

Maximum Likelihood Estimation Method is asymptotic optimization method in the known estimation technique, can reach carat Metro circle (Cramer-Rao Bound) in the situation that of high s/n ratio, and it calculates under white Gaussian noise multi-path environment.Although Maximum Likelihood Estimation Method is asymptotic optimization method under white Gaussian noise, owing to need to doing optimization and a large amount of mathematical operation of polytomy variable, complexity is higher, and hardware is realized comparatively difficulty, so practical degree is not high.

The maximum-likelihood method of simplifying

For digital baseband system, the base band pseudo-code signal after waveform shaping through channel after receiving end is accepted, through pseudo-code matched filtering and forming filter, the result obtaining and be of equal value to the sampling of matched filtering result under analog case.

There is document that signal is carried out to matched filtering after A/D sampling, then utilize Signal Matching filtering result near maximum point, to carry out secondary Taylor expansion, then utilize sample point to estimate, so maximum likelihood is estimated to be reduced under awgn channel:

Wherein, t is the vector of one section of continuous sampling time point composition, the autocorrelation matrix that R is signal, and h is the sample value in the t moment in matched filtering result.Although this method is simple, but noise is also not exclusively thermal noise (white Gaussian noise) in practice, in the system that has carrier wave, also have the non-ideal factors such as phase noise (non-white Gaussian noise) and non-linearity of power amplifier, so might not be asymptotic optimization in this case.

In sum, at present method or complexity is high, is difficult to realize; Too simplify, do not consider the non-ideal factor in channel, narrow application range.

Summary of the invention

(1) technical problem to be solved

The object of the invention is to propose a kind of time delay estimation method that is suitable for pseudo-random code ranging, the method has reduced computation complexity, considers non-ideal factor in channel simultaneously, makes the time-delay estimation method scope of application wider.

(2) technical scheme

A kind of time delay estimation method that the invention provides pseudo-random code ranging, the method comprises:

S1, receiving end are sampled and are obtained sampled signal the baseband signal receiving, and sampled signal is carried out to digital matched filtering obtain digital matched filtering signal;

S2, search for and obtain the first extreme point of digital matched filtering signal;

S3, the quadratic term coefficient a, the Monomial coefficient b that are defined in first Near The Extreme Point simulation matched filtering signal the second Taylor series formula and the estimated value of constant term c are: $\widehat{\mathrm{\θ}}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right],$ Select centered by extreme point, two lateral extent extreme points are no more than 2m+1 sample point p (n in 1/4 code-element period _-m), p (n _-m+1) ..., p (n _-1), p (n ₀) ..., p (n _m) to coefficient a, b, c does least-squares estimation: $\widehat{\mathrm{\θ}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]={\left(H^{T}H\right)}^{-1}{H}^{T}X,$ Obtain estimated value

the time delay of signal is estimated as:

Wherein, described m>=1, X is the column vector of sample point composition: X=[p (n _-m) p (n _-m+1) ... p (n _m)] ^t, H is measurement matrix: $H\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{ccc}{n}_{-m}^2& n_{-m}& 1\\ n_{-m+1}^2& n_{-m+1}& 1\\ .& .& .\\ .& .& .\\ .& .& .\\ n_m^2& {\mathrm{<figure-callout\; id="1"\; label="n\; m"\; filenames="HDA00002566275500021.png"\; state="\{\{state\}\}">n</figure-callout>}}_m& 1\end{array}\right].$

Preferably, the receiving end in described step S1 is two line structures that have in-phase component and quadrature component.

Preferably, in described step SI, also comprise that the digital matched filtering signal that matched filtering obtains to two-way carries out two norm computings, removes the step of frequency deviation and skew.

Preferably, in described step S1, also comprise digital matched filtering signal is carried out to Low-pass interpolation, make sample rate be greater than 5 divided by code-element period.

Preferably, described m value is fixing, (H ^th) ^-1h ^t=C is constant matrices, and coefficient is estimated as: $\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]=\mathrm{CX},$ Time delay is estimated as:

wherein T _ssample rate, n ' ₀for n ₀true moment value of moment.

(3) beneficial effect

The present invention is by providing a kind of time delay estimation method of pseudo-random code ranging, make to estimate time delay time do not need iteration optimization to ask extreme value, be only instead Linear Algebra Operation, greatly abbreviation the estimation computing of time delay.Precision is higher, when the increase result of the increase along with sample rate and signal to noise ratio is tending towards optimum, is highly suitable for the system that real-time system and complexity are not high, therefore has broad application prospects.

Accompanying drawing explanation

Fig. 1 is the flow chart of steps that the invention provides method;

Fig. 2 is receiver structure schematic diagram in specific embodiment;

Fig. 3 is matched filtering result schematic diagram in specific embodiment;

Fig. 4 is that in specific embodiment, the present invention is used in the performance chart under Gaussian channel.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further details.

The invention provides a kind of time delay estimation method of pseudo-random code ranging, as shown in Figure 1, its step mainly comprises:

S1, receiving end are sampled and are obtained sampled signal the baseband signal receiving, and sampled signal is carried out to digital matched filtering obtain digital filtered signal;

S2, search for and obtain the first extreme point of digital filtered signal;

S3, the quadratic term coefficient a, the Monomial coefficient b that are defined in first Near The Extreme Point simulation matched filtering signal the second Taylor series formula and the estimated value of constant term c are: $\widehat{\mathrm{\&theta;}}\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right],$ Select centered by extreme point, two lateral extent extreme points are no more than 2m+1 sample point p (n in 1/4 code-element period _-m), p (n _-m+1) ..., p (n _-1), p (n ₀) ..., p (n _m) to coefficient a, b, c does least-squares estimation: $\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]={\left(H^{T}H\right)}^{-1}{H}^{T}X,$ Obtain estimated value

the time delay of signal is estimated as:

Wherein, described m>=1, X is the column vector of sample point composition: X=[p (n _-m) p (n _-m+1) ... p (n _m)] ^t, H is measurement matrix: $H\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{ccc}{n}_{-m}^2& n_{-m}& 1\\ n_{-m+1}^2& n_{-m+1}& 1\\ .& .& .\\ .& .& .\\ .& .& .\\ n_m^2& {\mathrm{<figure-callout\; id="1"\; label="n\; m"\; filenames="HDA00002566275500021.png"\; state="\{\{state\}\}">n</figure-callout>}}_m& 1\end{array}\right].$ Utilize least square method can't the distribution of noise be done and be supposed, just noise held stationary during measuring, this makes the range of application of this method more extensive.

Wherein, the receiving end in step S1 is the structure that has in-phase component and quadrature component two-way.

Wherein, in step SI, also comprise that the digital matched filtering signal that matched filtering obtains to two-way carries out two norm computings, removes the step of frequency deviation and skew.

Wherein, step S1 also comprises digital matched filtering signal is carried out to Low-pass interpolation, makes sample rate be greater than 5/ code-element period.

Wherein, make m value fixing, (H ^th) ^-1h ^t=C is constant matrices, and coefficient estimated value is: $\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]=\mathrm{CX},$ Time delay estimated value is:

wherein T _ssample rate, n ' ₀for n ₀true moment value of moment.Like this, estimate it is only Linear Algebra Operation, greatly simplified the estimation computing of time delay.

Concrete step and principle:

S1, receiving end are sampled after to the baseband signal r receiving (t), sample rate is more than or equal to Nyquist Nyquist sample rate, obtain r (n), then r (n) is carried out to digital matched filtering, obtain matched filtering result p (n).For there being in-phase component (In-phase Component, I road) and quadrature component (Quadrature Component, Q road) system, when incoherent down-conversion, frequency deviation and skew be can there is, frequency deviation and skew removed thereby can carry out two norm computings to I, Q two-way matched filtering result.Then, p (n) is carried out to Low-pass interpolation, make sample rate be greater than 5 divided by code-element period, make like this result of matched filtering better; If sample rate has exceeded 5 divided by code-element period, can carry out interpolation;

S2, the signal p (n) after interpolation is searched for to first extreme point, it is positioned at time point n ₀, due to the characteristic of pseudo-code signal, first extreme point has indicated the first position in time, footpath that reaches roughly;

The maximum that may not adopt the analog signal p (t) that p (n) is corresponding due to sampled point, so need to utilize the value of p (n) to estimate p (t) maximum point position in time;

S3, the quadratic term coefficient a, the Monomial coefficient b that are defined near the second Taylor series formula in first extreme point position and the estimated value of constant term c are: $\widehat{\mathrm{\&theta;}}\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right],$ Select centered by extreme point, two lateral extent extreme points are no more than 2m+1 sample point p (n in 1/4 code-element period _-m), p (n _-m+1) ..., p (n _-1), p (n ₀) ..., p (n _m) to coefficient a, b, c does least-squares estimation:

signal due in estimated value is:

Wherein, m>=1, X is near the column vector of the sample point composition of matched filtering result extreme value: X=[p (n _-m) p (n _-m+1) ... p (n _m)] ^t, H is matrix: $H\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{ccc}{n}_{-m}^2& n_{-m}& 1\\ n_{-m+1}^2& n_{-m+1}& 1\\ .& .& .\\ .& .& .\\ .& .& .\\ n_m^2& {\mathrm{<figure-callout\; id="1"\; label="n\; m"\; filenames="HDA00002566275500021.png"\; state="\{\{state\}\}">n</figure-callout>}}_m& 1\end{array}\right].$

The principle of step S3 is: because the pseudo-code signal after Waveform shaping is through matched filtering, can present convexity at its extreme point, so, even if the nonlinear devices such as power amplifier can cause distortion to signal, but convexity can not change, so can do Taylor expansion at Near The Extreme Point, for simulation matched filtering signal p (t), at its extreme point t ₀near Taylor expansion expression formula is:

p(t)＝a(t-t ₀) ²+b(t-t ₀)+c+o(t ²)+n(t)

Wherein, a, b, c is respectively Taylor expansion coefficient, and n (t) is noise, o (t ²) be the second order dimensionless of t, can neglect.So just, can utilize Near The Extreme Point to utilize least square method to coefficient a, b, c estimates, obtains estimated value

thereby the coefficient of the quadratic function obtaining, so the time location at its symmetry axis place can be used as the accurate estimation of p (t) extreme point place time location, so just obtains propagation delay.Because least square method can't be done and suppose the distribution of noise, just noise held stationary during measuring.This makes this method range of application can be more extensive.

Although expression formula:

more complicated, in fact, can make n in form _-m=-m, n _-m+1=-m+1 ..., ₀=0, n _m=m..In the time that m is fixing, this condition of the system conventionally designing generally all meets, (H ^th) ^-1h ^t=C is constant matrices, can precompute, and so just can think p (t) is wanted to be translation n on time shaft ₀, and then flexible 1/T on time shaft _s, the maximum point t estimating can calculate by following expression:

$\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]=\mathrm{CX},$ ?

wherein T _ssample rate, n ' ₀for n ₀true moment value of moment.

Here adopt receiver as shown in Figure 2:

From the signal of antenna reception after bandpass filtering, by I, Q two-way down-conversion, sample through low-pass filtering and A-D converter ADC, ADC sample rate is 1GHz, pass through again matched filter: comprise forming filter and pseudo-code matched filter, what in this example, formed filter adopted is square root raised cosine filter, then obtains I, Q two-way output signal.

Output signal is carried out carrier wave recovery or is directly done two norm computings and eliminate carrier wave impact, then carry out more than Low-pass interpolation to 5 times character rate, finally obtain matched filtering result: as shown in Figure 3, the time value that wherein abscissa is matched filtering, ordinate is matched filtering result value, the signal to noise ratio wherein using is 0dB, and pseudo-code length is 127.

Choose maximum three sampling points [111.4590,127.3509,111.8500] and carry out least-squares estimation, wherein H matrix can adopt:

$H=\left[\begin{array}{ccc}1& -1& 1\\ 0& 0& 1\\ 1& 1& 1\end{array}\right]$

Be n _-1=-1, n ₀=0, n ₁=1, n ₀real corresponding moment n ' ₀=2.7300 × 10 ^-07s so now, constant matrices:

$C={\left(H^{T}H\right)}^{-1}{H}^T=\left[\begin{array}{ccc}0.5& -1& 0.5\\ -0.5& 0& 0.5\\ 0& 1& 0\end{array}\right]$

$\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]=\mathrm{CX}=\left[\begin{array}{ccc}0.5& -1& 0.5\\ -0.5& 0& 0.5\\ 0& 1& 0\end{array}\right]\&times;\left[\begin{array}{c}111.4590\\ 127.3509\\ 111.8500\end{array}\right]=\left[\begin{array}{c}-15.6964\\ 0.1955\\ 127.3509\end{array}\right]$

Obtain: $\hat{t}=-\frac{\hat{a}}{2\hat{b}}\&times;T_s+{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA00002566275500021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1^{\&prime;}=-0.0062\&times;5\&times;{10}^{-10}+2.7300\&times;{10}^{-07}\&ap;2.7300\&times;{10}^{-07}\left(s\right),$

So just can estimate the time delay that is less than chip period, increase the precision of time delay.

Under this numerical procedure, only need to do simple multiply-add operation as seen, multiplication, addition complexity increase to o (n with what estimate to count ²).

Fig. 4 is the performance curve for use the inventive method of Fig. 1 receiver, the simulation result under awgn channel.For other situations, also can obtain similar results.Can see, the in the situation that of medium signal to noise ratio, can reach estimated accuracy well.For general range finding application, mean square error is less than 10 ^-10s, the respective distances error 3cm (light velocity × 10 ^-10s) can well satisfy the demands.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, do not departing under the prerequisite of the technology of the present invention principle; can also make some improvement and replacement, these improvement and replacement also should be considered as protection scope of the present invention.

Claims (5)

1. a time delay estimation method for pseudo-random code ranging, is characterized in that, the method comprises:

S1, receiving end are sampled and are obtained sampled signal the baseband signal receiving, and sampled signal is carried out to digital matched filtering obtain digital matched filtering signal;

S2, search for and obtain the first extreme point of digital matched filtering signal;

S3, the quadratic term coefficient a, the Monomial coefficient b that are defined in first Near The Extreme Point simulation matched filtering signal the second Taylor series formula and the estimated value of constant term c are: $\widehat{\mathrm{\&theta;}}\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right],$ Select centered by extreme point, two lateral extent extreme points are no more than 2m+1 sample point p (n in 1/4 code-element period _-m), p (n _-m+1) ..., p (n _-1), p (n ₀) ..., p (n _m) to coefficient a, b, c does least-squares estimation: $\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]={\left(H^{T}H\right)}^{-1}{H}^{T}X,$ Obtain estimated value

the time delay of signal is estimated as:

Wherein, described m>=1, X is the column vector of sample point composition: X=[p (n _-m) p (n _-m+1) ... p (n _m)] ^t, H is measurement matrix: $H\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{ccc}{n}_{-m}^2& n_{-m}& 1\\ n_{-m+1}^2& n_{-m+1}& 1\\ .& .& .\\ .& .& .\\ .& .& .\\ n_m^2& n_m& 1\end{array}\right].$

2. method as claimed in claim 1, is characterized in that, the receiving end in described step S1 is two line structures that have in-phase component and quadrature component.

3. method as claimed in claim 2, is characterized in that, also comprises: the digital matched filtering signal that matched filtering obtains to two-way carries out two norm computings, removes frequency deviation and skew in described step SI.

4. either method as described in claim 1-3, is characterized in that, in described step S1, also comprises: digital matched filtering signal is carried out to Low-pass interpolation, make sample rate be greater than 5 divided by code-element period.

5. method as claimed in claim 1, is characterized in that, described m value is fixing, (H ^th) ^-1h ^t=C is constant matrices, and coefficient is estimated as: $\widehat{\mathrm{\&theta;}}=\left[\begin{array}{c}\hat{a}\\ \hat{b}\\ \hat{c}\end{array}\right]=\mathrm{CX},$ Time delay is estimated as:

wherein T _ssample rate, n ' ₀for n ₀true moment value of moment.

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