CN102914764A - Time difference positioning method for resisting sampling synchronous error of receiver - Google Patents

Abstract

The patent of the invention discloses a high-precision range difference-of-arrival (RDOA) positioning method for synchronous error existing in a sampling clock of a receiver. For the sampling synchronization of sampling clocks of a plurality of receivers, a clock reference is provided by generally using a global position system (GPS) and the high-precision synchronous sampling is realized. However, the leading edge of a pulse signal output by the sampling clock of each receiver has errors, so that sampling of the receiver is excited by a GPS clock pulse to generate a random error of a sampling period, and further the positioning precision of the RDOA is deteriorated. According to the positioning method disclosed by the invention, the influence on the positioning of the RDOA due to the synchronous error of the sampling clock is overcome by using the random change rule of the synchronous error of the sampling clock, so that the positioning precision of the RDOA is remarkably improved.

Description

A kind of time difference positioning method of anti-receiver sample-synchronous error

Technical field

The invention belongs to Passive Location, the high precision when relating in particular to a plurality of receiver sampling clocks and having synchronous error, arrive the location from range-difference measurements method fast.

Background technology

The high precision passive positioning has important using value in radar, sonar, satellite and systems such as communicating by letter.Arriving range difference (Range Difference Of Arrival, RDOA) location is a kind of important high-precision locating method, obtains a wide range of applications in sonar, radar and other radio-positioning navigation field.Existing RDOA localization method is broadly divided into geometry bracketing method and statistical decision method two large classes.Wherein, how much bracketing methods mainly utilize signal source that the RDOA measured value comprises and the geometry site between the receiver, the position of directly calculating target; Statistical decision method can be utilized unnecessary RDOA measured value, according to the statistical property of measuring error, and the optimum position result.Statistical decision method has a lot, comprises that mainly KF (Kalman Filtering), TSE (Taylor Series Expansion), DAC (Divide And Conquer), SI (Spheral Interpolation), SX (Spheral Intersection), PX (Plane intersection) and some improve one's methods.These Classic Geiger location approachs have obtained widespread use in passive positioning.

Patent of the present invention is mainly in the situation that there is the high precision RDOA localization method of synchronous error in the receiver sampling clock.For realizing the synchronous of a plurality of receiver sampling clocks, general using GPS (GPS) provides clock reference in passive location system, realizes the high-precise synchronization sampling.Its ultimate principle is that each receiver sampling clock excites forward position and the gps time of the pulse signal of realizing each receiver sampling clock output synchronous through the time clock of GPS.But because there is error in the forward position of the pulse signal of each receiver sampling clock output, so that there is the stochastic error in a sampling period in the sampling of receiver after the gps clock pulse excitation, cause the RDOA bearing accuracy to worsen.Therefore, be necessary to develop a kind of high-precision locating method of anti-receiver sampling clock synchronous error.

Summary of the invention

The objective of the invention is to exist the situation of synchronous error that a kind of high-precision RDOA localization method is provided for the receiver sampling clock.

According to the method, utilize the characteristics of receiver sampling clock synchronous error in the actual RDOA positioning system, model corresponding synchronous error model, then when the estimating target position, estimate simultaneously the sample-synchronous error, finally obtain hi-Fix by eliminating the sample-synchronous error.

The inventive method comprises the steps:

1) according to receiver sample-synchronous error model and systematic parameter (sampling rate), the discrete synchronous error collection of structure.

2) get concentrated a bit in measuring distance is poor, the offseting of discrete synchronous error, then use least square method to estimate corresponding location parameter, and calculate and estimate residual error.Traversal error collection obtains the location parameter corresponding with discrete synchronous error collection and estimates collection and set of residuals.

3) the search set of residuals is estimated as optimal estimation with the location parameter that wherein least residual is corresponding, also can obtain corresponding sample-synchronous estimation of error simultaneously.

Description of drawings

Fig. 1 has shown that in the range observation variance be σ _lThe positioning error accumulated probability curve of the inventive method and SI method in the time of=1.5 meters.

Fig. 2 has shown that in the range observation variance be σ ₁The positioning error accumulated probability curve of the inventive method and SI method in the time of=3.0 meters.

Fig. 3 has shown that in the range observation variance be σ ₁The positioning error accumulated probability curve of the inventive method and SI method in the time of=6.0 meters.

Embodiment

The RDOA location relates to a plurality of research stations and observes simultaneously same emitter Signals.Take two-dimensional localization as example, emissive source and research station are positioned at same plane, and each research station receives the same signal of emissive source radiation, calculate the RDOA with respect to reference station.Here do not consider the measuring process of RDOA.

Suppose in rectangular coordinate system, the position of N research station is S _i(x _i, y _i), i=1,2 ..., N, radiation source are positioned at S (x, y), are defined as follows parameter:

S _iDistance to initial point

$r_i=\sqrt{x_i^2+y_i^2},i=\mathrm{1,2}...,N---\left(1\right)$

S is to the distance of initial point

$r=\sqrt{x^2+y^2}---\left(2\right)$

S is to S _iDistance

$d_i=\sqrt{{(x-x_i)}^2+{(y-y_i)}^2},i=\mathrm{1,2}...,N---\left(3\right)$

S _iAnd S _jBetween the emissive source signal propagation distance that records poor

d _ij＝d _i-d _j i，j＝1，2，...，N，i≠j (4)

N research station is total

Individual different distance is measured combination, namely produces Individual range difference, wherein only having N-1 is independently, all the other range differences are fully definite by this N-1 range difference.Might as well select S ₁Be reference station, calculate one group of independently range difference set, be designated as d=(d ₁, d ₂..., d _N) ^TIf, there is measuring error, the range difference measured value is d _I1=d _i-d ₁+ n _I1, i=2,3 ..., N, wherein n _I1Expression S _iAnd S ₁Between the range difference measuring error, write as vector form N=(n ₂₁, n ₃₁..., n _N1) ^TFor the distributed model of range difference measuring error, suppose n _I1Obey the distribution of zero-mean, and n _I1And n _J1Separate, i here, j=2 ..., N; I ≠ j.

The sampling of a plurality of receivers have error synchronously the time, range difference measured value model can be expressed as d _I1=d _i-d ₁+ n _I1+ v _I1, i=2,3 ..., N, wherein v _I1Expression S _iAnd S ₁Between range difference measure by the error that causes synchronously and v _I1In discrete set { θ, 0, θ }, evenly distribute v _I1～U{-θ, 0, θ }, θ is the signal propagation distance in the sampling period.

In location Calculation, with the source to reference station apart from d ₁Separate parameter as one and estimate separately, but with its as and the separate redundant parameter of radiation source coordinate directly do least-squares estimation, obtaining d ₁After the initial estimation of radiation source coordinate, recycle the restriction relation that exists between them, construct another independently linear least-squares problem, to obtain comparatively accurate location estimation.In little error territory, if the statistical property of known measuring error can also be weighted processing.

The implementation step of localization method of the present invention is as follows:

1) the discrete synchronous error collection of structure is by error v _I1Model, the order

$v=\left[\begin{array}{c}{v}_{21}\\ v_{31}\\ .\\ .\\ .\\ v_{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">N</figure-callout>}1}\end{array}\right]$

Then v has M=3 ^N-1Plant combination, the set that makes v is I.

2) to any v ∈ I, calculate d _I1=d _I1-v _I1, i=2,3 ..., N.Introduce redundant variables d ₁, from (1) to (4) formula conversion obtains the linear orientation equation

$\frac{1}{2}\&CenterDot;(d_{i1}^2-r_i^2+{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">r</figure-callout>}}_1^2)={-x}_{i1}x-y_{i1}y-d_{i1}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1,i=2,...,N---\left(5\right)$

Only consider little error condition, write as matrix form

δ＝Ap+ε (6)

Wherein

$A=\left[\begin{array}{ccc}{-x}_{21}& {-y}_{21}& {-d}_{21}\\ .& .& .\\ .& .& .\\ .& .& .\\ {-x}_{N1}& {-y}_{N1}& {-d}_{N1}\end{array}\right],$ $p=\left[\begin{array}{c}x\\ y\\ {\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\end{array}\right],$

x _i1＝x _i-x ₁，y _i1＝y _i-y ₁，i＝2，...，N；

Suppose Q _ε=cov{ ε }=T ₁Q ₀T ₁, the weighted least-squares of p is estimated

${\hat{p}}_{\mathrm{WLS}}={\left(A^T{Q}_{\mathrm{\&epsiv;}}^{-1}A\right)}^{-1}{A}^T{Q}_{\mathrm{\&epsiv;}}^{-1}\mathrm{\&delta;}---\left(8\right)$

The variance of estimating is

$Q_p=\mathrm{cov}\left\{{\hat{p}}_{\mathrm{WLS}}\right\}={\left(A^T{T}_1^{-1}{Q}_0^{-1}{T}_1^{-1}A\right)}^{-1}---\left(9\right)$

Because ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1^2={(x-x_1)}^2+{(y-y_1)}^2,$ The structure linear equation

V＝Hu+ε ₁ (10)

$V=\left[\begin{array}{c}{(p\left(1\right)-x_1)}^2\\ {(p\left(2\right)-x_2)}^2\\ p^2\left(3\right)\end{array}\right],$ $H=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 1& 1\end{array}\right],$ $u=\left[\begin{array}{c}{(x-x_1)}^2\\ {(y-y_1)}^2\end{array}\right],$ ${\mathrm{\&epsiv;}}_1\&ap;{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">T</figure-callout>}}_2\&CenterDot;\mathrm{\&delta;p}=\left[\begin{array}{ccc}2(x-x_1)& 0& 0\\ 0& 2(y-y_1)& 0\\ 0& 0& 2{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\end{array}\right]\&CenterDot;\left[\begin{array}{c}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1\\ \mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2\\ \mathrm{\&Delta;}{\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">p</figure-callout>}}_3\end{array}\right]$

Suppose Then the weighted least-squares of u is estimated as

${\hat{u}}_{\mathrm{WLS}}={\left(H^T{Q}_{{\mathrm{\&epsiv;}}_1}^{-1}H\right)}^{-1}{H}^T{Q}_{{\mathrm{\&epsiv;}}_1}^{-1}V---\left(11\right)$

The variance of estimating is

$Q_u=\mathrm{cov}\left\{\mathrm{\&Delta;}{\hat{u}}_{\mathrm{WLS}}\right\}={\left(H^T{Q}_{{\mathrm{\&epsiv;}}_1}^{-1}H\right)}^{-1}={\left(H^T{T}_2^{-1}{Q}_p^{-1}{T}_2^{-1}H\right)}^{-1}---\left(12\right)$

Then utilize u and x=[x _sy _s] ^TBetween relation, calculate location estimation and the Positioning estimation error covariance thereof of emissive source.

Calculate e=d-v-b, wherein b=[b ₂₁... b _M1] ^T, $b_{m1}=\sqrt{{(x_m-{\hat{x}}_s)}^2+{(y_m-{\hat{y}}_s)}^2}-\sqrt{{(x_1-{\hat{x}}_s)}^2+{(y_1-{\hat{y}}_s)}^2},$

With

By

Obtain.The set E that the set U that the estimation that allows v traversal set I obtain M u forms and the estimation of M e form.

3) to e ∈ E, search makes the residual error cost function

Minimum e is corresponding

Be final estimation, and obtain corresponding location estimation

With

The positioning performance of two kinds of methods is assessed in experiment by the positioning error accumulated probability curve of contrast the inventive method and Chan ' s SI method.Use 4 base stations in the experiment, the base station location parameter is respectively S ₁: (35.9,1.4) km, S ₂: (20.0,0.0) km, S ₃: (5.9,2.3) km, S ₄: (32.0,7.0) km.Locating area be 1 dead ahead, base station, 200～400km, about-rectangular area of 100～100km.Locating area is divided into 10km * 10km grid, and target is placed on the summit of grid (totally 201 * 201 impact points) and tests.Sample frequency is 40MHz/s, and the sampling period is 25ns.Measuring error n _lStandard deviation sigma _iGetting respectively 1.5 meters, 3.0 meters and 6.0 meters tests.

Fig. 1～Fig. 3 illustrates respectively the method for patent of the present invention and Chan ' s SI method at σ _iGet respectively the positioning error accumulated probability curve in 1.5 meters, 3.0 meters and the 6.0 meters situations.Transverse axis is relative positioning error

$\frac{\sqrt{{(\hat{p}\left(1\right)-x)}^2+{(\hat{p}\left(2\right)-y)}^2}}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="119122DEST\_PATH\_HSA00000786574200011.png,DEST\_PATH\_HSB00000978894300012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}\&times;100\%$

Can find out from Fig. 1～Fig. 3, when having the sample-synchronous error, the method for patent of the present invention can significantly improve bearing accuracy.For example, when the standard deviation of range observation is 1.5 meters, the relative positioning error of the method for patent of the present invention is respectively 70%, 96% and 100% less than 0.5%, 1% and 1.8% probability, and the relative positioning error of Chan ' s SI method is respectively 43%, 73% and 92% less than 0.5%, 1% and 1.8% probability.When the standard deviation of estimating in the time difference was larger, the method for patent of the present invention is compared with Chan ' s SI method had clear superiority (referring to Fig. 2 and Fig. 3) equally.

Although the method for with reference to the accompanying drawings this patent having been invented is described with way of example, the invention is not restricted to above-mentioned these details, and the present invention contains various modification or the change of covering within the claim scope.

Industrial applicability

The localization method that the present invention can be proposed be applied to arrive the location from range-difference measurements system, satisfies the hi-Fix requirement in the situation that there is synchronous error in the receiver sampling clock.

Claims (5)

1. the time difference positioning method of an anti-receiver sample-synchronous error, it is characterized in that: utilize the actual characteristics that arrive receiver sampling clock synchronous error in range difference (RDOA) positioning system, set up corresponding synchronous error model, when the estimating target position, estimate simultaneously the sampling clock synchronous error, finally obtain hi-Fix by eliminating the sampling clock synchronous error.Its concrete steps are:

According to receiver sampling clock synchronous error model and systematic parameter (sampling rate), the discrete synchronous error collection of structure.

Get concentrated a bit in arriving the range difference measurement, the offseting of discrete synchronous error, then use least square method to estimate corresponding location parameter, and residual error is estimated in calculating.The discrete synchronous error collection of traversal obtains the location parameter corresponding with discrete synchronous error collection and estimates collection and set of residuals.

The search set of residuals is estimated as optimal estimation with the location parameter that wherein least residual is corresponding, also can obtain corresponding sampling clock synchronous error simultaneously and estimate.

2. the time difference positioning method of anti-receiver sample-synchronous error as claimed in claim 1 is characterized in that: by sampling clock synchronous error v _I1Determine N-1 dimensional vector v=[v ₂₁... v _N1], wherein N represents the receiver number, again by sampling clock synchronous error v _I1Discrete synchronous error collection { θ, 0, θ }, the set of determining all possible N-1 dimensional vector v is error collection I: $I=\{v_1,v_2,...,v_{3^{v-1}}\}$

v ₁＝[-θ，0，...，0]，v ₂＝[0，0，...，0]，v ₃＝[θ，0，...，0]，v ₄＝[0，-θ，...，0]，...，

Wherein θ is the signal propagation distance in the sampling period.

3. the time difference positioning method of anti-receiver sample-synchronous error as claimed in claim 1, it is characterized in that: get a vector among the error collection I, in arriving the range difference measurement, offset, then use least square method to estimate corresponding location parameter, and calculate corresponding residual error; Traversal error collection I obtains and error collection I one to one location parameter estimation collection and set of residuals.

4. the time difference positioning method of anti-receiver sample-synchronous error as claimed in claim 1 is characterized in that: determine that least square solution is

p＝(A ^TA) ^-1A ^Tδ

Wherein () ^TThe transposition of representing matrix or vector,

$A=\left[\begin{array}{ccc}{-x}_{21}& {-y}_{21}& {-\hat{d}}_{21}\\ .& .& .\\ .& .& .\\ .& .& .\\ {-x}_{N1}& {-y}_{N1}& -{\hat{d}}_{N1}\end{array}\right],$ $\mathrm{\&delta;}=\frac{1}{2}\left[\begin{array}{c}{\hat{d}}_{21}^2-r_2^2+r_1^2\\ {\hat{d}}_{13}^2-r_3^2+r_1^2\\ .\\ .\\ .\\ {\hat{d}}_{N1}^2-r_N^2+r_1^2\end{array}\right]$

x _I1=x _i-x ₁, y _I1=y _i-y ₁,

v _I1The sampling clock synchronous error, i.e. i-1 element of a vector v among the error collection I, d _I1Measure for arriving range difference, i=2 ..., N;

(x _i, y _i) be the position coordinates of N receiver, i=1 ..., N;

Determine that location parameter is the first two element of p

Determine location parameter

Corresponding residual error is ε=(δ-Ap) ^T(δ-Ap), wherein () ^TThe transposition of representing matrix or vector;

Each vector v among the traversal error collection I is determined respectively corresponding location parameter

And residual epsilon, the location parameter that all are corresponding

Form the location parameter collection, all corresponding residual epsilon form set of residuals.

5. the time difference positioning method of synchronous error when anti-receiver as claimed in claim 1 is sampled is characterized in that: the search set of residuals is estimated as final source location with the location parameter that wherein least residual is corresponding and estimates.

Images