WO2016095694A1 - 一种存在传感器误差的改进源定位算法 - Google Patents
一种存在传感器误差的改进源定位算法 Download PDFInfo
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- WO2016095694A1 WO2016095694A1 PCT/CN2015/095904 CN2015095904W WO2016095694A1 WO 2016095694 A1 WO2016095694 A1 WO 2016095694A1 CN 2015095904 W CN2015095904 W CN 2015095904W WO 2016095694 A1 WO2016095694 A1 WO 2016095694A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations
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- the invention belongs to the technical field of wireless sensor networks, and in particular relates to a source positioning method with sensor errors.
- Wireless sensor network is a multi-hop self-organizing network system composed of a large number of micro sensor nodes deployed in the monitoring area. The purpose is to collaboratively sense, collect and process. The object information is sensed in the network coverage area and sent to the observer.
- the positioning problem in the sensor network has attracted wide attention, and it has been applied in many fields, such as monitoring, navigation, target tracking and so on. Among all the positioning problems, passive source positioning plays an extremely important role in the military.
- the commonly used estimation method is to use the signal to reach the time difference of arrival (TDOA).
- TDOA time difference of arrival
- these sensors are often placed on mobile platforms such as airplanes, satellites or drones.
- FDOA Frequency Difference of Arrival
- the position and velocity of the target source can be described by a strong nonlinear equation with respect to the measurement of the time-frequency difference.
- Maximum like lihood (ML) is an effective tool to solve this problem, but using this method requires exhaustive search in the solution space. Not only is the algorithm computationally large and cannot be applied in real time.
- a preferred method is The time-frequency difference equation is linearized using the Taylor series expansion method.
- This method requires an initial estimate and does not guarantee convergence to the global optimal solution.
- the existing literature proposes some closed solutions.
- the well-known two-step weighted Least Squares (2-step WLS) method proposed by Ho et al. effectively solves the linearization problem of strong nonlinear equations by introducing two parameters.
- Wei et al. proposed a multidimensional scaling (MDS) analysis method to extend the classical MDS framework to a specific type of positioning problem.
- MDS multidimensional scaling
- Yu et al. Based on the Approximate Maximum Likelihood (AML) estimation method of time difference measurement, Yu et al. derived the time-frequency difference combined with the AML method, which can also realize real-time positioning and ensure global convergence.
- AML Approximate Maximum Likelihood
- n i1 /c represents the TDOA measurement noise of the zero-mean Gaussian distribution.
- the rate of change of the distance between the i-th sensor and the target is recorded as That is, the method of (1) is derived.
- the amount of FDOA measurement between the i-th sensor and the first sensor is
- the TDOA and FDOA measurements are combined to obtain a matrix form of two measurements, expressed as The corresponding measurement noise is
- X -1 on the right side of the above formula indicates that there is no CRLB under the error ⁇
- the second term on the right side of the above formula indicates that the addition of the sensor error brings about an increase in CRLB.
- estimator It contains the position and velocity information of the target to be located, then the probability density function for ⁇ under ⁇ conditions:
- the ML method solves the positioning problem by finding the appropriate ⁇ to minimize the J( ⁇ ). However, when there is an error in the sensor information, even if the solved ⁇ makes J( ⁇ ) reach the minimum value, the finally obtained solution ⁇ is not the optimal solution of the positioning problem (see the description of the drawing).
- the initial solution of ⁇ can be obtained by weighted least squares:
- FIG. 1 is a comparison of positioning accuracy of various algorithms in different scenes under different sensor errors
- FIG. 2 is a comparison of positioning accuracy of various algorithms in different scenes under different sensor errors in a far scene .
- the Matlab simulation results in the far scene are shown in Fig. 2.
- the traditional AML method is not applicable to the positioning scene with sensor error.
- the improved AML results presented in this paper are significantly better than the improved 2WLS method, and the threshold effect is also later.
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- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
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- Position Fixing By Use Of Radio Waves (AREA)
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Abstract
一种存在传感器误差的改进源定位算法，该算法是基于极大似然函数提出的一种改进的近似极大似然(AML)估计算法，通过更新带有传感器误差的代价函数以获取一个封闭的近似解，该算法不仅能实现实时定位，而且能保证全局收敛。仿真结果表明，算法在存在传感器误差场景下依然可以达到克拉美-罗下限(CRLB)，比已有的改进两步加权最小二乘(2-step WLS)算法更有效。
Description
本发明属于无线传感器网络技术领域，尤其涉及带有传感器误差的源定位方法。
无线传感器网络(wireless sensor network，WSN)是由部署在监测区域内大量的微型传感器节点组成，通过无线通信方式形成的一个多跳的自组织的网络系统，其目的是协作地感知、采集和处理网络覆盖区域中被感知对象信息，并发送给观察者。其中传感器网络中的定位问题引起了人们的广泛关注，它被应用于许多领域，如监控、导航、目标跟踪等等。在所有的定位问题中，被动源定位在军事方面有着极其重要的作用。
对于一个固定发射器，常用到的估计方法是利用信号达到不同传感器的时间差(Time difference of arrival,TDOA)进行求解。在现代定位的实际应用中，这些传感器常常被安放在移动平台上，如飞机、卫星或是无人机。当目标源和传感器之间存在相对运动时，到达频差(Frequency difference of arrival,FDOA)也可以被测量以增加定位精度。在每一个观测时刻，如果已知传感器的位置、速度信息和信号的传输速率，目标源的位置和速度可以通过关于时频差测量量的强非线性方程来描述。极大似然法(Maximum like lihood,ML)是解决这个问题的一种有效工具，但使用此方法需要在解空间内穷举搜索，不仅算法计算量大且不能被实时应用。一种可取的方法是
利用泰勒级数展开法线性化时频差方程。然而，该方法需要一个初始估计值，且不能保证收敛到全局最优解。为了避免这些问题，已有的文献提出了一些封闭的解方法。Ho等人提出的著名的两步加权最小二乘(Two-step Weighted Least Squares,2-step WLS)法，通过两个参数的引入有效地解决了强非线性方程的线性化问题。Wei等人提出了一种多维尺度(Multidimensional scaling,MDS)分析方法，将经典的MDS框架扩展到某类特定的定位问题中。Yu等人基于时差测量量的近似极大似然(Approximate Maximum Likelihood,AML)估计法，推导出了时频差结合AML法，也能实现实时定位并且保证了全局收敛性。
发明内容
1.设计移动源定位模型
考虑在三维空间中有M个传感器，第i个传感器的位置和速度(带有噪声)已知，分别记作si＝[xi yi zi]T， 
移动目标的位置和速度矢量分别为u＝[x y z]T， 
传感器的位置和速度在真值附近扰动，真值表示为 
在定位算法中，真值
和
是未知的。一般，我们用(·)o表示(·)的真值。
为了简化表示，我们用向量的形式来描述传感器信息，记作 
其中， 
传感器误差记为 
其中， 
假设Δβ是零均值高斯分布，它的协方差矩阵为E[ΔβΔβT]＝Qβ。
假设第i个传感器和目标之间的距离记作
表示为
式中，||·||表示向量的二阶形式。用c来表示信号的传输速度，则第i个传感器和第1个传感器之间的TDOA测量量为
其中，i＝2,3...M。ni1/c表示零均值高斯分布的TDOA测量噪声。M个传感器共M-1个TDOA测量量总记为d＝[d21 d31 … dM1]T＝do+n。
第i个传感器和目标之间距离的变化率记作
即对(1)式求导，得
用fc表示信号载频，则第i个传感器和第1个传感器之间的FDOA测量量为
式中，
表示零均值高斯分布的FDOA测量噪声。M个传感器共M-1个FDOA测量量总记为 
将TDOA和FDOA测量量合并，得到两个测量量的矩阵形式，表示为 
对应的测量噪声为 
协方差矩阵为E[ΔαΔαT]T＝Qα。并假设测量噪声Δα和传感器误差Δβ相互独立。
当定位问题中存在有测量误差α和传感器误差β时，CLRB可表示为CRLB(θ)＝X-1+X-1Y(Z-YTX-1Y)-1YTX-1。式中， 
可以看出，上式右边第一项X-1表示不存在误差β下的CRLB，上式右边第二项则表示传感器误差的加入带来CRLB的增大。
2.改进AML算法
定义估计量 
它包含待定位目标的位置和速度信息，则关于θ条件下的α的概率密度函数：
f(α/θ)＝(2π)-M/2(detQα)-1/2exp(-J/2) (5)
式中，
ML法通过寻找合适的θ使J(θ)达到最小值来求解定位问题。但是当传感器信息存在误差，即使求解的θ使J(θ)达到最小值，最终得到的解θ也不是该定位问题的最优解(见附图说明)。
为了考虑传感器的误差，我们重新定义(6)式：
J(θ)＝[h-g(θ)]TQ-1[h-g(θ)] (7)
式中，
协方差矩阵Q的定义可参考文献，
其 
令 
则公式(7)可简化为
J(θ)＝[y(θ)]TQ-1y(θ) (8)
上式对θ求偏导，得
式中，
令(9)式左边等于0，即得到下式：
2y'(θ)Q-1y(θ)＝0 (10)
将公式(10)中的y(θ)分解，得
式中，
令2y'(θ)Q-1＝A，将式(11)带入(10)中得
由于加权矩阵A包含有未知向量θ，故采用近似极大似然法求解θ。首先忽略加权矩阵A，即公式(12)可简化为
通过加权最小二乘即可获得θ的初始解：
下面结合附图和具体实例对本发明做进一步说明：图1为近场景下多种算法在不同传感器误差下的定位精度比较；图2为远场景下多种算法在不同传感器误差下的定位精度比较。
近场景下的Matlab仿真结果见图1，从图中可以看出，已有算法和本文的改进算法都可以很好的达到CRLB，这与文献中对近场景下运动目标定位精度较高的结论是一致的。
远场景下的Matlab仿真结果见图2，从图中可以看出，传统的AML法对于带有传感器误差的定位场景并不适用。而本文提出的改进AML结果明显优于改进的2WLS法，门槛效应也更晚出现。
Claims (3)
- 提出一种改进近似极大似然(Approximate Maximum Likelihood,AML)估计法，在存在传感器误差的情况下依然保证了定位结果的精确度。
- 在选取不同大小的传感器误差时，改进AML法定位效果均优于已有文献中的传统AML法和两步加权最小二乘(Two-step Weighted Least Squares,2-step WLS)法。
- 改进AML法计算简单且能够实现实时定位。在较高的信噪比下，本文算法能够达到CRLB，门槛效应也晚于2WLS法。
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| CN109959918A (zh) * | 2019-02-22 | 2019-07-02 | 西安电子科技大学 | 一种固态体定位的方法、装置及计算机存储介质 |
| CN112540343A (zh) * | 2020-11-19 | 2021-03-23 | 安徽大学 | 基于移动接收器协同分析的移动目标源定位方法 |
| CN115508774A (zh) * | 2022-10-12 | 2022-12-23 | 中国电子科技集团公司信息科学研究院 | 基于两步加权最小二乘的时差定位方法、装置和存储介质 |
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| CN109758274B (zh) * | 2019-02-28 | 2020-12-29 | 清华大学 | 单髁膝关节置换术中股骨远端相对于假体垫片力线轨迹的测量方法与系统 |
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| Title |
|---|
| CAO, YALU ET AL.: "An Improved Source Localization Algorithm in Presence of Sensor Location Errors", ACTA AERONAUTICA ET ASTRONAUTICA SINICA, vol. 35, no. 7, 25 July 2014 (2014-07-25), pages 1992 - 1998, ISSN: 1000-6893 * |
Cited By (3)
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| CN109959918A (zh) * | 2019-02-22 | 2019-07-02 | 西安电子科技大学 | 一种固态体定位的方法、装置及计算机存储介质 |
| CN112540343A (zh) * | 2020-11-19 | 2021-03-23 | 安徽大学 | 基于移动接收器协同分析的移动目标源定位方法 |
| CN115508774A (zh) * | 2022-10-12 | 2022-12-23 | 中国电子科技集团公司信息科学研究院 | 基于两步加权最小二乘的时差定位方法、装置和存储介质 |
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