CN106649198B - A kind of method of higher-dimension signal reconstruction quality in detection wireless sensor network - Google Patents
A kind of method of higher-dimension signal reconstruction quality in detection wireless sensor network Download PDFInfo
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- CN106649198B CN106649198B CN201611018905.7A CN201611018905A CN106649198B CN 106649198 B CN106649198 B CN 106649198B CN 201611018905 A CN201611018905 A CN 201611018905A CN 106649198 B CN106649198 B CN 106649198B
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Abstract
The invention discloses a kind of methods of higher-dimension signal reconstruction quality in detection wireless sensor network, are a kind of computational methods using force zero estimation and the performance indicator for detecting reconstructed signal after Linear Minimum Mean-Square Error Estimation.During signal reconstruction in wireless sensor network, wireless sensor collected signal can be indicated with the form of Fourier expansion.In view of the influence of noise in acquisition signal, need to rebuild signals and associated noises using estimator.When network size is larger, when signal dimension and larger wireless sensor quantity i.e. to be treated, the present invention provides a kind of methods for capableing of the easy probability density function for accurately obtaining generalized circular matrix characteristic value again, to the accurate detection performance index that can easily calculate system.
Description
Technical field
The present invention relates to a kind of method of higher-dimension signal reconstruction quality in detection wireless sensor network, more particularly to one kind exists
Refer to the mean square error for being reconstructed signal is detected after Linear Minimum Mean-Square Error Estimation (LMMSE) method using force zero estimation (ZF)
Target computational methods belong to the technical field of signal reconstruction in wireless sensor network.
Background technology
During signal reconstruction in wireless sensor network, random generalized circular matrix plays important role.Wirelessly
Sensor collected signal can be indicated with the form of Fourier expansion.In view of the geography residing for each sensor
Position is different, and collected signal can be expressed as between a generalized circular matrix and a vector for indicating the signal spectrum
Product.In view of the influence of noise in acquisition signal, need to rebuild signals and associated noises using estimator.
Classical algorithm has force zero estimation and Minimum Mean Squared Error estimation, and original signal is being rebuild using both estimators
Afterwards, it needs to calculate its mean square error to the signal of reconstruction, so that it is determined that the accuracy of signal reconstruction.The calculating of mean square error needs
Solve the probability density function of the characteristic value for the generalized circular matrix mentioned before.
When the bandwidth for acquiring the dimension of signal, the number of sensor and collected signal is relatively low, generalized circular matrix
The probability density function of characteristic value can be estimated by the method for Monte Carlo numerical computations.However, working as above-mentioned parameter
When being worth larger, the calculation amount needed for the numerical computations of Monte Carlo is exponentially increased, it is therefore desirable to one kind can it is easy again accurately
The method for obtaining the probability density function of this matrix exgenvalue.
Invention content
In view of the above-mentioned problems, technical problem to be solved by the invention is to provide higher-dimensions in a kind of detection wireless sensor network
The method of signal reconstruction quality, the present invention provide it is a kind of can the easy probability for accurately obtaining generalized circular matrix characteristic value again it is close
The method for spending function, to the accurate detection performance index that can easily calculate system.
The present invention uses following technical scheme to solve above-mentioned technical problem：
The present invention provides a kind of method detecting higher-dimension signal reconstruction quality in wireless sensor network, the wireless sense network
It is made of m wireless sensor in network, each wireless sensor acquires the signal of d dimensions respectively, and the bandwidth of the signal indicates
For n, collected signal is expressed as y=VHa+nw, wherein y indicates that the measured value of signal, a indicate to need reconstructed signal,
nwIndicate that white noise signal, V indicate that a dimension is ndThe generalized circular matrix of × m.
When using force zero estimation or Minimum Mean Squared Error estimation method reconstruction signal, the mean square error difference of reconstructed results
ForWithWherein,For the variance of white noise signal, β=
nd/ m, Eλ{ } indicates to solve the desired value about λ, and λ is matrix β VVHCharacteristic value.
The probability density function f of λ is solved by the following methodλ(d, β, λ), specially：
1) constitution optimization equation：And meet conditional equation：Wherein, μpFor the p rank squares of λ；
2) by Gaussian quadrature rule the fixed point position f of the integral operation in optimization method and conditional equationλ(d,β,
λ) weighted sum of value shows, i.e.,：
Wherein, λjFor j-th of sampling defined in Gaussian quadrature rule
The coordinate of point, N are sampled point number, wjFor corresponding λjWeights；
3) solving-optimizing equation and conditional equation obtain corresponding to λjFλ(d,β,λj) optimal value, to fit fλ
(d,β,λ)。
According to obtained fλ(d, β, λ) can calculate the mean square error of reconstructed results, to weigh according to mean square error
Amount carries out the quality of signal reconstruction using force zero estimation or Minimum Mean Squared Error estimation method.
As the present invention further technical solution, use force zero method of estimation rebuild signal for：
As the present invention further technical solution, use Minimum Mean Squared Error estimation method rebuild signal for：Wherein, I indicates unit matrix.
As the further technical solution of the present invention, the element of generalized circular matrix V is：Its
In, Vs,tIndicate the s row t column elements of V, xtIndicate the geographical location of t-th of wireless sensor.
As the further technical solution of the present invention, a is a ndDimensional vector.
As the further technical solution of the present invention, y is a m dimensional vector.
The present invention has the following technical effects using above technical scheme is compared with the prior art：When the dimension of acquisition signal
Number, the number of sensor and collected signal bandwidth value it is larger when, technical solution using the present invention can it is easy again
Accurately obtain the probability density function of generalized circular matrix characteristic value.
Description of the drawings
Fig. 1 is the numerical value figure for the system mean square error being calculated in the specific embodiment of the invention.
Specific implementation mode
Below in conjunction with the accompanying drawings and specific embodiment is described in further detail technical scheme of the present invention：
In the wireless sensor network that one is made of m wireless sensor, each sensor is responsible for one d dimension of acquisition
The bandwidth of signal, the signal is expressed as n.Collected signal can be expressed as with the reconstructed signal of needs：Y=VHa+nw,
In, y indicates the measured value of signal, is a m dimensional vector；A indicates to need reconstructed signal, is a ndDimensional vector；nwIt indicates
White noise signal；V indicates that a dimension is ndThe s row t column elements of the generalized circular matrix of × m, this matrix can be expressed as：Wherein, xtIndicate the geographical location of t-th of wireless sensor.
When application force zero estimates (ZF), the signal of reconstruction is expressed as：The mean square error of the reconstructed results
Therefore difference can be written as：
As application Minimum Mean Squared Error estimation (LMMSE), the signal of reconstruction is expressed as：It should
Therefore the mean square error of reconstructed results can be written as：Wherein, I indicates unit matrix.
When the value of m, n, d are larger, it is assumed that ndIt is expressed as β=n with the ratio of md/ m then applies force zero estimation or minimum equal
The mean square error of square estimation error reconstruction signal further can be accurately estimated as：
Wherein, λ is matrix β VVHCharacteristic value.Therefore, probability density function (PDF) f of λλ(d, β, λ) needs a kind of side
Method is provided, wherein d and β is two parameter.
Before the probability density function (PDF) for calculating λ, the p ranks square of λ is it is known that be denoted as μp.The p rank squares of λ exist
A.Nordio,C.-F.Chiasserini,E.Viterbo,“Performance of linear field
reconstruction techniques with noise and uncertain sensor locations,”IEEE
It is discussed in detail in Trans.on Signal Processing, Vol.56, No.8, pp.3535-3547, Aug.2008..
Constitution optimization equation：And meet conditional equation：
By Gaussian quadrature rule the fixed point position f of the integral operation in optimization method and conditional equationλ(d,β,λ)
The weighted sum of value shows, i.e.,：
Wherein, λjFor j-th of sampling defined in Gaussian quadrature rule
The coordinate of point, N are sampled point number, wjFor corresponding λjWeights, also by Gaussian quadrature rule obtain.Therefore, excellent by solving
Change equation and conditional equation, corresponds to each λjThe f of sampled pointλ(d,β,λj) optimal value can be found out, so that fitting obtains fλ
(d,β,λ)。
In Simulation Test Environment, we test when d=1 or 4,And m=ndThe parameter setting of/β, corresponds to
The preceding 12 rank square of eigenvalue λ is known.Believe assuming that system is respectively adopted force zero estimation and is rebuild with Minimum Mean Squared Error estimation method
Number, we are respectively compared the system mean square error obtained by monte carlo method and are calculated with by method proposed by the invention
System mean square error.
The numerical value figure of system mean square error as shown in Figure 1, by observation chart 1 as can be seen that Minimum Mean Squared Error estimation
The performance of method is better than force zero method of estimation, because the target of least mean-square error is minimum mean square error.It is prior
It is that, as β value must increase, the mean square error result obtained with monte carlo method by the calculated mean square error of the present invention is very
It is close.But the invention enables the calculation amounts of mean square error to be substantially reduced, in Fig. 1, the point of " " and "×" indicates Monte Carlo
What the lines of the simulation result that method obtains, dotted line and solid line indicated is the simulation result of the method for the present invention.
The above, the only specific implementation mode in the present invention, but scope of protection of the present invention is not limited thereto, appoints
What is familiar with the people of the technology within the technical scope disclosed by the invention, it will be appreciated that expects transforms or replaces, and should all cover
Within the scope of the present invention, therefore, the scope of protection of the invention shall be subject to the scope of protection specified in the patent claim.
Claims (6)
1. a kind of method of higher-dimension signal reconstruction quality in detection wireless sensor network, by m nothing in the wireless sensor network
Line sensor is constituted, and each wireless sensor acquires the signal of d dimensions respectively, and the bandwidth of the signal is expressed as n, collected
Signal is expressed as y=VHa+nw, wherein y indicates that the measured value of signal, a indicate to need reconstructed signal, nwIndicate white noise
Signal, V indicate that a dimension is ndThe generalized circular matrix of × m, which is characterized in that when using force zero estimation or least mean-square error
When method of estimation reconstruction signal, the mean square error of reconstructed results is respectivelyWithWherein,For the variance of white noise signal, β=nd/ m, Eλ{ } indicates to solve and close
In the desired value of λ, λ is matrix β VVHCharacteristic value；
The probability density function f of λ is solved by the following methodλ(d, β, λ), specially：
1) constitution optimization equation：And meet conditional equation：Wherein, μpFor the p rank squares of λ；
2) by Gaussian quadrature rule the fixed point position f of the integral operation in optimization method and conditional equationλ(d, β, λ) takes
The weighted sum of value shows, i.e.,：
Wherein, λjFor j-th of sampling defined in Gaussian quadrature rule
The coordinate of point, N are sampled point number, wjFor corresponding λjWeights；
3) solving-optimizing equation and conditional equation obtain corresponding to λjFλ(d,β,λj) optimal value, to fit fλ(d,β,
λ)；
According to obtained fλ(d, β, λ) can calculate the mean square error of reconstructed results, to weigh use according to mean square error
Force zero is estimated or Minimum Mean Squared Error estimation method carries out the quality of signal reconstruction.
2. the method for higher-dimension signal reconstruction quality, feature in a kind of detection wireless sensor network according to claim 1
Be, use force zero method of estimation rebuild signal for：
3. the method for higher-dimension signal reconstruction quality, feature in a kind of detection wireless sensor network according to claim 1
Be, use Minimum Mean Squared Error estimation method rebuild signal for：Wherein, I indicates unit square
Battle array.
4. the method for higher-dimension signal reconstruction quality, feature in a kind of detection wireless sensor network according to claim 1
It is, the element of generalized circular matrix V is：Wherein, Vs,tIndicate the s row t column elements of V, xt
Indicate the geographical location of t-th of wireless sensor.
5. the method for higher-dimension signal reconstruction quality, feature in a kind of detection wireless sensor network according to claim 1
It is, a is a ndDimensional vector.
6. the method for higher-dimension signal reconstruction quality, feature in a kind of detection wireless sensor network according to claim 1
It is, y is a m dimensional vector.
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| CN103107815A (en) * | 2013-01-09 | 2013-05-15 | 华为技术有限公司 | Method and device for signal reconstruction |
| CN103546910A (en) * | 2013-10-15 | 2014-01-29 | 贵州师范大学 | Method for calculating lower bound of transmission capacity of mine laneway wireless sensor network |
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