CN102594747B - Moving horizon Signal to Noise Ratio (SNR) estimation method for wireless sensor network with SNR constraint - Google Patents

Abstract

Disclosed is a moving horizon SNR estimation method for a wireless sensor network with an SNR constraint. The method includes the following steps: step one, obtaining a state space model of the wireless sensor network utilizing SNR formula, power control algorithm and flow velocity control algorithm; step two, considering needed upper and lower limit of the SNR for a node to send a signal, obtaining a wireless sensor network model with the SNR constraint; step three, with regard to a window length N set for the moving horizon and weight matrix II, Q and R, converting the moving horizon SNR estimation problem to a minimization problem of equivalence with inequality constraints; step four, using the lagrangian method for converting the minimization problem to an optimization problem of equivalence with equality constraints; and step five, solving the optimization problem of equivalence with the equality constraints based on LOQO interior point method, obtaining a moving horizon SNR estimator for the wireless sensor network, providing an optimal estimated value and a predicted value for the SNR. According to the moving horizon SNR estimation method, the model is reasonable, the SNR constraint is considered, and on-line calculation function is provided.

Description

A kind of wireless sensor network rolling time domain signal-noise ratio estimation method with signal to noise ratio constraint

Technical field

The present invention relates to wireless sensor network technology field, particularly a kind of rolling time domain signal-noise ratio estimation method of wireless sensor network.

Background technology

Signal to noise ratio is the key parameter of signal of communication, is one of measurement index of communication quality.Many occasions in radio communication, as the iterative decoding of the identification of modulation signal, Turbo Code, power in mobile communication are controlled, Adaptive Modulation is switched, self adaptation handover and channel allocation etc., all need to know the numerical value of signal to noise ratio, to obtain best performance.Therefore, signal-to-noise ratio (SNR) estimation is an important topic in cordless communication network.

In recent years, signal-to-noise ratio (SNR) estimation technology makes some progress, and researcher both domestic and external has proposed various signal-to-noise ratio estimation algorithms for different channel circumstances and communication system.Through the literature search of prior art is found, Wiesel, A. when document SNR estimation in time-varying fading channels(, become the signal-to-noise ratio (SNR) estimation in attenuation channel, IEEE Transactions on Communications, 2006, based on Maximum Likelihood Estimation, designed the SNR estimator that becomes attenuation channel while being applicable in 841-848.).Xu, X. noise variance and the signal-to-noise ratio (SNR) estimation of the ofdm system based on subspace method at document Subspace-based noise variance and SNR estimation for OFDM systems(, IEEE Wireless Communications and Networking Conference, 2005, based on subspace Eigenvalues Decomposition method, designed the SNR estimator that is applicable to ofdm system in 23-26.).Xu, H. at the signal-to-noise ratio estimation algorithm of a document A novel SNR estimation algorithm for OFDM(new ofdm system, IEEE Vehicular Technology Conference, 2005,3068-3071.) in, test data based on time-domain and the characteristics design of auto-correlation function SNR estimator, provided average signal-to-noise ratio estimated value.But Xu, X. and Xu, the estimated performance in H. institute put forward the methods all depends on the number of test data.Ren, G. at document A new SNR ' s estimator for QPSK modulations in an AWGN channel(four new phase shift keyings, be modulated at the signal-to-noise ratio (SNR) estimation in additive white Gaussian noise channel, IEEE Transactions on Circuits and Systems II:Express Briefs, 2005,331-335.), based on Quadrature Phase Shift Keying modulation system, utilize the second order of signal and noise, the signal noise ratio level that the relation between Fourth-order moment is estimated additive white Gaussian noise passage.Ren, G. the signal-to-noise ratio estimation algorithm of selecting based on ofdm system channel at document SNR estimation algorithm based on the preamble for OFDM systems in frequency selective channels(, IEEE Transactions on Communications, 2005,331-335.), the synchronization signal designs based on before a kind of signal-noise ratio estimation method of selecting for ofdm system channel.Yet, because the channel of wireless network only has limited channel width, make the signal noise ratio level in wireless sensor network signal transmitting procedure there is certain upper limit.In addition, due to the impact of noise jamming, during wireless network node transmitted signal, need to reach certain threshold value could successful transmitted signal.Therefore wireless sensor network is to having signal to noise ratio constraint in signals transmission.Although wireless network signal-to-noise ratio (SNR) estimation has obtained certain progress in recent years, but still in research starting stage.For the also not research of wireless network SNR Estimation with signal to noise ratio constraint, existing method all just provides the estimation of signal noise ratio level, cannot do signal-to-noise ratio (SNR) estimation to having the wireless sensor network of signal to noise ratio constraint.

Summary of the invention

The object of the invention is to can not to thering is the wireless sensor network of signal to noise ratio constraint, do the deficiency of signal-to-noise ratio (SNR) estimation for existing wireless sensor network signal-noise ratio estimation method, the present invention proposes a kind of wireless sensor network rolling time domain signal-noise ratio estimation method that is applicable to have signal to noise ratio constraint.

The technical solution adopted for the present invention to solve the technical problems is:

A wireless sensor network rolling time domain signal-noise ratio estimation method with signal to noise ratio constraint, concrete steps are as follows:

(1), utilize signal to noise ratio formula, power control algorithm and flow control algorithm, obtain following wireless sensor network state-space model

In formula, for the signal noise ratio level of the wireless sensor network joint of dB yardstick, for the wireless sensor network node expectation signal noise ratio level of dB yardstick, α is power adjustments parameter, and n (k) is random white noise, for velocity of flow adjust parameter, c is network blocking probability, and d (k) is flow velocity increment, h is radio sensor network channel bandwidth;

(2), with $x_k={\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\γ}}}^T\left(k\right)& {\widehat{\mathrm{\γ}}}^T\end{array}\right]}^T$ For the state variable of wireless sensor network model, setting wireless sensor network channel capacity is F, and radio sensor network channel bandwidth is H, and maximum signal to noise ratio is setting signal sending threshold value is the signal to noise ratio that obtains wireless sensor network is constrained to obtain having the wireless sensor network model of signal to noise ratio constraint

$\left\{\begin{array}{c}{x}_{k+1}={\mathrm{Ax}}_k+w_k\\ y_k={\mathrm{Cx}}_k+v_k\\ x_k\∈[{\stackrel{\‾}{\mathrm{\γ}}}_{\min },{\stackrel{\‾}{\mathrm{\γ}}}_{\max ]}\end{array}\right.---\left(2\right)$

In formula,

A and C are weight parameter matrix,

W _kfor the system noise of wireless sensor network,

Y _kmeasurement output signal for wireless sensor network;

V _kfor measuring noise;

(3), set weight matrix Π, Q and R, setting rolling time-domain window N=1, like this state variable x _kby initial condition x _k-1with turbulent noise w _k-1determine, and x _k-1with w _k-1uncorrelated, the wireless sensor network time domain signal-to-noise ratio (SNR) estimation of rolling is converted into inequality constraints minimization problem of equal value:

$\underset{{\∂}_1}{\min }{\mathrm{\Ψ}}_k\left({\∂}_1\right)---\left(3\right)$

$s.t.{\mathrm{\Ψ}}_k\left({\∂}_1\right)=\left|\right|x_{k-1}-{\hat{x}}_{k-1}|{|}_{{\mathrm{\Π}}^{-1}}^2+||w_{k-1}{\left|\right|}_{Q^{-1}}^2+||y_{k-1}C{x}_{k-1}{\left|\right|}_{R^{-1}}^2$

x _k＝Ax _k-1+w _k-1

y _k-1＝Cx _k-1+v _k-1

${\stackrel{\‾}{\mathrm{\γ}}}_{\min }\≤x_k\≤{\stackrel{\‾}{\mathrm{\γ}}}_{\max }$

In formula,

₁=(x _k-1, w _k-1) expression decision variable;

represent Euclid norm;

for k-1 priori estimates is constantly reference value, for k-1 evaluated error constantly, the degree of belief of expression to estimated value;

$\left|\right|w_{k-1}{\left|\right|}_{Q^{-1}}^2+\left|\right|y_{k-1}C{x}_{k-1}{\left|\right|}_{R^{-1}}^2$ Expression to the estimation of disturbing signal '

(4) the inequality constraints minimization problem of, step (3) being set is converted into the RegionAlgorithm for Equality Constrained Optimization of approximately equivalent:

s.t.

x _k＝Ax _k-1+w _k-1

y _k-1＝Cx _k-1+v _k-1

$\begin{array}{c}{x}_{k-1}-\mathrm{\α}={\stackrel{\‾}{\mathrm{\γ}}}_{\min }\\ \mathrm{\α}+\mathrm{\β}={\stackrel{\‾}{\mathrm{\γ}}}_{\max }\end{array}$

In formula, μ is barrier parameter, and λ is Lagrangian multiplier, α ⁱ, β ⁱ, λ ⁱ, with be respectively vectorial α, β, λ, x _k-1, with i element;

(5), by the RegionAlgorithm for Equality Constrained Optimization of setting in LOQO interior point method solution procedure (4), concrete steps are as follows:

S1-1: initialization, set testing time length K, in the interval range of feasible zone, arbitrary initial k-1 variable constantly and sequence { x _k-1, w _k-1, α, β, λ }.

S1-2: according to single order KKT optimal condition, with { x _k-1, w _k-1, α, β, λ } and be primary iteration point, calculate and estimate increment Delta x _k-1with Δ λ:

$\mathrm{\Δ}{x}_{k-1}=T^{-1}(-{\▿}_{x_{k-1}}\mathrm{\Ψ}-{(2A+B)}^{-1}\mathrm{\Λ}{r}_{\mathrm{\λ}}+2\mathrm{\μ}{(2A+B)}^{-1}e)---\left(5\right)$

$\mathrm{\Δ\λ}=H_x{T}^{-1}(2\mathrm{\μ}{(2A+B)}^{-1}e-{(2A+B)}^{-1}\mathrm{\Λ}{r}_{\mathrm{\λ}})+(I-H_x{T}^{-1}){\▿}_{x_{k-1}}\mathrm{\Ψ}-\mathrm{\λ}---\left(6\right)$

In formula, $\mathrm{\μ}=\frac{0.05{(2\mathrm{\α}+\mathrm{\β})}^T\mathrm{\λ}}{k},T=H_x{(2A+B)}^{-1}\mathrm{\Λ},$ for Hessian matrix, matrix Α, Β and Λ represent with α respectively ⁱ, β ⁱand λ ⁱthe diagonal matrix of element, e is that element is all 1 column vector, ${\▿}_{x_{k-1}}\mathrm{\Ψ}={2\mathrm{\Π}}^{-1}(x_{k-1}-{\hat{x}}_{k-1})-2C^T{R}^{-1}(y_{k-1}-{\mathrm{Cx}}_{k-1}),$

S1-3: calculate and estimate increment Delta w _k-1, Δ α and Δ β:

${\mathrm{\Δw}}_{k-1}=-H_w^{-1}{r}_w---\left(7\right)$

Δα＝-0.5Λ ^-1A(r _α+2Δλ) (8)

Δ β=-Λ ^-1b(r _β+ Δ λ) in (9) formula, for Hessian matrix,

S1-4: upgrade estimated value { x _k-1, w _k-1, α, β, λ }:

x _k-1=x _k-1+ρ△x _k-1

w _k-1=w _k-1+ρ△w _k-1

α＝α+ρΔα (10)

β＝β+ρΔβ

λ＝λ+ρΔλ

In formula, ρ is step-size in search and ρ=0.35 that LOQO interior point method solver is set;

S1-5: adopt some solver in the LOQO in Matlab to judge whether estimated value meets required precision, if meet required precision, estimated value { x _k-1, w _k-1, α, β, λ } and be optimal estimation value, then forward S1-6 to.If do not meet, forward S1-2 to;

S1-6: based on rolling optimization principle, according to optimal estimation value x _k-1, w _k-1calculate current k optimal estimation constantly

$x_k^{*}=A{x}_{k-1}+w_{k-1}---\left(11\right)$

S1-7: upgrade

S1-8: judgement end condition.If k=K, finishes, obtain signal-to-noise ratio (SNR) estimation optimal value; Otherwise k=k+1, forwards S1-2 to.

Technical conceive of the present invention is: the present invention has considered that in wireless sensor network signal transmitting procedure, having signal to noise ratio retrains, provided a kind of state-space model with signal to noise ratio constraint, design the wireless sensor network SNR estimator based on rolling time domain method of estimation, provided the optimal estimation value of signal to noise ratio.

First, utilize signal to noise ratio formula, power control algorithm and flow control algorithm, obtain the state-space model of wireless sensor network; Then, according to the restriction of the network bandwidth, obtained the wireless sensor network model of signal to noise ratio constraint; Then, given rolling time-domain window length, provides the performance index of rolling time domain signal-to-noise ratio (SNR) estimation; Finally, utilize LOQO interior point method solver and random device design rolling time domain SNR estimator.Rolling time domain signal-noise ratio estimation method can rolling optimization, in line computation.

From technique scheme, can find out, beneficial effect of the present invention is mainly manifested in: the present invention designs the SNR estimator of wireless sensor network based on rolling time domain method of estimation, compare with existing signal-noise ratio estimation method, rolling time domain signal-noise ratio estimation method can effectively be processed restricted problem, and can rolling optimization and in line computation, thereby can estimate more exactly the signal noise ratio level of wireless sensor network.

Accompanying drawing explanation

Fig. 1 is cellular radio sensor network structure chart in the embodiment of the present invention.

Fig. 2 is the flow chart of solve equation constrained optimization problem in the embodiment of the present invention.

Fig. 3 is in the embodiment of the present invention, adopts the design sketch of the inventive method.

Embodiment

For making the object, technical solutions and advantages of the present invention more clear, below in conjunction with drawings and Examples, technical scheme of the present invention is further described.

With reference to Fig. 1～Fig. 3, a kind of wireless sensor network rolling time domain signal-noise ratio estimation method with signal to noise ratio constraint, the rolling time domain signal-noise ratio estimation method that the present invention is proposed is for cellular radio sensor network, its objective is to estimate the signal noise ratio level of wireless sensor network and with reference to signal noise ratio level.Next introduce concrete implementation step:

(1), utilize this cellular radio sensor network, network structure is as shown in Figure 1.Wireless sensor network in the signal noise ratio level of k moment node i is:

${\mathrm{\γ}}_i\left(k\right)=\frac{G_{\mathrm{ii}}\left(k\right)p_i\left(k\right)}{{\mathrm{\Σ}}_{j\∈D}{G}_{\mathrm{ij}}\left(k\right)p_j\left(k\right)+{\mathrm{\σ}}_i^2\left(k\right)}---\left(12\right)$

In formula, G _ij(k) be the channel gain of node j to node i, p _i(k) be the through-put power of node i, for the white Gaussian noise that node i receives, set D is all node set that are connected with node i.

Flow control algorithm in k moment node i is

in formula, f _i(k) be the k flow velocity of node i constantly.

At k constantly, the power control algorithm of node i is

${\stackrel{\‾}{p}}_i(k+1)={\stackrel{\‾}{p}}_i\left(k\right)+\mathrm{\α}[{\widehat{\mathrm{\γ}}}_i\left(k\right)-{\stackrel{\‾}{\mathrm{\γ}}}_i\left(k\right)]---\left(14\right)$

In formula, $\stackrel{}{}{\stackrel{\‾}{\mathrm{\γ}}}_i\left(k\right)=10\log {\mathrm{\γ}}_i\left(k\right).$

(2), utilize signal to noise ratio formula (12) and power control algorithm (14), the signal to noise ratio formula that obtains wireless sensor network dB yardstick is

${\stackrel{\‾}{\mathrm{\γ}}}_i(k+1)=(1-\mathrm{\α}){\stackrel{\‾}{\mathrm{\γ}}}_i\left(k\right)+\mathrm{\α}{\widehat{\mathrm{\γ}}}_i\left(k\right)+n_i\left(k\right)---\left(15\right)$

Utilize shannon formula f _i(k)=log ₂[1+ γ _i' (k)], in conjunction with flow control algorithm (13), the signal noise ratio level that obtains wireless sensor network expectation is

In formula, γ _i' (k) for expecting signal to noise ratio.

In order to write conveniently, remove subscript i here, convolution (14) and (16), can obtain the state-space model of node i

According to network characteristic, setting power regulates parameter alpha=0.2, velocity of flow adjust parameter for network blocking probability c=0.3, n (k) and d (k) are that average is that 0 variance is 0.1 random quantity.Can obtain thus wireless sensor network model is

$\begin{array}{c}\stackrel{\‾}{\mathrm{\γ}}(k+1)=0.8\stackrel{\‾}{\mathrm{\γ}}\left(k\right)+0.2\widehat{\mathrm{\γ}}\left(k\right)+n\left(k\right)\\ \widehat{\mathrm{\γ}(k+1)=0.751\hat{\mathrm{\γ}}}\left(k\right)+2.499d\left(k\right)\end{array}---\left(18\right)$

(2), setting measurement noise v _kthat average is 0, the random quantity that variance is 0.1, channel capacity F=250kbps, bandwidth H=830kHz.Convolution (18), the wireless sensor network state-space model that obtains having signal to noise ratio constraint is

$x_{k+1}=\left[\begin{array}{cc}0.8& 0.2\\ 0& 0.751\end{array}\right]x_k+w_k$

$y_k=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]x_k+w_k---\left(19\right)$

0≤x _k≤10dB

Wherein, weight parameter matrix $A=\left[\begin{array}{cc}0.8& 0.2\\ 0& 0.751\end{array}\right],C=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right].$

(3), set rolling time-domain window length N=1, weight matrix $\mathrm{\Π}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],Q=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ With $R=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right].$ The wireless sensor network time domain signal-to-noise ratio (SNR) estimation of rolling is converted into minimization problem of equal value:

$s.t.{\mathrm{\Ψ}}_k\left({\∂}_1\right)=\left|\right|x_{k-1}-{\hat{x}}_{k-1}|{|}_{{\mathrm{\Π}}^{-1}}^2+||w_{k-1}{\left|\right|}_{Q^{-1}}^2+||y_{k-1}C{x}_{k-1}{\left|\right|}_{R^{-1}}^2$

$x_k=\left[\begin{array}{cc}0.8& 0.2\\ 0& 0.751\end{array}\right]x_{k-1}+w_{k-1}$

$y_{k-1}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]x_{k-1}+w_{k-1}$

0≤x _k≤10

(4), inequality constraints minimization problem is converted into the RegionAlgorithm for Equality Constrained Optimization of approximately equivalent:

$x_k=\left[\begin{array}{cc}0.8& 0.2\\ 0& 0.751\end{array}\right]x_{k-1}+w_{k-1}$

$x_k=\left[\begin{array}{cc}0.8& 0.2\\ 0& 0.751\end{array}\right]x_{k-1}+w_{k-1}$

x _k-1-α＝0

α+β＝10

(5), adopt LOQO interior point method and random device to solve formula (21).Fig. 2 is that the present invention utilizes LOQO interior point method and random device to solve the flow process of formula (21), and concrete steps are as follows:

S1-1: initialization, set testing time length K=100, in the interval range of feasible zone, arbitrary initial k-1 variable constantly ${\hat{x}}_{k-1}={\left[\begin{array}{cc}10& 9.6\end{array}\right]}^T,$ Y _k-1=[0 0] ^twith sequence x _k-1=[5.6 6] ^t,

w _k-1＝[0 0] ^T，α＝[54 55] ^T，β＝[50 46] ^T，λ＝[1 1] ^T。

S1-2: according to single order KKT optimal condition, with { x _k-1, w _k-1, α, β, λ } and be primary iteration point, calculate and estimate increment Delta x _k-1, Δ λ:

$\mathrm{\Δ}{x}_{k-1}=T^{-1}(-{\▿}_{x_{k-1}}\mathrm{\Ψ}-{(2A+B)}^{-1}\mathrm{\Λ}{r}_{\mathrm{\λ}}+2\mathrm{\μ}{(2A+B)}^{-1}e)---\left(22\right)$

$\mathrm{\Δ\λ}=H_x{T}^{-1}(2\mathrm{\μ}{(2A+B)}^{-1}e-{(2A+B)}^{-1}\mathrm{\Λ}{r}_{\mathrm{\λ}})+(I-H_x{T}^{-1}){\▿}_{x_{k-1}}\mathrm{\Ψ}-\mathrm{\λ}---\left(23\right)$

In formula, $A=\left[\begin{array}{cc}{\mathrm{\α}}^1& 0\\ 0& {\mathrm{\α}}^2\end{array}\right]=\left[\begin{array}{cc}54& 0\\ 0& 55\end{array}\right],B=\left[\begin{array}{cc}{\mathrm{\β}}^1& 0\\ 0& {\mathrm{\β}}^2\end{array}\right]=\left[\begin{array}{cc}50& 0\\ 0& 46\end{array}\right],\mathrm{\Λ}=\left[\begin{array}{cc}{\mathrm{\γ}}^1& 0\\ 0& {\mathrm{\γ}}^2\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],$

$H_x={\mathrm{\Π}}^{-1}+C^T{R}^{-1}C=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right],T=H_x+{(2A+B)}^{-1}\mathrm{\Λ}=\left[\begin{array}{cc}2.0063& 0\\ 0& 2.0064\end{array}\right],e=\left[\begin{array}{c}1\\ 1\end{array}\right],$

$\mathrm{\μ}=\frac{0.05{(2\mathrm{\α}+\mathrm{\β})}^T\mathrm{\λ}}{k}=\frac{15.7}{k},{\▿}_{x_{k-1}}\mathrm{\Ψ}2{\mathrm{\Π}}^{-1}\left(x_{k-1}{-\hat{x}}_{k-1}\right)-2C^T{R}^{-1}(y_{k-1}-{\mathrm{Cx}}_{k-1})=\left[\begin{array}{c}2.4\\ 4.8\end{array}\right],$

S1-3: calculate and estimate increment Delta w _k-1, Δ α, Δ β:

${\mathrm{\Δw}}_{k-1}=-H_w^{-1}{r}_w---\left(24\right)$

Δα＝-0.5Λ ^-1A(r _α+2Δλ) (25)

Δβ＝-Λ ^-1B(r _β+Δλ) (26)

In formula, $H_w=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],r_w=2Q^{-1}{w}_{k-1}=\left[\begin{array}{c}0\\ 0\end{array}\right],$

S1-4: upgrade estimated value { x _k-1, w _k-1, α, β, λ }:

x _k-1＝x _k-1+0.35Δx _k-1

w _k-1＝w _k-1+0.35Δw _k-1

α＝α+0.35Δα (27)

β＝β+0.35Δβ

λ＝λ+0.35Δλ

S1-5: adopt some solver in the LOQO in Matlab to judge whether estimated value meets required precision.If meet estimated value { x _k-1, w _k-1, α, β, λ } and be optimal estimation value, then forward S1-6 to.If do not meet, forward S1-2 to.

S1-6: based on rolling optimization principle, according to optimal estimation value x _k-1, w _k-1calculate current k optimal estimation constantly

$x_k^{*}=A{x}_{k-1}+w_{k-1}---\left(28\right)$

S1-7: upgrade

S1-8: judgement end condition.If k=100, finishes, obtain signal-to-noise ratio (SNR) estimation optimal value; Otherwise k=k+1, forwards S1-2 to.

Adopt described step, calculate result that 100 sampling instants obtain as shown in Figure 3, wherein, signal noise ratio level and estimated value that Fig. 3 (a) is system, abscissa is sampling number, ordinate is signal noise ratio level; Expectation signal noise ratio level and estimated value thereof that Fig. 3 (b) is system, abscissa is sampling number, ordinate is expectation signal noise ratio level.。As can be seen from Figure 3, for the wireless sensor network with signal to noise ratio constraint, rolling time domain signal-noise ratio estimation method is effectively processed restricted problem, and the estimated value of signal to noise ratio all drops within the scope of given signal to noise ratio.The time domain of simultaneously rolling method of estimation has advantages of rolling optimization and in line computation, thereby can provide more exactly the signal noise ratio level of wireless sensor network.

What more than set forth is the good estimation effect that example table that the present invention provides reveals.It is pointed out that the present invention is not only limited to above-described embodiment, for the wireless sensor network of other types, adopt the method that the present invention provides to design rolling time domain estimator, all can provide the signal noise ratio level of wireless sensor network.

Claims (1)

1. a wireless sensor network rolling time domain signal-noise ratio estimation method with signal to noise ratio constraint, is characterized in that, concrete steps are as follows:

(1), utilize signal to noise ratio formula, power control algorithm and flow control algorithm, obtain following wireless sensor network state-space model:

In formula, for the signal noise ratio level of the wireless sensor network joint of dB yardstick, for the wireless sensor network node expectation signal noise ratio level of dB yardstick, α is power adjustments parameter, and n (k) is random white noise, for velocity of flow adjust parameter, c is network blocking probability, and d (k) is flow velocity increment, h is radio sensor network channel bandwidth;

(2), with $x_k={\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\γ}}}^T\left(k\right)& {\widehat{\mathrm{\γ}}}^T\end{array}\right]}^T$ For the state variable of wireless sensor network model, setting wireless sensor network channel capacity is F, and maximum signal to noise ratio is setting signal sending threshold value is the signal to noise ratio that obtains wireless sensor network is constrained to obtain having the wireless sensor network model of signal to noise ratio constraint:

$\left\{\begin{array}{c}{x}_{k+1}={\mathrm{Ax}}_k+w_k\\ y_k={\mathrm{Cx}}_k+v_k\\ x_k\∈[{\stackrel{\‾}{\mathrm{\γ}}}_{\min },{\stackrel{\‾}{\mathrm{\γ}}}_{\max ]}\end{array}\right.$

In formula,

A and C are weight parameter matrix,

Wk is the system noise of wireless sensor network,

Y _kmeasurement output signal for wireless sensor network;

V _kfor measuring noise;

(3), set weight matrix Π, Q and R, setting rolling time-domain window N=1, state variable x _kby initial condition x _k-1with turbulent noise w _k-1determine, and x _k-1with w _k-1uncorrelated, the wireless sensor network time domain signal-to-noise ratio (SNR) estimation of rolling is converted into inequality constraints minimization problem of equal value:

$\underset{{\∂}_1}{\min }{\mathrm{\Ψ}}_k\left({\∂}_1\right)$

$s.t.{\mathrm{\Ψ}}_k\left({\∂}_1\right)=\left|\right|x_{k-1}-{\hat{x}}_{k-1}|{|}_{{\mathrm{\Π}}^{-1}}^2+||w_{k-1}{\left|\right|}_{Q^{-1}}^2+||y_{k-1}C{x}_{k-1}{\left|\right|}_{R^{-1}}^2$

x _k＝Ax _k-1+w _k-1

y _k-1＝Cx _k-1+v _k-1

${\stackrel{\‾}{\mathrm{\γ}}}_{\min }\≤x_k\≤{\stackrel{\‾}{\mathrm{\γ}}}_{\max }$

In formula,

represent decision variable;

represent Euclid norm;

for k-1 priori estimates is constantly reference value, for k-1 evaluated error constantly, the degree of belief of expression to estimated value;

$\left|\right|w_{k-1}{\left|\right|}_{Q^{-1}}^2+\left|\right|y_{k-1}C{x}_{k-1}{\left|\right|}_{R^{-1}}^2$ The estimation of expression to disturbing signal;

(4) the inequality constraints minimization problem of, step (3) being set is converted into the RegionAlgorithm for Equality Constrained Optimization of approximately equivalent:

s.t.

x _k＝Ax _k-1+w _k-1

y _k-1＝Cx _k-1+v _k-1

$\begin{array}{c}{x}_{k-1}-\mathrm{\α}={\stackrel{\‾}{\mathrm{\γ}}}_{\min }\\ \mathrm{\α}+\mathrm{\β}={\stackrel{\‾}{\mathrm{\γ}}}_{\max }\end{array}$

In formula, μ is barrier parameter, and λ is Lagrangian multiplier, α ⁱ, β ⁱ, λ ⁱ, with be respectively vectorial α, β, λ, x _k-1, with i element;

(5), by the RegionAlgorithm for Equality Constrained Optimization of setting in LOQO interior point method solution procedure (4), concrete steps are as follows:

S1-1: initialization, set testing time length K, in the interval range of feasible zone, arbitrary initial k-1 variable constantly y _k-1and sequence { x _k-1, w _k-1, α, β, λ };

S1-2: according to single order KKT optimal condition, with { x _k-1, w _k-1, α, β, λ } and be primary iteration point, calculate and estimate increment Delta x _k-1with Δ λ:

$\mathrm{\Δ}{x}_{k-1}=T^{-1}(-{\▿}_{x_{k-1}}\mathrm{\Ψ}-{(2A+B)}^{-1}\mathrm{\Λ}{r}_{\mathrm{\λ}}+2\mathrm{\μ}{(2A+B)}^{-1}e)$

$\mathrm{\Δ\λ}=H_x{T}^{-1}(2\mathrm{\μ}{(2A+B)}^{-1}e-{(2A+B)}^{-1}\mathrm{\Λ}{r}_{\mathrm{\λ}})+(I-H_x{T}^{-1}){\▿}_{x_{k-1}}\mathrm{\Ψ}-\mathrm{\λ}$

In formula, $\mathrm{\μ}=\frac{0.05{(2\mathrm{\α}+\mathrm{\β})}^T\mathrm{\λ}}{k},T=H_x{(2A+B)}^{-1}\mathrm{\Λ},$ for Hessian matrix, matrix Α, Β and Λ represent with α respectively ⁱ, β ⁱand λ ⁱthe diagonal matrix of element, e is that element is all 1 column vector, ${\▿}_{x_{k-1}}\mathrm{\Ψ}={2\mathrm{\Π}}^{-1}(x_{k-1}-{\hat{x}}_{k-1})-2C^T{R}^{-1}(y_{k-1}-{\mathrm{Cx}}_{k-1}),$

S1-3: calculate and estimate increment Delta w _k-1, Δ α and Δ β:

${\mathrm{\Δw}}_{k-1}=-H_w^{-1}{r}_w$

Δα＝-0.5Λ ^-1A(r _α+2Δλ)

Δβ＝-Λ ^-1B(r _β+Δλ)

In formula, for Hessian matrix,

S1-4: upgrade estimated value { x _k-1, w _k-1, α, β, λ }:

x _k-1=x _k-1+ρ△x _k-1

w _k-1=w _k-1+ρ△w _k-1

α＝α+ρΔα

β＝β+ρΔβ

λ＝λ+ρΔλ

In formula, ρ is step-size in search and ρ=0.35 that LOQO interior point method solver is set;

S1-5: adopt some solver in the LOQO in Matlab to judge whether estimated value meets required precision, if meet required precision, estimated value { x _k-1, w _k-1, α, β, λ } and be optimal estimation value, then forward S1-6 to; If do not meet, forward S1-2 to;

S1-6: based on rolling optimization principle, according to optimal estimation value x _k-1, w _k-1calculate current k optimal estimation constantly

$x_k^{*}=A{x}_{k-1}+w_{k-1}$

S1-7: upgrade

S1-8: judgement end condition, if k=K finishes, obtains signal-to-noise ratio (SNR) estimation optimal value; Otherwise k=k+1, forwards S1-2 to.