CN101162482A - Gauss cooperated based on node and semi-particle filtering method - Google Patents

Abstract

A Gauss sum semi-particle faltering method based on node cooperation is characterized in that the method includes Gauss sum semi-particle faltering and the first node selection based on Gauss sum semi-particle faltering; as for the current first node, sampling values are generated by a QMC node and then the posterior probability distribution of the current status of Gauss sum distribution approximate object is generated by means of the sampling values; then, based on node cooperation, the first node of the next moment is selected and the posterior probability distribution of the current status of an object is transmitted to the first node of a next moment; finally, the first node of the next moment updates the posterior probability distribution of the status of the object according to self measurement value.

Description

Gaussian sum semi-particle filtering method based on node cooperation

Technical field

The present invention relates to the target following in the wireless sensor network, particularly a kind of gaussian sum semi-particle filtering method (GSQPF) based on node cooperation belongs to the technical field that distributed signal is handled.

Background technology

Along with the development of computer network, radio communication and mini system, the wireless sensor network that has merged above three kinds of technology arises at the historic moment.Sensor node has data processing and the ability of communicating by letter, and utilize the sensor on the node that the environment around it is monitored to obtain measurement data, by the processing power of node measurement data is carried out signal Processing to extract the essential characteristic of surrounding environment then, at last the result who obtains is passed to the stay of two nights by wireless channel.Wireless sensor network can be realized the communication of people and physical world existing network extension to physical world, reaches the communication of " omnipresent ".A main application of wireless sensor network is target following.Because the restriction of the resource of sensor node own, single-sensor node are finished particle filter and are realized that target following is unpractical, need be by the cooperation of the node particle filter of cooperating.So, how the cooperation particle filter realizes being exactly urgent problem.

Summary of the invention

The objective of the invention is to propose a kind of gaussian sum semi-particle filtering method based on node cooperation, the distributed object of, low complex degree efficient to realize, robust is followed the tracks of, and has good practical value, for target following provides a kind of new method.

Technical scheme of the present invention is: a kind of gaussian sum semi-particle filtering method based on node cooperation, it is characterized in that: comprise the gaussian sum semi-particle filtering and select two parts based on the head node of gaussian sum semi-particle filtering, head node for current time, produce sample value with the QMC point earlier, then produce the posterior probability distribution that gaussian sum distributes and is similar to the target current state with these sample values, then based on node cooperation, select the head node in the next moment, the distribution of the posterior probability of target current state is transferred to the head node in the next moment, at last, the head node in the next moment distributes according to the posterior probability of the measured value renewal dbjective state of oneself.

In the process of carrying out the gaussian sum semi-particle filtering, can utilize the QMC point to replace random number to produce sample value, and utilize these sample values to produce the posterior probability distribution that gaussian sum distributes and is similar to dbjective state, distributing based on these gaussian sums then obtains each neighbor node of current head node to upgrading the contribution amount expression formula of next moment dbjective state, and the neighbor node of selecting a contribution amount maximum at last becomes the head node in the next moment.

The job step of entire method is as follows:

(1) the QMC generation of ordering:

Go up equally distributed low diversity sequence u obeying [0,1] _j(j=1 ..., N) be called the QMC point, common QMC point comprises: Vander Corput sequence, Halton sequence and Sobol sequence.

(2) gaussian sum semi-particle filtering:

Current head node receives the tracking results { W that previous moment head node sends _Tj, μ _Tj, ∑ _Tj} _J=1 ^GAfter, at first utilize the QMC point to obtain the prediction distribution of target posterior probability

$p\left(x_{t+1}\right|z_t)=\underset{j=1}{\overset{G}{\mathrm{\Σ}}}{\stackrel{\‾}{W}}_{(t+1)j}N\left(x_{t+1};{\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j},{\stackrel{\‾}{\mathrm{\Σ}}}_{(t+1)j}\right)$

Here

${\stackrel{\‾}{W}}_{(t+1)j}=W_{\mathrm{tj}}$

${\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_{(t+1)j}^i$

${\stackrel{\‾}{\mathrm{\Σ}}}_{(t+1)j}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}(x_{(t+1)j}^i-{\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j}){(x_{(t+1)j}^i-{\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j})}^T$

Then receive new measured value z according to head node _(t+1), obtain the APPROXIMATE DISTRIBUTION of destination probability

$p\left(x_{(t+1)}\right|y_{(t+1)})\≈\underset{j=1}{\overset{G}{\mathrm{\Σ}}}{W}_{(t+1)j}N(x_{(t+1)};{\mathrm{\μ}}_{(t+1)j},{\mathrm{\Σ}}_{(t+1)j})$

Here

${\mathrm{\μ}}_{(n+1)j}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{(n+1)j}^i{x}_{(n+1)j}^i$

${\mathrm{\Σ}}_{(t+1)j}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{(t+1)}^i(x_{(t+1)j}^i-{\mathrm{\μ}}_{(t+1)j}){(x_{(t+1)j}^i-{\mathrm{\μ}}_{(t+1)j})}^T$

$W_{(t+1)j}=W_{\mathrm{tj}}\frac{{\mathrm{\Σ}}_{i=1}^N{w}_{(t+1)j}^i}{\underset{j=1}{\overset{G}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{(t+1)j}^i}$

Thereby obtain the tracking results { w of current head node _{(t+1) j}, μ _{(t+1) j}, ∑ _{(t+1) j}} _J=1 ^G

(3) head node is selected:

" cooperation " relation in the cooperation gaussian sum semi-particle filtering realizes by the head node selection strategy.We utilize mutual information I (x _T+1z _T+1 ^k| z _t) contribution amount of measuring each neighbor node, according to the result of step (2) gaussian sum semi-particle filtering, can be expressed as this mutual information

${\tilde{I}}_k\≈\underset{j=1}{\overset{G}{\mathrm{\Σ}}}{\stackrel{\‾}{W}}_{(t+1)j}\log \left({\left(2\mathrm{\πe}\right)}^{t/2}\right|{\stackrel{\‾}{\mathrm{\Σ}}}_{(t+1)j}\left|\right)-\underset{i=1}{\overset{G}{\mathrm{\Σ}}}{W}_{(t+1)\mathrm{kj}}\log \left({\left(2\mathrm{\πe}\right)}^{t/2}\right|{\mathrm{\Σ}}_{(t+1)\mathrm{kj}}\left|\right)$

If set M={1,2.....K} represents the neighbor node of head node, order

$L=\arg {\max }_{k\∈M}\left\{{\tilde{I}}_k\right\}$

Then node L is exactly next head node constantly.When the L element was not unique, it was consistent that the contribution amount of two or above node is just arranged, and that selects one at random as next head node constantly.Select by head node, can realize the mutual transmission of tracking results between head node, thereby realize cooperation gaussian sum semi-particle filtering.

Advantage of the present invention and beneficial effect:

1, utilizes gaussian sum semi-particle filtering method realization target following will reduce the internodal traffic greatly, be fit to very much this resource-constrained network of wireless sensor network based on node cooperation.

2, select by head node, can be distributed to whole network to the computation complexity of gaussian sum semi-particle filtering effectively, realize distributed treatment.Also find by emulation, select to have robustness preferably based on the head node of gaussian sum semi-particle filtering.

3, utilize the QMC point to replace random number to produce sample value, can solve the divergence problem of tracking effectively.Its thinking also can be applicable to other particle filters to improve performance.

4, utilize the posterior probability of other approximate targets that distribute to distribute, can derive cooperation filtering algorithm based on other distributions.

5, utilize head node to select to realize cooperation filtering, each constantly only has a node to follow the tracks of processing, is carved with a plurality of nodes during widenable to each and follows the tracks of the similar algorithm of processing with further raising tracking performance.

6, the inventive method also can be expanded and be used for the detection tracking problem based on model such as channel estimation and equalization.

Description of drawings

Fig. 1 is a kind of implementation framework of the gaussian sum semi-particle filtering (GSQPF) based on node cooperation;

Fig. 2 is simulated effect figure of the present invention;

Fig. 3 is the simulated effect figure that head node is selected.

Embodiment:

The distributed object that the gaussian sum semi-particle filtering method that the present invention is based on node cooperation is mainly used in the wireless sensor network is followed the tracks of, this filtering method has characteristics such as complexity is low, distributed treatment, is highly suitable for resource-constrained wireless sensor network.Specific embodiments is as follows:

Make { x _t, t=0,1,2...} represents the state of target at moment t, corresponding measurement sequence is { z _t, t=1,2,3...}, then the measurement equation of the equation of motion of target and node can be expressed as:

x _t+1＝f(x _t)+u _t

z _t＝g(x _t)+v _t

F (x) wherein, g (x) can be linear, also can be non-linear, state-noise u _tWith measurement noise v _tIt all is the additive white Gaussian noise of zero-mean.As f (x), g (x) is linear, can obtain the analytic solution of dbjective state so according to Kalman filtering.But as f (x), g (x) is not linear, and that dbjective state does not have analytic solution, is exactly the approximate solution that a kind of dbjective state is provided for target following in this case based on the gaussian sum semi-particle filtering of node cooperation.

The essence of the inventive method is exactly to utilize some gaussian sums to distribute to be similar to the posterior probability distribution p (x of dbjective state _t| z _t), because the parameter that gaussian sum distributes has only average and variance, therefore, finish gaussian sum semi-particle filtering based on node cooperation, only need these parameter informations of transmission between sensor node, complexity reduces greatly.Introduce to implement a kind of three concrete steps of the gaussian sum semi-particle filtering based on node cooperation below:

1) the QMC generation of ordering

Go up equally distributed low diversity sequence u obeying [0,1] _j(j=1 ..., N) be called the QMC point, common QMC point comprises: Vander Corput sequence, Halton sequence and Sobol sequence.

2) gaussian sum semi-particle filtering

Gaussian sum semi-particle filtering algorithm comprises two steps again:

2.1) prediction that distributes of posterior probability.Current head node receives the tracking results { W that previous moment head node sends _Tj, μ _Tj, ∑ _Tj} _J=1 ^GAfter, at first, produce QMC point u _Tj ⁱ(i=1 ..., N, j=1,2 ..., G), again QMC point u _Tj ⁱBe transformed to and obey distribution N (x _tμ _Tj, ∑ _Tj) sampling x _Tj ⁱThen, produce QMC point u once more _{(t+1) j} ⁱ(i=1 ..., N, j=1,2 ..., G), also QMC point u _{(t+1) j} ⁱObey distribution p (x according to being transformed to _T+1| x _Tj ⁱ) sample value x _{(t+1) j} ⁱOrder ${\stackrel{\‾}{W}}_{(t+1)j}=W_{\mathrm{tj}},$ Can obtain the prediction distribution of target posterior probability so:

$p\left(x_{t+1}\right|z_t)=\underset{j=1}{\overset{G}{\mathrm{\Σ}}}{\stackrel{\‾}{W}}_{(t+1)j}N(x_{t+1};{\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j},{\stackrel{\‾}{\mathrm{\Σ}}}_{(t+1)j})$

Here

${\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_{(t+1)j}^i$

${\stackrel{\‾}{\mathrm{\Σ}}}_{(t+1)j}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}(x_{(t+1)j}^i-{\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j}){(x_{(t+1)j}^i-{\stackrel{\‾}{\mathrm{\μ}}}_{(t+1)j})}^T$

2.2) renewal that distributes of posterior probability.When head node receives new measured value z _(t+1)The time, upgrade posterior probability distribution p (x according to following processes _(t+1)| z _(t+1)): sampling earlier obtains QMC point { u _{(t+1) j} ⁱ} _I=1 ^N(j=1 2..G), then is converted into these QMC points and obeys distribution Sampling ${\hat{w}}_{(t+1)j}^i=p\left(z_{(t+1)}\right|x_{(t+1)j}^i),$ Order then

${\hat{w}}_{(t+1)j}^i=p\left(z_{(t+1)}\right|x_{(t+1)j}^i)$

Normalization obtains w _{(t+1) j} ⁱ, now, just can be approximately posterior probability:

$p\left(x_{(t+1)}\right|y_{(t+1)})\≈\underset{j=1}{\overset{G}{\mathrm{\Σ}}}{W}_{(t+1)j}N(x_{(t+1)};{\mathrm{\μ}}_{(t+1)j},{\mathrm{\Σ}}_{(t+1)j})$

Here

${\mathrm{\μ}}_{(n+1)j}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{(n+1)}^i{x}_{(n+1)j}^i$

${\mathrm{\Σ}}_{(t+1)j}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{(t+1)j}^i(x_{(t+1)j}^i-{\mathrm{\μ}}_{(t+1)j}){(x_{(t+1)j}^i-{\mathrm{\μ}}_{(t+1)j})}^T$

$W_{(t+1)j}=W_{\mathrm{tj}}\frac{{\mathrm{\Σ}}_{i=1}^N{w}_{(t+1)j}^i}{\underset{j=1}{\overset{G}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{(t+1)j}^i}$

3) head node is selected

Select to realize by head node based on " cooperation " in the gaussian sum semi-particle filtering of node cooperation relation.We utilize mutual information I (x _T+1z _T+1 ^k| z _t) contribution amount of tolerance head node each neighbor node, I (x _T+1z _T+1 ^k| z _t) can be expressed as:

$I_k=I(x_{t+1};z_{t+1}^k|z_t)=E_{p(x_{t+!},z_{t+!}^k|z_t)}\left[\log \frac{p(x_{t+1},z_{t+1}^k|z_t)}{p\left(x_{t+1}\right|z_t)p\left(z_{t+1}^k\right|z_t)}\right]$

According to the result of step (2) gaussian sum semi-particle filtering, can top mutual information be approximately

${\tilde{I}}_k\≈\underset{j=1}{\overset{G}{\mathrm{\Σ}}}{\stackrel{\‾}{W}}_{(t+1)j}\log \left({\left(2\mathrm{\πe}\right)}^{t/2}\right|{\stackrel{\‾}{\mathrm{\Σ}}}_{(t+1)j}\left|\right)-\underset{i=1}{\overset{G}{\mathrm{\Σ}}}{W}_{(t+1)\mathrm{kj}}\log \left({\left(2\mathrm{\πe}\right)}^{t/2}\right|{\mathrm{\Σ}}_{(t+1)\mathrm{kj}}\left|\right)$

If set M={1,2.....K} represents the neighbor node of head node, order

$L=\arg {\max }_{k\∈M}\left\{{\tilde{I}}_k\right\}$

Then node L is exactly next head node constantly.When the L element was not unique, it was consistent that the contribution amount of two or above node is just arranged, and that selects one at random as next head node constantly.By the head node selection strategy, can realize the mutual transmission of tracking results between head node, thereby realize gaussian sum semi-particle filtering based on node cooperation.

To the algorithm that the present invention proposes, we utilize Matlab to carry out performance simulation, and its performance such as Fig. 2 and Fig. 3 show.

As can be seen from Figure 2, a kind of tracking performance of the cooperation gaussian sum semi-particle filtering based on node cooperation is very outstanding, and the aircraft pursuit course that obtains is very near the movement locus of target reality.As can be seen from Figure 3, the head node that selection obtains according to head node is evenly distributed in the both sides of target following curve, has stronger robustness.

Claims (3)

1. gaussian sum semi-particle filtering method based on node cooperation, it is characterized in that: comprise the gaussian sum semi-particle filtering and select two parts based on the head node of gaussian sum semi-particle filtering, head node for current time, produce sample value with the QMC point earlier, then produce the posterior probability distribution that gaussian sum distributes and is similar to the target current state with these sample values, then based on node cooperation, select the head node in the next moment, the distribution of the posterior probability of target current state is transferred to the head node in the next moment, at last, the head node in the next moment distributes according to the posterior probability of the measured value renewal dbjective state of oneself.

2. the gaussian sum semi-particle filtering method based on node cooperation according to claim 1, it is characterized in that in the process of carrying out the gaussian sum semi-particle filtering, utilize the QMC point to replace random number to produce sample value, and utilize these sample values to produce the posterior probability distribution that gaussian sum distributes and is similar to dbjective state, distributing based on these gaussian sums then obtains each neighbor node of current head node to upgrading the contribution amount expression formula of next moment dbjective state, and the neighbor node of selecting a contribution amount maximum at last becomes the head node in the next moment.

3. according to claim 1 or 2 described a kind of gaussian sum semi-particle filtering methods, it is characterized in that comprising following three steps based on node cooperation:

(1) the QMC generation of ordering: go up equally distributed low diversity sequence u obeying [0,1] _j(j=1 ..., N) be called the QMC point:

(2) gaussian sum semi-particle filtering: current head node receives the tracking results { W that previous moment head node sends _Tj, μ _Tj, ∑ _Tj} _J=1 ^GAfter, at first utilize the QMC point to obtain the prediction distribution p (x of target posterior probability _T+1| z _t), then receive new measured value gas z according to head node _(t+1), obtain the APPROXIMATE DISTRIBUTION p (x of destination probability _(t+1)| y _(t+1)), thereby obtain the tracking results { W of current head node _{(t+1) j}, μ _{(t+1) j}, ∑ _{(t+1) j}} _J=1 ^G

(3) head node is selected: according to the result of step (2) gaussian sum semi-particle filtering, obtain the module that head node is selected

If set M={1,2.....K} represents the neighbor node of head node, order $L=\arg {\max }_{k\∈M}\left\{{\tilde{I}}_k\right\},$ Then node L is exactly next head node constantly; When the L element was not unique, it was consistent that the contribution amount of two or above node is just arranged, and that selects one at random as next head node constantly; Select by head node, can realize the mutual transmission of tracking results between head node.

Images