CN109412602B - Distributed sparse signal detection method and device based on low bit quantization observation value - Google Patents

Distributed sparse signal detection method and device based on low bit quantization observation value Download PDF

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CN109412602B
CN109412602B CN201811145555.XA CN201811145555A CN109412602B CN 109412602 B CN109412602 B CN 109412602B CN 201811145555 A CN201811145555 A CN 201811145555A CN 109412602 B CN109412602 B CN 109412602B
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李刚
王学谦
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Tsinghua University
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Abstract

The invention discloses a distributed sparse signal detection method and a distributed sparse signal detection device based on a low bit quantization observation value, wherein the method comprises the following steps: collecting the analog observed values received by each sensor; quantizing the analog observed value by using a local threshold value of the sensor node to obtain a quantized value, and transmitting the quantized value to the fusion center; acquiring test statistics of the local maximum potential detector by using all the quantized values through the fusion center, and acquiring a decision threshold; and obtaining a detection result according to the test statistic and the judgment threshold value. The method reduces the communication bandwidth by transmitting the low-bit quantized data in the sensor network, has simple operation, obviously reduces the calculation complexity and improves the accuracy of signal detection.

Description

Distributed sparse signal detection method and device based on low bit quantization observation value
Technical Field
The invention relates to the technical field of signal detection, in particular to a distributed sparse signal detection method and device based on low bit quantization observation values.
Background
Sparse signals are widely present in the context of various signal processing, such as radar signal processing, image processing, acoustic signal processing, and the like. In recent years, a compressed sensing technology has attracted extensive attention for sparse signal processing, and is one of the current research hotspots. The theory of compressed sensing breaks through the boundary of the Nyquist sampling theorem, namely when the signal to be reconstructed is a sparse signal, a small amount of observation data can be utilized to accurately reconstruct the signal, and a large amount of data does not need to be acquired according to the Nyquist theorem.
In addition to reconstructing sparse signals, detecting sparse signals is also one of the essential links in signal processing. Inspired by the compression perception theory, some researchers put forward a compression detection theory and aim to realize the detection of sparse signals from a small amount of observation data. Compared with sparse reconstruction, the sparse signal detection method has the advantages that observation data are less in need of sparse signal detection, the calculation amount of the algorithm is lower, and the requirement on the signal to noise ratio is lower. For the detection of sparse signals, many scholars propose corresponding detection algorithms and analyze the performance of detection.
In recent years, distributed detection algorithms using sensor networks have also received a lot of attention. In the network, a plurality of sensors are scattered at a plurality of positions of a monitoring area, each sensor node senses the surrounding environment and transmits the processed data to the fusion center, and the fusion center makes the final judgment whether the signals exist or not. The sensor network has the characteristics of micro size, low power consumption, high integration level, low cost and the like. A plurality of sensor nodes are utilized to detect a target, the problem of blind areas during single-node observation can be well avoided, and the detection probability is greatly improved. In addition, the signal-to-noise ratio of the signal to be detected is favorably improved through an information fusion technology, so that the sensor network can realize a better detection function.
For distributed sparse signal detection, the related art method considers building a detector with analog values. However, in practice, the numerous sensor nodes in the sensor network are often constrained by cost, power consumption and volume, and both computational storage capacity and communication bandwidth are limited. Due to these limitations, rather than transmitting analog values, sensor networks tend to reduce communication bandwidth and subsequent computational complexity by transmitting low bit quantized data.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
To this end, it is an object of the present invention to propose a distributed sparse signal detection method based on low bit-quantized observations. The method reduces the communication bandwidth by transmitting the low-bit quantized data in the sensor network, has simple operation, obviously reduces the calculation complexity and improves the accuracy of signal detection.
Another objective of the present invention is to provide a distributed sparse signal detection apparatus based on low bit quantization observation values.
In order to achieve the above object, an embodiment of the present invention provides a distributed sparse signal detection method based on low bit quantization observation values, including the following steps: collecting the analog observed values received by each sensor; quantizing the analog observed value by using a local threshold value of the sensor node to obtain a quantized value, and transmitting the quantized value to a fusion center; acquiring test statistics of a local maximum potential detector by using all the quantized values through the fusion center, and acquiring a decision threshold; and obtaining a detection result according to the test statistic and the judgment threshold value.
According to the distributed sparse signal detection method based on the low-bit quantized observation value, the communication bandwidth is reduced by transmitting the low-bit quantized data in the sensor network, the operation is simple, the calculation complexity is obviously reduced, and the accuracy of signal detection is improved.
In addition, the distributed sparse signal detection method based on low bit quantization observation values according to the above embodiments of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the quantization formula is:
Figure BDA0001816727300000021
wherein the bit quantizer
Figure BDA0001816727300000022
L1, 2, …, L denoting the index of the sensors, L denoting the number of sensors,
Figure BDA0001816727300000023
number of bits used to represent each observation, ylRepresents the simulated observation, { τl,m,m＝0,1,…,2qDenotes a quantized threshold value, { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}q。
Further, in one embodiment of the present invention, the test formula is:
Figure BDA0001816727300000024
where t (U) denotes the test statistic of the local maximum potential detector, U ═ U1,u2,…,uL]Representing all the quantitative observations received at the fusion center, P represents the probability density function,
Figure BDA0001816727300000025
indicating the snow information eta indicates a decision threshold, H0Hypothesis that target is absent, H1The assumption, sparsity p, that indicates the presence of the target.
Further, in one embodiment of the present invention, said counting according to said testObtaining a detection result by the amount and the decision threshold, further comprising: outputting H if the test statistic is greater than or equal to the decision threshold1(ii) a If the test statistic is less than the decision threshold, outputting H0。
Further, in one embodiment of the present invention,
Figure BDA0001816727300000031
wherein H0Hypothesis indicating absence of information, H1An assumption indicating the presence of a signal, L indicates the index value of the sensor node, and L nodes are present, { w }lL1, 2, …, L represents additive white Gaussian noise independent of each other,
Figure BDA0001816727300000032
representing a known linear observation vector that is,
Figure BDA0001816727300000033
representing the unknown sparse signal observed by the ith sensor,
Figure BDA0001816727300000034
representing the compressed analog observations, (-)TRepresenting a transpose operation.
In order to achieve the above object, an embodiment of another aspect of the present invention provides a distributed sparse signal detection apparatus based on low bit quantization observation values, including: the acquisition module is used for acquiring the analog observation values received by the sensors; the transfer module is used for quantizing the analog observed value by utilizing a local threshold value of the sensor node to obtain a quantized value and transferring the quantized value to the fusion center; the judgment module is used for acquiring the test statistic of the local maximum potential detector by using all the quantized values through the fusion center and acquiring a judgment threshold; and the detection module is used for acquiring a detection result according to the test statistic and the judgment threshold value.
According to the distributed sparse signal detection device based on the low-bit quantized observation value, the communication bandwidth is reduced by transmitting the low-bit quantized data in the sensor network, the operation is simple, the calculation complexity is obviously reduced, and the accuracy of signal detection is improved.
In addition, the distributed sparse signal detection apparatus based on low bit quantization observation values according to the above embodiments of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the quantization formula is:
Figure BDA0001816727300000035
wherein the bit quantizer
Figure BDA0001816727300000036
L1, 2, …, L denoting the index of the sensors, L denoting the number of sensors,
Figure BDA0001816727300000037
number of bits used to represent each observation, ylRepresents the simulated observation, { τl,m,m＝0,1,…,2qDenotes a quantized threshold value, { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}q。
Further, in one embodiment of the present invention, the test formula is:
Figure BDA0001816727300000038
where t (U) denotes the test statistic of the local maximum potential detector, U ═ U1,u2,…,uL]Representing all the quantitative observations received at the fusion center, P represents the probability density function,
Figure BDA0001816727300000041
the presentation snow information η represents a decision threshold,H0hypothesis that target is absent, H1The assumption, sparsity p, that indicates the presence of the target.
Further, in an embodiment of the present invention, the detection module further includes: outputting H if the test statistic is greater than or equal to the decision threshold1(ii) a If the test statistic is less than the decision threshold, outputting H0。
Further, in one embodiment of the present invention,
Figure BDA0001816727300000042
wherein H0Hypothesis that signal is absent, H1An assumption indicating the presence of a signal, L indicates the index value of the sensor node, and L nodes are present, { w }lL1, 2, …, L represents additive white Gaussian noise independent of each other,
Figure BDA0001816727300000043
representing a known linear observation vector that is,
Figure BDA0001816727300000044
representing the unknown sparse signal observed by the ith sensor,
Figure BDA0001816727300000045
representing the compressed analog observations, (-)TRepresenting a transpose operation.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a distributed sparse signal detection method based on low-bit quantized observations according to an embodiment of the present invention;
FIG. 2 is a flow diagram of a sparse signal local maximum potential detector based on low bit quantized observations according to one embodiment of the present invention;
FIG. 3 is an experimental setup diagram for sparse signal local maximum potential detection based on low-bit quantized observations, according to an embodiment of the present invention;
FIG. 4 is an experimental diagram of a quantizer of a local sensor node according to one embodiment of the invention;
fig. 5 is a schematic structural diagram of a distributed sparse signal detection apparatus based on low-bit quantization observation values according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The following describes a method and an apparatus for detecting a distributed sparse signal based on low bit quantized observations according to an embodiment of the present invention with reference to the accompanying drawings, and first, a method for detecting a distributed sparse signal based on low bit quantized observations according to an embodiment of the present invention will be described with reference to the accompanying drawings.
Fig. 1 is a flowchart of a distributed sparse signal detection method based on low-bit quantization observation values according to an embodiment of the present invention.
As shown in fig. 1, the distributed sparse signal detection method based on low bit quantization observation values includes the following steps:
in step S101, analog observations received by each sensor are collected.
As shown in FIG. 3, each sensor receives an analog observation y according to the detection scenario set in the figurel,
Figure BDA0001816727300000056
In step S102, the analog observed value is quantized by using a local threshold of the sensor node to obtain a quantized value, and the quantized value is transmitted to the fusion center.
Further, in one embodiment of the present invention, the quantization formula is:
Figure BDA0001816727300000051
wherein the bit quantizer
Figure BDA0001816727300000052
L1, 2, …, L denoting the index of the sensors, L denoting the number of sensors,
Figure BDA0001816727300000053
number of bits used to represent each observation, ylRepresents the simulated observation, { τl,m,m＝0,1,…,2qDenotes a quantized threshold value, { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}q。
In step S103, test statistics of the local maximum potential detector are acquired by the fusion center using all the quantized values, and a decision threshold is acquired.
Further, in one embodiment of the present invention, the test formula is:
Figure BDA0001816727300000054
where t (U) denotes the test statistic of the local maximum potential detector, U ═ U1,u2,...,uL]Representing all the quantitative observations received at the fusion center, P represents the probability density function,
Figure BDA0001816727300000055
indicating the snow information eta indicates a decision threshold, H0Hypothesis that target is absent, H1The assumption, sparsity p, that indicates the presence of the target.
In step S104, a detection result is acquired based on the test statistic and the decision threshold.
Further, in the embodiment of the present invention, obtaining the detection result according to the test statistic and the decision threshold further includes: if the test statistic is greater than or equal to the decision threshold, then output H1(ii) a If the test statistic is less than the decision threshold, outputting H0。
Wherein,
Figure BDA0001816727300000061
wherein H0Hypothesis that signal is absent, H1An assumption indicating the presence of a signal, L indicates the index value of the sensor node, and L nodes are present, { w }lL1, 2, …, L represents additive white Gaussian noise independent of each other,
Figure BDA0001816727300000062
representing a known linear observation vector that is,
Figure BDA0001816727300000063
representing the unknown sparse signal observed by the ith sensor,
Figure BDA0001816727300000064
representing the compressed analog observations, (-)TRepresenting a transpose operation.
As shown in fig. 2, the distributed sparse signal detection method based on low-bit quantization observation values according to the embodiment of the present invention includes the steps of:
1 each sensor receives an analog observed value yl,
Figure BDA0001816727300000065
2 using local threshold value { tau } of sensor nodel,m,m＝0,1,…,2qAnd equation (5), quantifying the received analog observations ylTo obtain a quantized value ulAnd quantizes the value ulIs transmitted to the fusion center,
Figure BDA0001816727300000066
3 in the fusion center, all quantized values u are used1,u2,…,uLAnd equation (7), calculating test statistic t (u) of local maximum potential detector;
4: calculating a decision threshold eta according to a formula (15) at a fusion center;
5, comparing T (U) with eta;
and (3) outputting:
Figure BDA0001816727300000067
in summary, the following describes in detail an implementation process of the distributed sparse signal detection method based on low bit quantization observation values according to the present invention.
According to the distributed sparse signal detection method based on the low-bit quantized observation value, only low-bit quantized (single-bit, 2-bit and 3-bit quantized) observation values are utilized, and compared with a distributed sparse signal detection method based on an analog value in the related art, the distributed sparse signal detection method based on the low-bit quantized observation value can save the bandwidth of a sensor network.
Defining a function:
Figure BDA0001816727300000071
F-1(. cndot.) represents the inverse function of F (-)
Figure BDA0001816727300000072
Figure BDA0001816727300000073
Figure BDA0001816727300000074
(μ,σ2) Denotes mean μ and variance σ2A gaussian distribution of (a).
First, as shown in fig. 3, the distributed sparse signal detection method based on low bit quantization observation values according to the embodiment of the present invention considers the problem of sparse signal detection, and the mathematical model of distributed sparse signal detection is as follows:
Figure BDA0001816727300000075
wherein H0Hypothesis that target is absent, H1An assumption indicating the presence of an object, L indicates the index value of the sensor node, and L nodes are total, { wlL1, 2, L represents additive white gaussian noise independent of each other,
Figure BDA0001816727300000076
representing a known linear observation vector that is,
Figure BDA0001816727300000077
representing the unknown sparse signal observed by the ith sensor,
Figure BDA0001816727300000078
representing the compressed analog observations, (-)TRepresenting a transpose operation.
Further, in embodiments of the present invention, consider using a Bernoulli-Gaussian distribution for sparse signal xlAnd modeling. First, joint sparsity is described, which refers to a sparse signal x for different sensors llAre identical and define a binary vector s to describe { x }lJoint sparsity of 1, 2.., L }:
Figure BDA0001816727300000079
wherein N is 1, 2. Set of assumptions snThe elements in N ═ 1, 2.., N } are bernoulli random variables that are independent of each other:
Figure BDA00018167273000000710
wherein the parameter p is belonged to (0, 1)]. According to the formula (3), in the sparse signal xlThe probability of an element in (b) being a non-zero value is p,
Figure BDA00018167273000000711
further, assume that in sparse signal xlAll non-zero elements in (A) obey mutually independent Gaussian distributions
Figure BDA00018167273000000712
Therefore, the embodiment of the invention can obtain the application of the sparse signal xlElement x in (1)l,nBernoulli-gaussian distribution of (a):
Figure BDA0001816727300000081
where δ (·) represents an impulse function. In equation (4), the bernoulli parameter p is sparsity. Specifically, to ensure the sparsity of the signal, the sparsity p is a very small number close to 0, i.e., p → 0+It is difficult to know the exact value of the sparsity p before the detection process. In an embodiment of the invention, it is assumed that the sparsity p is unknown, but the variance of the non-zero elements
Figure BDA0001816727300000082
Variance of sum noise
Figure BDA0001816727300000083
Are assumed to be known. In the practical case where the temperature of the molten metal is high,
Figure BDA0001816727300000084
the estimation can be done in the absence of a signal,
Figure BDA0001816727300000085
may be obtained by analyzing the statistical properties of the signal. Q-bit quantizer at the l-th local node
Figure BDA0001816727300000086
Is defined as:
Figure BDA0001816727300000087
wherein, L is 1, 2., L,
Figure BDA0001816727300000088
the number of bits used to represent each observation, { τl,m,m＝0,1,...,2qDenotes the quantized threshold, the output u of the quantizerlRepresenting a simulated observation ylInterval in { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}qFor example, when q is 2, v1＝‘00’,v2＝‘01’,v3＝‘10’，v4And 11'. As shown in FIG. 4, all of the quantified observations received by the fusion center are represented as
Figure BDA0001816727300000089
And when the fusion center receives the U, the fusion center judges whether the sparse signal exists or not.
Further, since the sparsity p is unknown, the hypothesis testing problem for sparse signals in equation (1) can be ascribed to the parametric testing problem for sparsity, as follows:
Figure BDA00018167273000000810
the above is a single-side hypothesis testing problem, and since sparsity is a very small positive number close to 0, the single-side hypothesis testing problem in equation (6) is also an asymptotic hypothesis testing problem. In the related art, it has been demonstrated that the local maximum potential detector has asymptotic optimality for the single-sided asymptotic hypothesis testing problem.
Based on quantized observations, the embodiments of the present invention provide a new detector, i.e., a local maximum potential detector, for the problem of distributed sparse signal detection, and provide a formula for the local maximum potential detector based on quantized observations:
Figure BDA00018167273000000811
where T (U) represents the test statistic of the local maximum potential detector, η represents the decision threshold,
Figure BDA0001816727300000091
Figure BDA0001816727300000092
Figure BDA0001816727300000093
in the embodiment of the invention, a theoretical detection performance analysis formula of a local maximum potential detector based on a quantitative observation value is given:
Figure BDA0001816727300000094
wherein a represents an asymptotic probability density function,
Figure BDA0001816727300000095
further, the false alarm probability P of the local maximum potential detector based on the quantized observationFADetection probability PDAnd the decision threshold η is:
PFA＝P(T(U)>η|H0)＝1-F(η), (13)
PD＝P(T(U)>η|H1)＝1-F′(μQ,η), (14)
η＝F-1(1-PFA), (15)
specifically, in order to maximize the detection performance of the local maximum potential detector, the quantization threshold needs to be adjusted so that the mean value μ is maximized. In the embodiment of the invention, the optimal local quantization threshold values under single-bit quantization, 2-bit quantization and 3-bit quantization are respectively given by solving a numerical algorithm, as shown in tables I-III. Where table I is the optimal single-bit quantizer threshold, where L is 1,2, …, L; table II is the optimal 2-bit quantizer threshold, where L ═ 1,2, …, L; table III is the optimal 3-bit quantizer threshold, where L is 1,2, …, L.
TABLE I
Figure BDA0001816727300000096
Figure BDA0001816727300000101
TABLE II
Figure BDA0001816727300000102
TABLE III
Figure BDA0001816727300000103
The method comprises the following specific steps of:
inputting the number L of sensor nodes, the number q of quantization bits and observationVector hl,
Figure BDA0001816727300000104
Variance of non-zero coefficient
Figure BDA0001816727300000105
Variance of noise
Figure BDA0001816727300000106
Optimal quantization threshold value { tau ] of each local sensor nodel,m,m＝0,1,…,2q},
Figure BDA0001816727300000107
As shown in tables I-III, the false alarm probability PFA；
According to the distributed sparse signal detection method based on the low-bit quantization observation value, which is provided by the embodiment of the invention, the communication bandwidth is reduced by transmitting low-bit quantization data in the sensor network, the operation is simple, the calculation complexity is obviously reduced, and the accuracy of signal detection is improved.
Next, a distributed sparse signal detection apparatus based on low bit quantization observation values proposed according to an embodiment of the present invention is described with reference to the drawings.
Fig. 5 is a schematic structural diagram of a distributed sparse signal detection apparatus based on low-bit quantization observation values according to an embodiment of the present invention.
As shown in fig. 5, the distributed sparse signal detection apparatus 10 based on low-bit quantized observation values includes: acquisition module 100, delivery module 200, decision module 300 and verification module 400.
The acquisition module 100 is configured to acquire analog observation values received by each sensor. And the transmission module 200 is configured to quantize the analog observation value by using a local threshold of the sensor node to obtain a quantized value, and transmit the quantized value to the fusion center. And the decision module 300 is configured to obtain test statistics of the local maximum potential detector by using all the quantized values through the fusion center, and obtain a decision threshold. And a detection module 400, configured to obtain a detection result according to the test statistic and the decision threshold. The device utilizes low bit quantization, saves the bandwidth of a sensor network and improves the accuracy of signal detection. The distributed sparse signal detection device 10 based on the low-bit quantized observation value reduces the communication bandwidth and the calculation complexity by transmitting the low-bit quantized data in the sensor network, and improves the accuracy of signal detection.
Further, in one embodiment of the present invention, the quantization formula is:
Figure BDA0001816727300000111
wherein the bit quantizer
Figure BDA0001816727300000112
L1, 2, …, L denoting the index of the sensors, L denoting the number of sensors,
Figure BDA0001816727300000113
number of bits used to represent each observation, ylRepresents the simulated observation, { τl,m,m＝0,1,…,2qDenotes a quantized threshold value, { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}q。
Further, in one embodiment of the present invention, the test formula is:
Figure BDA0001816727300000114
where T (U) represents the test statistic of the local maximum potential detector, U is the quantitative observation, P is XXX,
Figure BDA0001816727300000115
let XXX, eta denote the decision threshold, H0Hypothesis that target is absent, H1The assumption, sparsity p, that indicates the presence of the target.
Further, in an embodiment of the present invention, the detection module 400 further comprises: if the test statistic is largeIs equal to or greater than the decision threshold, then H is output1(ii) a If the test statistic is less than the decision threshold, outputting H0。
Further, in one embodiment of the present invention,
Figure BDA0001816727300000116
wherein H0Hypothesis that signal is absent, H1An assumption indicating the presence of a signal, L indicates the index value of the sensor node, and L nodes are present, { w }lL1, 2, …, L represents additive white Gaussian noise independent of each other,
Figure BDA0001816727300000117
representing a known linear observation vector that is,
Figure BDA0001816727300000118
representing the unknown sparse signal observed by the ith sensor,
Figure BDA0001816727300000119
representing the compressed analog observations, (-)TRepresenting a transpose operation.
It should be noted that the foregoing explanation of the embodiment of the distributed sparse signal detection method based on a low-bit quantized observation value is also applicable to the apparatus of the embodiment, and is not repeated here.
According to the distributed sparse signal detection device based on the low-bit quantization observation value, provided by the embodiment of the invention, the communication bandwidth is reduced by transmitting low-bit quantization data in the sensor network, the operation is simple, the calculation complexity is obviously reduced, and the accuracy of signal detection is improved.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (6)

1. A distributed sparse signal detection method based on low bit quantization observations is characterized by comprising the following steps:
collecting the analog observed values received by each sensor;
quantizing the analog observation value by using a local threshold value of the sensor node to obtain a low-bit quantized value, and transmitting the quantized value to a fusion center, wherein the quantization formula is as follows:
Figure FDA0002892506820000011
wherein the bit quantizer
Figure FDA0002892506820000012
L denotes the index of the sensor, L denotes the number of sensor nodes, ulRepresents the low-bit quantized value or values,
Figure FDA0002892506820000013
number of bits used to represent each observation, ylRepresents the simulated observation, { τl,m,m＝0,1,…,2qDenotes a quantized threshold value, { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}q；
Acquiring test statistics of a local maximum potential detector by using all the quantized values through the fusion center, and acquiring a decision threshold;
the test formula for the local maximum potential detector is:
Figure FDA0002892506820000014
where t (U) denotes the test statistic of the local maximum potential detector, U ═ U1,u2,…,uL]Representing all the quantized values received by the fusion center, P represents the probability density function,
Figure FDA0002892506820000015
denotes the root number of the fee snow information, eta denotes the decision threshold value, H0Hypothesis that target is absent, H1An assumption that the target exists is represented, and p represents sparsity;
Figure FDA0002892506820000016
Figure FDA0002892506820000021
wherein,
Figure FDA0002892506820000022
Figure FDA0002892506820000023
hlrepresenting a known linear observation vector that is,
Figure FDA0002892506820000024
representing the variance of the non-zero elements in the signal,
Figure FDA0002892506820000025
representing the variance of the noise; and
and obtaining a detection result according to the test statistic and the judgment threshold value.
2. A low bit-quantization observation-based distributed sparse signal detection method as recited in claim 1, wherein said obtaining a detection result based on said test statistic and said decision threshold value, further comprises:
outputting H if the test statistic is greater than or equal to the decision threshold1；
If the test statistic is less than the decision threshold, outputting H0。
3. A low bit-quantization observation-based distributed sparse signal detection method according to claim 2, wherein:
Figure FDA0002892506820000026
wherein H0Hypothesis that signal is absent, H1An assumption indicating the presence of a signal, L indicates the index value of the sensor node, and L nodes are present, { w }lL1, 2, …, L represents additive white Gaussian noise independent of each other,
Figure FDA0002892506820000027
representing a known linear observation vector that is,
Figure FDA0002892506820000028
representing the unknown sparse signal observed by the ith sensor,
Figure FDA0002892506820000029
representing the compressed analog observations, (-)TRepresenting a transpose operation.
4. A distributed sparse signal detection apparatus based on low bit quantization observations, comprising:
an acquisition module: the device is used for collecting the analog observed values received by each sensor;
the transfer module is used for quantizing the analog observation value by using a local threshold value of the sensor node to obtain a low-bit quantized value and transferring the quantized value to the fusion center, wherein the quantization formula is as follows:
Figure FDA0002892506820000031
wherein the bit quantizer
Figure FDA0002892506820000032
L denotes the index of the sensor, L denotes the number of sensor nodes, ulRepresents the low-bit quantized value or values,
Figure FDA0002892506820000033
number of bits used to represent each observation, ylRepresents the simulated observation, { τl,m,m＝0,1,…,2qDenotes a quantized threshold value, { v }k,k＝1,2,…,2qDenotes a binary symbol, vk∈{0,1}q；
The judgment module is used for acquiring the test statistic of the local maximum potential detector by using all the quantized values through the fusion center and acquiring a judgment threshold;
the test formula for the local maximum potential detector is:
Figure FDA0002892506820000034
where t (U) denotes the test statistic of the local maximum potential detector, U ═ U1,u2,…,uL]Representing all the quantized values received by the fusion center, P represents the probability density function,
Figure FDA0002892506820000035
denotes the root number of the fee snow information, eta denotes the decision threshold value, H0Hypothesis that target is absent, H1An assumption that the target exists is represented, and p represents sparsity;
Figure FDA0002892506820000036
Figure FDA0002892506820000037
wherein,
Figure FDA0002892506820000038
Figure FDA0002892506820000041
hlrepresenting a known linear observation vector that is,
Figure FDA0002892506820000042
representing the variance of the non-zero elements in the signal,
Figure FDA0002892506820000043
representing the variance of the noise; to be provided withAnd
and the detection module is used for acquiring a detection result according to the test statistic and the judgment threshold value.
5. The low bit-quantization observation-based distributed sparse signal detection device of claim 4, wherein the detection module further comprises:
outputting H if the test statistic is greater than or equal to the decision threshold1；
If the test statistic is less than the decision threshold, outputting H0。
6. A low bit-quantization observation-based distributed sparse signal detection apparatus as defined in claim 5, wherein:
Figure FDA0002892506820000044
wherein H0Hypothesis that signal is absent, H1An assumption indicating the presence of a signal, L indicates the index value of the sensor node, and L nodes are present, { w }lL1, 2, …, L represents additive white Gaussian noise independent of each other,
Figure FDA0002892506820000045
representing a known linear observation vector that is,
Figure FDA0002892506820000046
representing the unknown sparse signal observed by the ith sensor,
Figure FDA0002892506820000047
representing the compressed analog observations, (-)TRepresenting a transpose operation.
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