=Paper=
{{Paper
|id=Vol-2608/paper1
|storemode=property
|title=Algorithmic support for the detection characteristics improving of the monitoring object
|pdfUrl=https://ceur-ws.org/Vol-2608/paper1.pdf
|volume=Vol-2608
|authors=Elena Chernetsova,Anatoly Shishkin
|dblpUrl=https://dblp.org/rec/conf/cmis/ChernetsovaS20
}}
==Algorithmic support for the detection characteristics improving of the monitoring object==
https://ceur-ws.org/Vol-2608/paper1.pdf
Algorithmic Support for the Detection Characteristics
Improving of the Monitoring Object
Elena Chernetsova1[0000-0001-5805-3111] and Anatoly Shishkin2[0000-0003-1992-5663]
1
Russian State Hydrometeorological University, Metallistov Av.,3, St-Peterburg, 195027,
Russia
chernetsova@list.ru
2
Russian State Hydrometeorological University, Metallistov Av.,3, St-Peterburg, 195027,
Russia
an.dm.shishkin@mail.ru
Abstract. The paper presents: an object detection algorithm for coherent recep-
tion of signals coming from a monitoring network consisting of several sensors;
an algorithm for detecting an extended object by analog signals of sensors of a
monitoring network. These algorithms use statistics that take into account the
most stable features of the distribution of the source data. They can be imple-
mented in an automated decision support system. At the same time, decisions
on the detection of a monitoring object made by an automated system will be
more reliable
Keywords: Monitoring, Object, Sensor, Signal, Algorithm, Detection.
1 Introduction
To carry out environmental monitoring, it is necessary to conduct continuous obser-
vations over time, based on a well-thought-out distribution of measuring instruments
in space, for which it is necessary to use a stationary distributed multi-sensor remote
monitoring system [1]. It should work efficiently, preferably at a real time scale. Effi-
ciency also means reducing the time frame for deciding on the classification of the
observed object. Therefore, it is necessary to automate not only the data collection
process, but also the classification algorithms of the monitoring object in order to
attract the attention of the human operator only to objects that actually threaten the
ecological state of the observed area and even at the stage of automated data process-
ing to weed out objects that do not threaten the ecological state of the zone of respon-
sibility. A stationary network of stations included in the monitoring system requires
the availability of communication channels with a Monitoring Control Point (MCP)
[2]. Laying a cable communication network is often unprofitable. Therefore, for
communication purposes it is necessary to use a radio channel or satellite communica-
tion [3]. Since the sensors of the monitoring network receive energy from the batter-
ies, in order to save energy in the monitoring network, it is often justified not to pre-
process the signal on the sensor, but to send analog signals to the MCP, which is
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
charged with processing the sensor signals and detecting the monitoring object [4].
Information exchange over the radio channel raises the problem of detecting an ana-
log signal with an unknown law of fluctuations against the background of noise with
an unknown distribution [5]. To solve this problem, in this paper, it is proposed to
develop the following algorithms:
• an algorithm for detecting a monitoring object during coherent reception of signals
coming from a monitoring network consisting of several sensors;
• the sample size for detecting the object of the analog signals of the sensors of the
monitoring network.
2 Theoretical Analysis
2.1 The most powerful accordingly to the signal-to-noise ratio criterion
algorithm for processing spatially distributed data from a monitoring
network consisting of several sensors
Let us consider the problem of coherent detection of a signal from an object distrib-
uted in N resolution elements, which are sensors of a monitoring network. It was
shown in [6] that the detector calculates the likelihood ratio:
N
1 0 k (k ) 1 1 k
l( X ) ( ) exp[( ) xn 2 ]2 (1)
( N ) 1 2 0 2 1 n 1
k
where xn - detector output envelope samples , n 1, 2,....., N
0 and 1 - signal variances received from ( N k ) sensors, that did not fix the object
and k sensors, fixed object accordingly .
From equation (1) we can see, that detector which is most powerful accordingly
to the signal-to-noise ratio criterion can be implemented by a rather complex circuit,
and, in addition, for its implementation a priori information is required about the pa-
rameters of signal ( 1 ) and noise ( 0 ) , which, as a rule, in real monitoring condi-
tions are unknown. Therefore the rule (1) characterizes the potential for detecting an
object and cannot be realized in many practical cases.
It is necessary to develop an most powerful by signal / noise criterion algorithm
for coherent detection of a signal from a monitoring object received from ( N k ) sen-
sors on the background of noise interference provided that the signal and noise pa-
rameters, as well as the position of the fixed object k sensors among N sensors of
the monitoring network are a priory unknown. Detection is formulated as the statisti-
cal task of testing general linear hypotheses [7-10] and the rule is found in the class
of so-called invariant rules [11].
We use the following premises:
1. There are statistically independent radio pulses sent by N ( N 1) sensors. In the
absence of the object of observation, these pulses have the same average power.
The law of the distribution of the noise background is considered normal.
2. In the presence of an object of observation, the resulting fluctuation in resolution is
the additive sum of the signal with unknown amplitude m (m 1,2..., k ) and
Gaussian noise with unknown variance 2 . Coherent processing is assumed. In-
dependent voltage samples are taken at the output of the linear path of the MCP
receiver at time instants following the resolution interval. x n (n 1,2,..., N ) .
3. Processing is carried out during the p periods of the signal, so that each reference
element n will correspond to a sample vector ( xn1 ,...., xnp ) with multidimensional
normal probability density
| A| 1 p p
g( X n ) p/2
exp aij ( xni ni )( xnj nj ). (2)
(2 ) 2 i 1 j 1
The mean values and the covariance matrix of the vector are determined from the
expressions E ( xni ) ni ; E ( xni ni )( xnj nj ) ij ; ij A 1 , where E - is the
sign of mathematical averaging, and n 0 , if n ( N k ) , and n 0 at n k . It
is also believed that the matrix A (aij ) - is common to all vectors N , having di-
mension p , but unknown .
The challenge is that by sample
x11 . . . x1 p
. . . . .
X . . . . .
. . . . .
x N1 . . . x Np
determine the presence or absence of a signal about the existence of a monitoring
object. Matrix X consists of p column vectors ( x1i ,......., x Ni ) , and each such vector
has its own mean value vector i (1i ,..., Ni ) .
Given the accepted assumptions, the task of detection is to test complex hypotheses
H 0 and H1 regarding parameters i and A .
H 0 : i 0 H1 : i 0 i 1,2,...., p А is unknown (3)
Hypothesis testing (3) fits into the scheme of testing multidimensional linear hy-
potheses. As follows from the general theory [12], principles of invariance and suffi-
ciency allows you to reduce the sample X when testing hypotheses (3) to maximally
invariant statistics of the form
p p N xi x j
T (4)
N
i 1 j 1
( xni xi )( x nj x j )
n 1
and the set of parameters i and (aij ) - to maximal invariant
p p
2 N aij i j (5)
i 1 j 1
N
In expressions (4), (5) x i ( j ) N 1 x xi( j ) ; i ( j ) E ( x i ( j ) ). Numerator of the
n 1
formula (4) has off center p 2 - off-center distribution with the noncentrality pa-
rameter 2 and p degrees of freedom, and the denominator has central distribution
2 ( N p ) , so the statistics ( N p)T / p has off-central F distribution with p and
( N p ) degrees of freedom and with the noncentrality parameter 2 .
Regarding the parameter 2 of F - distribution initial hypotheses (3) can now be
formulated as follows :
H 0 : 0; H1 : 0 (6)
Using the method of constructing optimal rules [13], it can be shown that the most
powerful invariant criterion for testing hypotheses (6) has a critical region of the form
T C. (7)
Threshold level C determined by the given probability of false alarm from the
condition
F p, ( N p) ( y )dy (8)
C
where Fp,( N p ) -is central F distribution with p and ( N p ) degrees of freedom.
The expressions (4), (7) determine the functional scheme of the detector with
completely unknown correlation properties of vectors ( x n1 ,..., x np ) . For practical
implementation, expressions (7), (8) can be concretized, for example, in the case of
the absence of inter-period correlation. In this case, the discovery rule and parameter
2 take the form
p 2
N xi
C, (9)
i 1 2
( xni x i )
p
2 qi , (10)
i 1
N
where q i ( n ) i2 / N 2 - is the average for all N signal-to-noise ratio for one
n 1
observation period. The detector efficiency is determined by the power function of
rule (7), (8), which shows the dependence of the probability of correct detection on
the parameter 2 . It can be calculated directly from off-center tables of F - distribu-
tion [14].
2.2 A most powerful according to the signal-to-noise ratio criterion algorithm
for detecting an extended object by analog signals of monitoring network
sensors
To develop an algorithm for classifying an extended object (for example, classify-
ing the observed water surface as clean or polluted by oil emissions) using a distrib-
uted multisensor geographic information system, suppose:
The central post decides to detect / not detect an object (contamination) based on
signals received from N sensors under the same observation conditions ;
The resulting radio signal of each sensor is the additive sum of the non-fluctuating
signal of unknown amplitude i( j ) 0 ( j =1,2- is numbers of object - e.g. clean
water surface and dirty water surface, i N ) and Gaussian noise with unknown
dispersion i2 . At the output of the receiver’s linear path, the amplitude samples
xi( j ) are taken for the signal of each sensor.
Observation of objects is carried out for some time T , during which readings for
the signal of each sensor n are taken. Thus, for each object, the sample space is
represented as n sample vectors x(1) ( x(11) ,..., x(1n) ) ; x( 2) ( x( 2) ,..., x( 2n) ) ;
1, n .
Vectors x(1) and x( 2) have a normal probability density
A 1 N N ( j) ( j)
g ( x( j ) ) exp[ ik ( xi k )] (11)
N /2 2 i 1k 1
(2 )
The mean values and elements of the covariance matrix are determined from the
expressions
E ( x( kj ) ) ( kj ) ; E ( x( ij ) ( ij ) )( x( kj ) ( kj ) ) ik ; ( ik ) A 1 , where E – is the
sign of mathematical averaging. We consider that the matrix A ( ik ) is common to
vectors x(1) and x( 2) , but its elements are unknown.
The classification task is by the sample x(1) , x( 2) , 1, n determine whether ob-
jects belong to the same class or belong to different classes.
Based on the assumptions made, this problem can be formulated as two hypotheses
- 1. objects are of the same type; 2. objects are of the different type:
(1) ( 2) (1) ( 2)
H0 : i i ; H1 : i i for all i 1, N (12)
( j)
In expression (12) the parameter i is matrix column having dimension (n 1)
with elements (1(i j ) ,..., ni
( j)
).
As follows from the general theory [15], the principles of invariance and suf-
ficiency allow us to reduce the sample space x(1) , x( 2) , 1, n , when testing hy-
potheses (12) for maximally invariant statistics (MI) of the form
(1) (2) (1) ( 2)
N N n( x i x i )( x x )
T k k (13)
i 1 k 1 n (1) (1) (1) (1) n ( 2) ( 2) ( 2) ( 2)
( x1 x i )( xk x k ) ( xi x )( xk x k )
1 1
and the parameter space is to MI
n
2 ik ( i(1) i(2) )( k(1) k(2) ) (14)
2
( j) n
In expressions (13) and (14) is marked: x k n 1 x( kj ) ; k( j ) Е ( x kj ); k= 1, N .
1
It can be shown that there is uniformly the most powerful (UMP) criterion for test-
ing hypotheses (12), (12), which rejects the hypothesis H 0 in case if
T > C, (15)
where С – is the threshold constant .
The constant С should be determined from the condition that under the hy-
pothesis H 0 ( 2 0) the probability of the fulfillment of condition (15) was no
more than a certain predetermined significance level . Whereas statistics 1 / 2T
under the hypothesis H0 has central F distribution with 1 N and
2 ( 2n N 1) degrees of freedom [16], the constant C can be found from the ex-
pression
Fv v ( )d
1 2
(16)
c
The rule (15) can be specified for the case when the matrix A is diagonal. In this
case, it has the form
(1) ( 2)
N n( x i x i ) 2
n C1 (17)
(1) 2 n
i 1 (1) ( 2) ( 2) 2
( x 1 x i ) ( xi xi )
1 1
where C1 CN /(2n N 1) .
( j)
From the expressions (13) and (17) it can be seen that x i ( j 1,2; i 1, N ) - are
maximum likelihood estimates for parameters i( j ) , calculated for the sensor N sig-
nals for the first and second objects, and the value in the denominator is the sum of
the parameter i2 estimates calculated for the signal of the first and second object of
i-th sensor. Thus, to distinguish between objects, it is necessary to estimate the ampli-
tudes of the N sensor signals, calculate the square of the distance between the pa-
rameters of the signals of the classified objects by the sensors of the same name, and
sum them with weights inversely proportional to the noise variance. The amount re-
ceived is compared with a threshold, in case of exceeding which a decision is made
on whether the objects belong to different classes.
Expression (15) can also be used to detect a distributed object, if we put
x( 2) 0; 1, n . Formula (17) in this case takes the form [17]:
N 2
nxi
C 2 , где C 2 CN /( n N 1) . (18)
i 1 n ( x x ) 2
i i
1
Considering that under the hypotesis H1 statistics T has off-central F distribu-
tion with off-center parameter 2 and 1 , 2 degrees of freedom, the probability of
correctly distinguishing between objects is determined by the expression [18]:
P (T C ) 0 F ( , 2 ) d
1 2
(19)
and can be calculated according to the tables of off-central F distribution [19].
3 Results
Figure 1 shows the curves characterizing the effectiveness of the detector of oil
pollution of the water surface depending on the resolving power of the network of
contact sensors constructed in accordance with expressions (4), (7). Characteristics
calculated for false alarm probability value 102 and the number of received
signal periods p 2 provided that the value of the signal-to-noise ratio averaged
over all N sensors for one observation period q i is independent of resolution (uni-
form distribution of translational buoys (contact sensors) along the length of contami-
nation). For comparison, the same figure shows the power function of the potential
most powerful rule (MP) of coherent detection of a known signal [20] in the presence
of only one sensor ( N 1 ).
It can be seen from the figure 1 that ignorance of the noise and signal levels in
the decision elements leads to losses in the signal-to-noise ratio. However, with in-
creasing resolution, the detector’s efficiency increases. This is due to the fact that the
increase allows a more accurate assessment of noise and signal levels. So, when
N 8 the loss in the signal-to-noise ratio is ~4 dB, and when N 22 - less than 1 dB.
Fig. 1. The probability of detecting oil pollution of the water surface by signals received from a
network of contact sensors
Figure 2 shows the dependences of the probability P(N ) of correct distinguishing
between two objects, calculated by the formula (19), for different values of the signal
sample size n.
Fig. 2. The dependence of the probability of distinguishing objects P (N) for a different number
of sensors in the monitoring system (N) for several values of the signal sample size (n)
In this case, the noncentrality parameter 2 of F distribution was assumed con-
stant, independent of the number N of sensors in the monitoring system . As can be
seen from Figure 2, the dependences have an optimum in the probability of distin-
guishing between objects, and its position depends on the size of the sample n. The
presence of an optimum and its position are apparently due to the following reasons.
On the one hand, with an increase in the number of sensors in the monitoring system,
the difference in signals increases, that is, the “distance” between objects in the pa-
rameter space increases. Let us explain what was said by the following example. Let
the objects have the same area, but a different distribution of them among the sensors.
The value of the parameters of the amplitudes of the signals from the first and second
objects i(1) and i(2) for N =3 is presented in table form 1.
3
At N = 1, the distance in the parameter space between objects A and B is ( iА -
1
3
B 2
i ) =9-9=0 and it’s not possible to distinguish between them. At the same time,
1
3
for N= 3 we get ( iА - iB )2=(3-1)2+(4-5)2+(2-3)2=6, i.e. the difference in parame-
1
ters is significant. On the other hand, with a decrease in the number of sensors in the
monitoring network, the correlation between the signals of objects of various classes
increases. Moreover, the accuracy of parameter estimates can be improved by increas-
ing the accumulation time, i.e., increasing the size of the sample n.
Table 1. The value of the parameters of the amplitudes of the signals from the first and second
objects
Object i 1 2 3
A i А 3 4 2 3
А
i =9
1
B iB 1 5 3 3
B
i =9
1
4 Conclusion
The proposed algorithm in the sense of signal-to-noise ratio for processing spatially
distributed data coming from a monitoring network consisting of several sensors with
the following practically important properties: a) does not depend on a priori un-
known parameters 2 and n ( n 1,2,..., N ) and provides a constant probability of
false alarm at any noise level; b) is invariant to the location of k sensors that recorded
the object and (N-k) sensors that have not fixed the object, among N sensors of the
monitoring network; c) has the highest probability of correct detection, depending on
the average signal-to-noise ratio and for large N p close to potential.
The proposed algorithm for detecting an extended object by the analog signal of
sensors of the monitoring network can be used to identify objects if, for example, as
x i( 2) , i 1, N , a priori estimates of the parameters of the recognized object are used.
The practical significance of the results lies in the development of analog signal
detection algorithms that are resistant to changes in the signal-to-noise ratio in the
communication channels of the sensors of the monitoring network with a monitoring
and control post. Algorithms can be implemented programmatically using various
programming languages and used to automate the process of classifying monitoring
objects at a monitoring and control point.
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