Synthesis of a radar recognition algorithm with ability to meet reliability of decisions

nd the recognition problem ( L 2 ) needs to 
be researched further [2, 3, 5, 6, 10, 13]. Besides, the observation cycle cannot be too 
long; thus, that measure is also unfeasible. In that case, a common solution in most 
researches is “if the observation cycle has reaches the limited value but no final result 
returned by the sequential algorithm, then the unsatisfied quality acceptance are 
informed and the regular one-step decision rule is applied”. 
 On purpose “guarantee reliability of decisions”, this paper focuses on: 
 - Synthesizing a sequential (multi-step) algorithm of radar recognition and 
decision-making solution if the observation cycle is critical. 
 - Analyzing and evaluating the algorithm quality. 
2. Algorithm synthesis 
 In the radar target recognition, the observation cycle extension is equivalent to the 
increase in the number of contacts with targets. Call ξm to be RP at the cycle “ m ” 
 (n)
( m 1,2...), then after the n-cycle, there are a set of “n ” RPs ξ  ξ1 ,ξ2 ,,ξ n . 
Generally, due to the large observation cycle compared with the signal fluctuation, the 
 ()n
RP can be considered independently and the PDF of the set ξ is given by [7-9, 11]: 
 n
 (n ) ( n ) ( n ) (1)
 pl ξ p ξ H l  p l() ξ m , (2) 
 m 1
 (1)
where pl(ξ m ) p ( ξ m H l ); l 1  L : CPDF of the H l -class of targets at the 
m-observation cycle. 
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 Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
 The fundamental of the multi-steps decision algorithm is to divide the whole 
 ()n n *
dynamic of ξ into “ L 1” separated regions [] ξ i ; i 0  L and make decision 
in [2, 6, 13]: 
 ()()*n n *(n ) *( n )
 “With i 0  L , if ξ [] ξ i then HH i ”. (3) 
 *(n ) *(n )
in which H : decision at the n-cycle; Hk() l ; k , l 1  L : decision “targets belonging to 
 *(n ) *( n 1)
the class H k() l ”; HH0 : decision “prolongs the observation cycle”. 
 *(n ) *(n )
 Apart from the decision H0 , the reliability of decisions H k ; k 1  L is the 
 *(n )
posteriori probability PHH k/ k  which satisfy the condition: 
 ()n
 *(n )PPk k/ k *
 PHHP k/ k M k ; k 1  L , (4) 
 ()n
  PPl k/ l
 l 1
 * *(n ) (n ) *( n )
where Pk ; k 1  L : the required reliability of the decision H k ; PPHHk/ l k/ l ; 
k, l 1  L : conditional decision probability at the “n ”-cycle. 
2.1. Multi-steps recognition algorithm 
 n
 Suppose that the set ξ is obtained after “n ” observation cycles. At this time, 
the posteriori probability of target classes is given by the formula: 
 P p()()n ξ n 
 n k k 
 PH / ξ ; l 1  L . (5) 
 l  L
 ()()n n 
  Pl p l ξ 
 l 1
 *(n )
 Thus, the decision selection in Hl ; l 1  L can be carried out by the posteriori 
probability maximum: 
 “If k arg max P H / ξ()()()n arg max P p n ξ n then *(n ) *( n ) ”. (6) 
 l  l l  HH k
 l 1  L l 1  L
 Next, check the reliability of the decision if it is satisfactory then this decision is 
final and vice versa switch to the adjacent cycle. Hence, the multi-steps decision 
algorithm can be described as below: 
“If k arg max P H / ξ()n then HH*(n ) *( n ) when ()*n and 
 l  k PHP k/ ξ  k
 l 1  L
 HH*(n ) *( n ) when PHP/ ξ()*n ”. (7) 
 0 k  k
 The recognition program of the algorithm (7) comprises L processing channels 
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Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
corresponding to L target classes. A channel is responsible for a target class to calculate 
the posteriori probability through the expression (5). The final decision is based on the 
maximum of all the channels. 
2.2. Decision-making solution in critical cycle 
 If the observation cycle reaches the critical point in the time extension ( n Nmax ) 
while the algorithm (7) has not returned a decision, then the level of the classification 
detail should be reduced. Accordingly, a decision 
 *(NNNNmax ) *( max ) *( max ) *( max ) *( N max )
“ H Hk [ Hl ; l [ l k ]] - targets in a group of classes [lk  ] ” is 
made instead of seeking a target class based on the maximum of a processing channel 
 *(NNmax ) *( max ) *(Nmax )
HH k . The elements in the group []lk have to qualify the reliability 
 *(Nmax ) *(Nmax )
with the minimum number of classes Lk . Here, the reliability of decision Hk is 
a sum of posteriori probabilities: 
 
 ()()NNmax max . (8) 
 PHPH l// ξ   l ξ 
 l [][] l*(NNmax ) l l *( max )
 k   k
 Considering the initial reliability of single decisions, we give a condition for the 
group decision: 
 P*(NNNmax ) P H/ ξ ( max ) max P** ; l [ l *( max ) ] P . (9) 
 k  l  l k   k
 l [] l*(Nmax )
 k
 *(Nmax )
 The determination of classes in group decisions []lk according to (9) is as the 
following process: 
 (N )
 1) k arg max P H / ξ max ; ()*n ; 
 l   PHP k/ ξ  k
 l 1L
 *( Nmax ) *( Nmax ) *(Nmax )
 2) H k  [H k ]; Put “k ” into the group []lk ; 
 3) l arg max P H / ξ()Nmax ; 
 i 
 i [] l*(Nmax )
 k
 i 1  L
 *(Nmax )
 4) Add the class “l ” into the group []lk ; 
 5) If P H/ ξ(NNmax ) max P* ; l [ l *( max ) ] then jump backward into 
  l  l k 
 l [] l*(Nmax )
 k
the step (3); 
 *(NNNmax ) *( max ) *( max )
 6) Hk [ Hl ; l [ l k ]] . 
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 Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
 Hence, the multi-steps recognition algorithm with decision-making solution in 
critical cycle has a following form: 
 “With k arg max P H / ξ()n : (10) 
 l 
 l 1  M
 If ()*n then HH*(n ) *( n ) (single decision); 
 PHP k/ ξ  k k
 *(NNN ) *( ) *( )
 If ()*n then H*(n ) Hmax [ H max ; l [ l max ]] when n N 
 PHP k/ ξ  k k l  k max
 *(n ) *( n )
(group decision)” or HH 0 when n Nmax ”. 
 *(N )
Here, ()n is calculated by (5) and (2); the group term []l max is defined by 
 PH l / ξ  k
the above 6-steps process. 
 In order to implement the algorithm (10) in classic radar target recognition 
systems with the one-step decision rule (1), some function blocks should be added: 
 - A processing channel needs a storage of observation cycles and a calculator of 
conditional probability density function - formula (2); 
 - A calculator of posteriori probability for target classes - formula (5); 
 - A decision-making element - algorithm (10). 
3. Algorithm analysis and evaluation 
3.1. Quality analysis of single decisions 
 If omitting the observation time extension, then the single decision making in (10) 
 ()n
complies the criterion “maximum posteriori probability for the set ξ ”: 
“If k arg max P H / ξ()()()n arg max P p n ξ n then *(n ) *( n ) ”. (11.a) 
 l  l l  HH k
 l 1  L l 1  L 
 Therefore, this is optimized through “minimum sum of non-conditional 
probability”: 
 LLL
 (n ) *( n ) *( n ) ( n )
 FPHHPHPHHPPVDK  lk,  l kl /  lkl/ min . 
 l k l k l k
 k, l 1 k , l 1 k , l 1
 (n ) *( n )
where PPHHk/ l k/ l  : decision probability of target class “k ” at the observation 
cycle “ n ” in the existence of target class “l ”. 
 If “ n 1” then (11.a) is not different from the one-step algorithm along with the 
 ()n
criterion (1.a). Obviously, if “n ” increases then the sum of false probabilities FVDK 
decreases. The reason is that the amount of information for the recognition is 
 ()n
accumulated in observation cycles (the algorithm employs CPDF of all the sets ξ ). 
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Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
 1
 When the priori probability is obscure, set P ; l 1  L and (11.a) becomes: 
 l L
 n 
 “If k argmax p(n ) ξ ( n ) argmax p (1) () ξ then HH*(n ) *( n ) ”. (11.b) 
 l   l m  k
 l 1  L l 1  L m 1 
 This is the criterion “maximum likelihood function”; the optimization means 
“minimum average of false conditional recognition probability”: 
 LL
 (n )1 *( n ) 1 ( n )
 FPHHPTB  k/ l  k/ l min . 
 LLl k l k
 k, l 1 k , l 1
 If “ n 1” then (11.b) is not different from (1.b). Apparently, if “ n ” increases then 
the sum of false probabilities F ()n decreases. Here, the information accumulation over 
 TB 
observation cycles is explained as follows: 
 Suppose that at the first cycle ( n 1), priori probabilities are equivalently 
 (1) 1
considered: P Hl P l ; i 1  L , in the next cycles ( n 2 ) the priori 
 n 1 L
probabilities are taken to be the posteriori probabilities in the previous cycles 
PHPPH ()n / ξ ; therefore, we have a formula: 
 ln l l n 1
 n
 (1)
 (n ) (1) (1) p ()ξ
 P pξn p ξ  l m
 l l n i m m 1
 PH l/ ξ n LL . 
  n L 
 P(n ) p (1)ξm 1 P ( m ) p (1) ξ P ( m ) p (1) ξ
 c c n  c c m   c c m 
 c 1 c 1 m 1 c 1 
 Thus, the algorithm (11.b) is equivalent to: 
 (n ) (1) *(n ) *( n )
 “If k argmax P Hl /ξ n argmax P l p l ξ n  then HH k ”. (12) 
 l 1  L l 1  L
 It can be seen that (12) is the one-step algorithm with the criterion “maximum 
posteriori probability - for ξn received at the decision moment”. Here, the information 
acquisition at the previous cycles is presented by the posteriori probability PH l/ ξ n 1 
 ()n
and applied for the priori probabilities Pl for the decision-making in the next cycle. 
3.2. Evaluation of required reliability 
3.2.1. For single decisions 
 *(n ) *( n )
 Assume that at the n-cycle, the system makes the decision HH k ; 
 *
k 1  M . According to the algorithm (2), this is equivalent to ξ()()n ξ n . If that, 
 k
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 Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
from (10), we have: 
 P p()n ξ n L
 n k k * ()*()n n n n
 PHP/ ξ ; P p ξ P P p ξ . (13) 
 k  L k k k k l l 
 ()n n l 1
  Pl p l ξ 
 l 1
 Take the integration for the two sides in the range ()*n and 
 [] ξ k
substitute p()()n ξ n d ξ () n P H *() n/ H P () n into that, we have: 
  l k l k/ l
 *
 ξ()n 
 k
 ()n
 *(n )PPk k/ k *
 PHHP k/ k M k . (14) 
 ()n
  PPl k/ l
 l 1
 *(n )
 Thus, the condition (4) is always satisfied with each decision H k ; k 1  M . 
3.2.2. For group decisions 
 Suppose that at the cycle n Nmax , the system makes a group decision 
 *(NN ) *( ) * *(N )
HHmax max . Set ξ()Nmax to be a decision region H max , according to (10), 
 k k k
along with the process of class determination in a group decision we have: 
 *
 If ξ()()NNmax ξ max then: 
 k
 ()()NNmax max 
 Pl p l ξ 
 P H/ ξ(NNmax ) max P** ; l [ l *( max ) ] P 
  l   L l k   k
 *(NN ) *( )
 l []] lmax l l max ()()NNmax max
 k  k  Pm p m ξ 
 m 1
 L
 P p()()()()NNNNmax ξ max P* P p max ξ max . (15) 
 l l k  m m 
 l [] l*(Nmax ) m 1
 k
 *
 Take the integration of the two sides in a range ξ()Nmax , transform the 
 k
 * *(N )
expression and replace ξ()()NNmax ξ max to be H max , we have: 
 k k
 
 *(NNNmax ) *( max )** *( max ) 
 P Hl/ Hk  P  H l / H k  P k max P l ; l [ l k ]
 l [][] l*(NNmax ) l l *( max ) 
 k  k   
 Thus, the reliability of a group decision is not smaller than the required value of 
the posteriori probability all over the classes in the group. 
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Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
4. Conclusion 
 In this paper, a radar recognition algorithm with the ability to meet the reliability 
of decisions has been synthesized. The analysis results show that: 
 - Compared with conventional multi-step algorithms, the synthesized algorithm 
allows group decision-making to ensure the reliability of decisions when the 
observation time cannot prolong. However, if the observation time is not limited, then 
the conventional multi-step algorithm is capable of quality assurance without reducing 
the level of the classification detail. 
 - Compared with one-step algorithms, the synthesized algorithm not only raises 
the recognition quality in general but also allows guaranteeing the reliability of 
decisions. The solution for this is the observation time extension or detailed 
classification reduction. 
 - The algorithm is applicable for classic recognition systems by adding a small 
number of hardware resources. 
References 
1. Blacknell D., Griffiths H. (2013). Radar Automatic Target Recognition and Non-
 Cooperative Target Recognition. The Institution of Engineering and Technology, London. 
2. De, S. K. and Baron, M. (2012). Step-up and Step-down Methods for Testing Multiple 
 Hypotheses in Sequential Experiments. Journal of Statistical Planning and Inference. 
3. Massimo Franceschetti, Stefano Marano, Vincenzo Matta, Chernoff (2017). Test for Strong-
 or-Weak Radar Models. IEEE Transactions on signal processing. 
4. Shirman Y. D. (2002). Computer Simulation of Aerial Target Radar Scattering, 
 Recognition. Artech House. 
5. Tartakovsky A., Li X., Yaralov G. (2003). Sequential detection of targets in multichannel 
 systems. Information Theory, IEEE Transactions. 
6. Tartakovsky, A., Nikiforov, I., Basseville, M. (2014). Sequential Analysis: Hypothesis 
 Testing and Changepoint Detection. Chapman and Hall/CRC, Boca Raton, FL, USA. 
7. Гейстер С. Р. (2000). Адаптивное обнаружение – распознавание с селекцией помех по 
 спектральным портретам. Военная академия РБ, Минск. 
8. Гейстер С. Р., Нгуен Н. Х. (2002). Решающее правило радиолокационного 
 распознавания со структурно параметрической адаптацией. Электромагнитные 
 волны и электронные системы. Т. 7, № 6. 
9. Горелик А. Л., Барабаш Ю. Л., Кривошеев О. В., Эпштейн С. С. (1990). Селекция и 
 распознавание на основе локационной информации. Радио и связь. 
10. Неуймин А. С., Жук С. Я. (2014). Последовательное обнаружение траектории цели с 
 использованием решающих статистик отметок. Известия вузов. Радиоэлектроника. 
 Т. 57, № 6. 
11. Охрименко А. Е. (1983). Основы радиолокации и РЭБ. Воениздат, Минск. 
94 
 Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
12. Перов А. И. (2003). Статистическая теория радиотехнических систем. 
 Радиотехника. 
13. Фу К. (1971). Последовательные методы в распознавании образов и обучении машин, 
 Наука. 
 TỔNG HỢP THUẬT TOÁN NHẬN DẠNG MỤC TIÊU RA ĐA 
 VỚI KHẢ NĂNG ĐÁP ỨNG ĐỘ TIN CẬY CỦA CÁC QUYẾT ĐỊNH 
 Tóm tắt: Bài báo trình bày phương án tổng hợp thuật toán nhận dạng mục tiêu ra đa với 
khả năng đáp ứng độ tin cậy của các quyết định. Thuật toán được xây dựng trên cơ sở lý thuyết 
phân tích lần lượt kết hợp với việc thay đổi mức chi tiết phân lớp một cách linh hoạt khi không 
thể kéo dài thời gian quan sát. So với các thuật toán nhận dạng một bước đã có, thuật toán đề 
xuất cho phép đảm bảo xác suất hậu nghiệm của các quyết định đưa ra luôn lớn hơn giá trị cho 
trước. Thuật toán này có thể áp dụng trong những hệ thống nhận dạng mục tiêu ra đa. 
 Từ khóa: Nhận dạng mục tiêu ra đa; phân tích lần lượt; ra quyết định nhiều bước. 
 Received: 20/5/2019; Revised: 21/11/2019; Accepted for publication: 22/11/2019 
  
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