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(a) (b) Fig. 7. mesh plot of the reflected power in ambiguous range-Doppler maps: (a) SNR=13dB, (b) SNR=10dB Fig. 8 shows the final merit function for a fixed mode m K = 5 . When no target exists, it’s obvious that the merit function tends to noisy (Fig.8(a)). When a target with an average SNR=10dB is present (the nuisance parameters are assumed known), it’s clear that the noisy merit function has a distinct peak at a particular location in the ambiguous range-Doppler map (Fig.8(b)). The corresponding target final state can be extracted by thresholding the resultant merit function. 6.1 Selection of Threshold In order to calculate the threshold, we first have to define the probability of false alarm P fa . In our situation, Pfa is defined as the probability of detecting a false track in the absence of target (i.e., under the hypothesis H 0 ). This is equal to the probability of the maximum noise merit function exceeding the threshold VT P fa = Pr ( max Γ K ( K , mK ) > T xK, mK x V ) (54) where x K ∈{noise states} . Given the desired P fa , the threshold is determined as the (1− Pfa )-quantile of the test statistic, i.e., max x , ( , ) given in K m Γ K K x K mK (54). Unfortunately, the statistical distribution of the test statistic is rather complicated [11], sometimes even infeasible. This mainly because 1) the max operator in the DP recursion brings in nontrivial nonlinearities and non-Gaussianity; 2) the samples of the test statistic are 22
actually correlated since the backward search process in the DP recursion may end with a common previous location xk −1 for two different locations at frame k . The threshold is, hence, evaluated via computer simulation. (a) (b) Fig. 8. mesh plot of the merit function ( K = 6) for a fixed mode m K = 5 : (a) no target exists (b) a target with average SNR=10dB exists 6.2 Performances Evaluation We now move to the analysis of the detection and tracking performance of the proposed algorithm. As in [7], we define the following performance measures for evaluating the proposed TBD algorithms. Definition 1 The probability of target detection P d is defined as the probability of the maximum final merit function exceeds the threshold VT and meanwhile, the corresponding retrieved cell, say, ( iˆ , ˆ K l K ), is within ε r cells in range and ε d cells in Doppler from the actual location, ( iK , l K ), and the ambiguity number estimate m ˆ K is equal to the true one. Hence Pd = Pr ⎛( max K( K, mK) ⎞ ⎜ Γ x > V T , ) ∪E ⎟ ⎝ xK m d (55) K ⎠ where the event E d is expressed as abs( iˆ K −iK) ≤ ε r, abs( lˆ K −lK) ≤ ε d , mˆ K = m K . (56) 23
Page 2 and 3: The 3 rd VACPS Research Workshop Pr
Page 4 and 5: Organizing Committee Victorian Asso
Page 6 and 7: Preface On the occasion of the publ
Page 8 and 9: Paper as a low-cost base material f
Page 10 and 11: Acknowledgements We gratefully ackn
Page 13 and 14: Career planning and Job Interview i
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Page 18 and 19: Track-Before-Detect Procedures for
Page 20 and 21: 3. Dynamic model for approaching ta
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Page 42 and 43: Demonstration and Performance Analy
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conclude that the hydrophobic PHB c
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