TY - JOUR
T1 - Two Strategies in Transient Change Detection
AU - Egea-Roca, Daniel
AU - Guepie, Blaise Kevin
AU - Lopez-Salcedo, Jose A.
AU - Seco-Granados, Gonzalo
AU - Nikiforov, Igor V.
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2022/3/9
Y1 - 2022/3/9
N2 - The paper addresses the transient change detection (TCD) problem, assuming that the duration of change is finite. The TCD criterion minimizes the worst-case probability of missed detection among all tests with a prescribed worst-case probability of false alarm. We study the fixed sample size (FSS) test as a solution to the TCD problem. First, the operating characteristics of the FSS test have been established for arbitrary pre- and post-change distributions. Next, a numerical method of the sample (block) size optimization has been considered for three particular log-likelihood ratio distributions, i.e., Gaussian, $\chi ^{2}$ and exponential. Moreover, simple asymptotic equations for the optimal operating characteristics and block size have been proposed in the Gaussian case. Numerical results are provided to confirm the theoretical findings for the above-mentioned distributions. The accuracy and sharpness of the asymptotic analytical equation is analyzed in the Gaussian case. Finally, the FSS test is compared to the finite moving average (FMA) test obtained by optimizing the CUSUM-type test with respect to the TCD optimality criterion for the above-mentioned distributions. The application of the FSS and FMA tests to the radio-navigation integrity monitoring is also considered.
AB - The paper addresses the transient change detection (TCD) problem, assuming that the duration of change is finite. The TCD criterion minimizes the worst-case probability of missed detection among all tests with a prescribed worst-case probability of false alarm. We study the fixed sample size (FSS) test as a solution to the TCD problem. First, the operating characteristics of the FSS test have been established for arbitrary pre- and post-change distributions. Next, a numerical method of the sample (block) size optimization has been considered for three particular log-likelihood ratio distributions, i.e., Gaussian, $\chi ^{2}$ and exponential. Moreover, simple asymptotic equations for the optimal operating characteristics and block size have been proposed in the Gaussian case. Numerical results are provided to confirm the theoretical findings for the above-mentioned distributions. The accuracy and sharpness of the asymptotic analytical equation is analyzed in the Gaussian case. Finally, the FSS test is compared to the finite moving average (FMA) test obtained by optimizing the CUSUM-type test with respect to the TCD optimality criterion for the above-mentioned distributions. The application of the FSS and FMA tests to the radio-navigation integrity monitoring is also considered.
KW - Neyman-Pearson test
KW - Transient change detection
KW - finite moving average
KW - fixed sample size test
KW - hypothesis testing
UR - http://www.scopus.com/inward/record.url?scp=85126276440&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/beac2d1b-5288-38f5-8662-5448a3f11d36/
U2 - 10.1109/tsp.2022.3158008
DO - 10.1109/tsp.2022.3158008
M3 - Article
VL - 70
SP - 1418
EP - 1433
ER -