Truncated Sequential Non-Parametric Hypothesis Testing Based on Random Distortion Testing

Khanduri, Prashant; Pastor, Dominique; Sharma, Vinod; Varshney, Pramod K.

doi:10.1109/tsp.2019.2923140

“…However, there are three reasons why this is not the case. First, this study assumes that truncation such as in [30], [31] is not conducted, so the maximum sample number max(𝑁 𝑠 ) is not known in advance. Secondly, the amount of memory space 𝑀 to store the inverse matrices will depend on the random max(𝑁 𝑠 ).…”

Section: B Recursive Sequential Detector (Proposed Method)mentioning

confidence: 99%

Sequential Detection under Correlated Observations using Recursive Method

Suratman,

Istiqomah,

Rahmawati

2024

Jurnal Teknik Elektro

0

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Sequential analysis has been used in many cases when the decision is supposed to be taken quickly such as for signal detection in statistical signal processing, namely sequential detector. For identical error probabilities, a sequential detector needs a smaller average sample number (ASN) than its counterpart of a fixed sample number quadrature detector based on Neyman-Pearson criteria. The optimum sequential detector was derived based on the assumption that the observations are uncorrelated (independent). However, in realistic scenario, such as in radar, the assumption is commonly violated. Using a sequential detector under correlated observations is sub-optimal and it poses a problem. It demands a high computational complexity, since it needs to recalculate the inverse and the determinant of the signal covariance matrix for each new sample taken. This paper presents a technique for reducing the computational complexity, which involves using recursive matrix inverse to subsequently calculate conditional probability density functions (pdf). This eliminates the need to recalculate the inverse and determinant, leading to a more reasonable solution in real-world scenario. We evaluate the performance of the proposed (recursive) sequential detector by using Monte-Carlo simulations and we use the conventional and non-recursive sequential detectors for comparisons. The results show that the recursive sequential detector has equal probabilities of false alarm and miss-detection with the conventional sequential detector and performs better than the non-recursive sequential detector. In terms of ASN, it maintains comparable results to the two conventional detectors. The recursive approach has reduced the computational complexity for matrix multiplication to from and it also has rendered the calculation of matrix determinant to be unnecessary. Therefore, by having better probabilities of error and reduced computational complexities under correlated observations, the proposed recursive sequential detector may become a viable alternative to obtain a more agile detection system as required in future applications, such as in radar and cognitive radio.

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“…Injecting these inequalities into (23) and (21) and using δ k = 0 for all k ∈ N for Gaussian noise yields the bounds:…”

Section: Analysis: Pfa and Pmdmentioning

confidence: 99%

“…The theoretical analysis, the control over the error probabilities and the notion of buffer were not present in the past works [20]. A preliminary version without any analysis was presented in [1] and a truncated version of SeqRDT, T-SeqRDT, has been developed in [21], [22], where the sequential test is forced to stop if a decision is not made until a certain time. Beyond biomedical signal processing applications [20], the proposed theoretical framework can be of interest in many real world applications, including communications, radar, fault-detection and structural health monitoring.…”

Section: Introductionmentioning

confidence: 99%

Sequential Random Distortion Testing of Non-Stationary Processes

Khanduri

¹

,

Pastor

²

,

Sharma

³

et al. 2019

IEEE Trans. Signal Process.

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In this work, we propose a non-parametric sequential hypothesis test based on random distortion testing (RDT). RDT addresses the problem of testing whether or not a random signal, Ξ, observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, τ , from a fixed model, ξ0. The test is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. The need to control the probabilities of false alarm (PFA) and missed detection (PMD), while reducing the number of samples required to make a decision, leads to a novel sequential algorithm, SeqRDT. We show that under mild assumptions on the signal, SeqRDT follows the properties desired by a sequential test. We introduce the concept of a buffer and derive bounds on PFA and PMD, from which we choose the buffer size. Simulations show that SeqRDT leads to faster decisionmaking on an average compared to its fixed-sample-size (FSS) counterpart, BlockRDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).

show abstract

“…where a 1 a 2 = min(a 1 , a 2 ) for a 1 , a 2 ∈ R. (23) and (21) and using δ k = 0 for all k ∈ N for Gaussian noise yields the bounds:…”

Section: Analysis: Pfa and Pmdmentioning

confidence: 99%

On Sequential Random Distortion Testing of Non-Stationary Processes

Khanduri

¹

,

Pastor

²

,

Sharma³

et al. 2018

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this work, we propose a non-parametric sequential hypothesis test based on random distortion testing (RDT). RDT addresses the problem of testing whether or not a random signal, Ξ, observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, τ , from a fixed model, ξ0. The test is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. The need to control the probabilities of false alarm (PFA) and missed detection (PMD), while reducing the number of samples required to make a decision, leads to a novel sequential algorithm, SeqRDT. We show that under mild assumptions on the signal, SeqRDT follows the properties desired by a sequential test. We introduce the concept of a buffer and derive bounds on PFA and PMD, from which we choose the buffer size. Simulations show that SeqRDT leads to faster decisionmaking on an average compared to its fixed-sample-size (FSS) counterpart, BlockRDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).

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Truncated Sequential Non-Parametric Hypothesis Testing Based on Random Distortion Testing

Cited by 7 publications

References 32 publications

Sequential Detection under Correlated Observations using Recursive Method

Sequential Detection under Correlated Observations using Recursive Method

Sequential Random Distortion Testing of Non-Stationary Processes

On Sequential Random Distortion Testing of Non-Stationary Processes

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