Sequential Detection under Correlated Observations using Recursive Method

Abstract

Sequential analysis has been used in many cases when the decision is required to be made 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, the assumption is commonly violated in realistic scenario, such as in radar. 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 computational complexity, which involves using recursive matrix inverse to 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 scenarios. We evaluate the performance of the proposed (recursive) sequential detector 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 results comparable to those of the two conventional detectors. The recursive approach has reduced the computational complexity for matrix multiplication to O(n2) from O(n3) and has rendered the calculation of matrix determinants unnecessary. Therefore, by having a better probability 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 radar and cognitive radio.

Keywords

• covariance matrix
• matrix determinant
• matrix inverse
• neyman-pearson
• quadrature detector
• sequential analysis
• sequential detector