scholarly journals Simplifying the Performance Analysis of the SPRT for GPS Acquisition

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Niamh O'Mahony ◽  
Gérard Lachapelle ◽  
Colin C. Murphy
Keyword(s):  
Performance Analysis ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Noise Power ◽  
Receiver Design ◽  
Probability Ratio ◽  
Acquisition Strategies ◽  
Noncoherent Integration ◽  
Sequential Probability ◽  
Theoretical Performance

A new approximation for the distribution of the probability ratio in a sequential probability ratio test (SPRT) using noncoherent integration across a full code period is presented. The new approximation is valid for the carrier-to-noise power ratios (C/N0) typically encountered in GPS acquisition (20 dB-Hz ≤ C/N0 ≤ 50 dB-Hz), and it allows accurate theoretical performance analysis of the SPRT to be carried out for signals in this C/N0 range, eliminating the need for lengthy simulations for each scenario under investigation. Thus, the SPRT performance can be readily compared to that of other acquisition strategies for receiver design. Previous approximations in the literature are not valid in the range 20 dB-Hz ≤ C/N0 ≤ 50 dB-Hz.

scholarly journals The VPRT: A Sequential Testing Procedure Dominating the SPRT

1993 ◽  
Vol 9 (3) ◽  
pp. 431-450 ◽  
Author(s):  
Noel Cressie ◽  
Peter B. Morgan
Keyword(s):  
Sample Size ◽  
Decision Problem ◽  
Sequential Analysis ◽  
Testing Procedure ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Sequential Decision ◽  
Probability Ratio ◽  
Sampling Cost ◽  
Sequential Probability

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

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