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Identification of Spurious Events

The non-stationary and non-Gaussian noise in the detector leads to a large number of spurious detections, where by a detection we mean that the Signal-to-Noise Ratio (SNR) maximized over the template bank has crossed a certain preset threshold. In order to differentiate between a false alarm and a `correct' detection, we must make use of several independent discrimination techniques. The $r^2$ test is one such technique and is described in the GRASP manual in section [*].

It is also useful to investigate whether the outputs of the templates in the template bank can be used collectively as a discriminator between a false alarm and a correct detection. This would be different from a discriminator constructed using only the template which maximises the correlation between the detector output and the template or in other words the SNR. Such a technique might be a robust indicator of the presence of a chirp signal in the detector output.

One possibility is to measure the times-of-arrival($t_a$) at each template. The time-of-arrival at each template is the time when the correlated output reaches a maximum in that template. This maximization is carried out after the phase parameter is maximised over. The basic expectation here is that the $t_a$ measured at templates in the neighbourhood of the template which maximises the SNR will follow a certain pattern if the signal is actually present in the detector output. If the distribution of the $t_a$ (as a function of the template number) for a spurious detection can be shown to be very different from the case when a true signal is actually present, then this can be quantified and used as a discriminator.

In order to test this idea, experiments were carried out. Chirp signals were artificially injected into the 40-m data and filtered through the bank of templates. High signal to noise ratio events were identified. Some of these detections correctly corresponded with the injected signal. In particular, for these events the estimated values of the masses and the time of arrival tallied well with those of the actual signal injected.

In Figure [*] we plot the measured value of the times-of-arrival at each template, contrasting the case where a `real' chirp signal is present (black points) and where no signal is injected but there is a large SNR observed (red points). The black points are obtained for segment number 2 (in the 14nov94.1 data) where by convention segment number 0 is the first segment of data. (Note: The length of the data segments were taken to be 262144 and the parameters PRESAFETY and POSTSAFETY were set to be 16384 and 49152 respectively. Three minutes of the data was skipped at the beginning of each locked stretch of the data.) The maximum signal to noise ratio is obtained for template number 383 with a SNR of 13.62.

Figure: Variation of time of arrival across template bank.
\begin{figure}\index{colorpage}
\begin{center}
\epsfig{file=Figures/timesofarrival.eps,angle=0,width=4.5in}\end{center}\end{figure}

Here again we use the index 0 to denote the first template. The masses corresponding to the template number 383 tally well with the those of the injected signal (1.4,1.4 solar mass binary). We observe a well-defined pattern for the $t_a$ across the template bank. The templates are roughly arranged in the order of decreasing masses and consequently of larger chirp times. The red points are obtained for segment 33. The maximum SNR obtained in this case is 8.48. In this segment no chirp signal had been injected. Again we plot the $t_a$ obtained at various templates. The behaviour is remarkably similar to the case where there is actually a signal present in the detector output. The arrows point to the template which maximises the correlation.

A possible explanation for this phenomenon is as follows. Consider first the case where a signal has been injected into the data (the black points on the graph). In this case the template and signal achieve a good correlation if the large amplitudes parts of their waveforms are well aligned. In other words the template matches well with the injected signal if the time of coalescence is the same for both the template and the injected signal. The sum of the chirp times $t_{chirp} = \tau_0+\tau_1+\tau_{1.5}+\tau_2$ is almost equal to the length of the chirp waveform and the time of coalescence is the sum, $t_C = t_a + t_{chirp}$. The templates are evenly placed in the $\tau_0,\tau_1$ parameter space and consequently the total chirp time increases almost linearly with the template number. Since $t_C$ is being held constant, $t_a$ must decrease linearly with the template number.

Consider now the case when there is no injected signal. Nevertheless, a large SNR (8.48) has been obtained. We assume that the high SNR is caused by a short burst of noise in the data. The correlation between any template and a noise burst will be maximised for a time-of-arrival for which the last few cycles of the template coincide with the noise burst. Now since the the chirp times increase roughly linearly as the template number increases we again have the time of arrival decreasing linearly. Thus, we conclude that it is difficult to distinguish between a correct detection and a false alarm using this test.

Another possible discriminator could be the variation of the maximum correlation (maximized over the phase and the arrival times) as a function of template number. In Figure [*] we plot the maximum SNR obtained for a template against the template number. The black curve represents segment number 2 corresponding to a true detection and the red curve represents segment number 33 corresponding to a spurious detection. Again the variation of the SNR with template number in the two cases does not help in distinguishing a true detection from a false alarm.

Figure: Variation of SNR across the template bank
\begin{figure}\index{colorpage}
\begin{center}
\epsfig{file=Figures/snracrosstemplates.eps,angle=0,width=4.5in}\end{center}\end{figure}


next up previous contents
Next: GRASP Routines: Supernovae and Up: Binary Inspiral Search on Previous: Examples   Contents
Bruce Allen 2000-11-19