Observing gravitational waves requires a data analysis strategy, which is in many ways different from conventional astronomical data analysis. There are several reasons why this is so:

- Gravitational wave antennas are essentially omni-directional, with their response better than 50% of the root mean square over 75% of the sky (see Figure 4, right panel, recalling that the rms response is 2/5 of the peak). Hence, data analysis systems will have to carry out all-sky searches for sources.
- Interferometers are typically broadband covering three to four orders of magnitude in frequency. While this is obviously to our advantage, as it helps to track sources whose frequency may change rapidly, it calls for searches to be carried out over a wide range of frequencies.
- In Einstein’s theory, gravitational radiation has two independent states of polarization. Measuring polarization is of fundamental importance (as there are other theories of gravity in which the number of polarization states is more than two and in some theories even dipolar and scalar waves exist [392]) and has astrophysical implications too (for example, gravitational-wave–polarization measurement is one way to resolve the mass-inclination degeneracy of binary systems observed electromagnetically, as discussed in Section 7.1.1). Polarization measurements would be possible with a network of detectors, which means analysis algorithms that work with data from multiple antennas will have to be developed. This should also benefit coincidence analysis and the efficiency of event recognition.
- Unlike typical detection techniques for electromagnetic radiation from astronomical sources, most astrophysical gravitational waves are detected coherently, by following the phase of the radiation, rather than just the energy. That is, the SNR is built up by coherent superposition of many wave cycles emitted by a source. The phase evolution contains more information than the amplitude does and the signal structure is a rich source of the underlying physics. Nevertheless, tracking a signal’s phase means searches will have to be made not only for specific sources but over a huge region of the parameter space for each source, placing severe demands both on the theoretical understanding of the emitted waveforms as well as on the data analysis hardware.
- Finally, gravitational wave detection is computationally intensive. Gravitational wave antennas acquire data continuously for many years at the rate of several megabytes per second. About 1% of this data is signal data; the rest is housekeeping data that monitors the operation of the detectors. The large parameter space mentioned above requires that the signal data be filtered many times for different searches, and this puts big demands on computing hardware and algorithms.

Data analysis for broadband detectors has been strongly developed since the mid 1980s [362, 334, 333]. The field has a regular series of annual Gravitational Wave Data Analysis Workshops; the published proceedings are a good place to find current thinking and challenges. Early coincidence experiments with interferometers [273] and bars [32] provided the first opportunities to apply these techniques. Although the theory is now fairly well understood [207], strategies for implementing data analysis depend on available computer resources, data volumes, astrophysical knowledge, and source modeling, and so are under constant revision.

We will begin with a discussion of the matched filtering algorithm and next use it to estimate the SNRs for binary coalescences in various detectors. After that, we will develop the theory of matched filtering further to work out the computational costs to carry out online searches, that is to search at the same rate as the data is acquired. In the final section, we will use the formalism developed in earlier sections to discuss parameter estimation. The foundations of signal analysis lie in the statistics of making “best estimates” of whether a signal is present in noisy data or not. See the Living Review by Jaranowski and Królak [207] for a discussion of this in the gravitational wave context.

5.1 Matched filtering and optimal signal-to-noise ratio

5.1.1 Optimal filter

5.1.2 Optimal signal-to-noise ratio

5.1.3 Practical applications of matched filtering

5.2 Suboptimal filtering methods

5.3 Measurement of parameters and source reconstruction

5.3.1 Ambiguity function

5.3.2 Metric on the space of waveforms

5.3.3 Covariance matrix

5.3.4 Bayesian inference

5.1.1 Optimal filter

5.1.2 Optimal signal-to-noise ratio

5.1.3 Practical applications of matched filtering

5.2 Suboptimal filtering methods

5.3 Measurement of parameters and source reconstruction

5.3.1 Ambiguity function

5.3.2 Metric on the space of waveforms

5.3.3 Covariance matrix

5.3.4 Bayesian inference

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