## 2 Literature Review
### Comparison with Other Algorithms  
In recent years, several studies have been conducted to compare the performance of subspace system identification with other time domain (TD), frequency domain, (FD) and time frequency domain (TFD). This subsection provides a review of the studies with focus on advantages and drawbacks of the subspace system identification. [PERSON] et al. [86] assessed the performance of SSI-COV and FDD for the modal identification of ambient excited structures. The results indicated that subspace system identification is a more appropriate choice for modal identification of closely spaced modal frequencies, however coupling effect yielded unreliable result for second pairs of the closely spaced natural frequencies. Furthermore, subspace system identification had the drawback of requiring human judgment to determine system order. [PERSON] et al. [87] presented an analytical comparison among eigensystem realization algorithm (ERA), subspace system identification, and auto-regressive moving average (ARMA) techniques for modal identification of ambient-excited structures. It is indicated that subspace system identification has provided the most accurate results for analytical and experimental tests. [PERSON] et al. [88] compared SSI-COV and poly-reference least squares complex frequency (p-LSCF) algorithms using field data obtained from a concrete arch bridge. Both SSI-COV and p-LSCF found to give good results for mode shapes and natural frequency. However, better results were obtained for the daily variation of damping ratio using p-LSCF. [PERSON] et al. [28] used SSI-DATA, multiple-reference natural excitation technique combined with eigensystem realization algorithm (MNExT-ERA) [89], enhanced frequency domain decomposition (EFDD) [90], deterministic-stochastic subspace identification (DSI) [91], observer/Kalman filter identification (OKID)-ERA [92] and general realization algorithm (GRA) [93] for modal identification of a full-scale structure on a shaking table. The mode shapes identified by the subspace system identification algorithm were the most accurate. The measured damping ratio for SSI-DATA and MNeXT-ERA was higher than the ones obtained from EFDD. [PERSON] et al. [94] studied performance of subspace system identification, ERA, ARMA and Ibrahim time-domain (ITD) methods. A more stable result was reported for modal identification in a numerical  
Figure 3: Methodology of the calculating modal parameters from the state-space parameters of subspace system identification algorithm. model using subspace system identification. However, ERA outperforms for field testing. [PERSON] and [PERSON] [95] studied subspace system identification and FDD methods. Resolution problem was reported for FDD with output-only measurements data. [PERSON] et al. [96] compared the modal identification results of SSI-COV and FDD. The obtained results for both of the methods were too similar. [PERSON] et al. [97] implemented modal analysis of the Lupu Bridge in Shanghai using subspace system identification, ERA, PolyMAX, polynomial power spectrum method (PPM), power spectrum z-transform method (PZM), EFDD, frequency spatial domain decomposition (FSDD), and wavelet transform (WT) under ambient excitation. The PolyMAX, PPM, PZM, EFDD, and FSDD are in FD. Subspace system identification and ERA are TD methods used in modal identification of structures whereas WT is in time/frequency-domain. Subspace system identification provided the most accurate results for modal parameters, but computational burden of the algorithm was found to be significant. [PERSON] and [PERSON] [98] conducted a comparative study among ERA applied to RDS, AR and SSI-DATA. All of the methods were robust enough to deal with modal identification in ambient condition, but subspace system identification showed superior performance. Generally, the comparison showed that subspace system identification algorithm outperformed for identification of natural frequency, mode shape, and damping ratio.