## 1 Introduction  
Optical frequency combs (OFCs), a high precision metrological technology based on femtosecond lasers, have been widely applied in absolute distance measurement [1]. The OFCs can simply provide optical frequency calibration for continuous-wave lasers in multi-wavelength interferometric ranging [2; 3; 4; 5]. Otherwise, they have been directly used for time-of-flight (TOF) ranging based on the ultrashort pulse trains or multi-wavelength ranging based on the equally-spaced come-lines [6; 7; 8; 9; 10]. In particular, a dual-comb configuration [11; 12; 13; 14] emerges as a competitive absolute ranging method due to the sub-micrometer precision, high update rate (kHz-level) and dead-zone free operation, showing potential applications in large-scale manufacturing, aerospace engineering, as well as remote sensing. A dual-comb ranging system implements a pair of femtosecond lasers with an offset repetition rate and utilizes asynchronous optical sampling (ASOPS) for absolute ranging. The two lasers are always tightly phase-locked to a common narrow linewidth continuous-wave laser, enabling the transition from micrometer precision TOF measurement to nanometer precision interferometric measurement [11]. However, the unprecedented measurement precision is at the expense of increased complexity of the system setup. For the sake of industrial applications, absolute ranging with a pair of free running femtosecond lasers provides a significantly simplified setup, thus attracting much attention in recent years [15; 16; 17]. Nevertheless, the technical noise, as well as the quantum noises inevitably degrade the distance measurement precision [16; 17]. Several methods have been developed to increase the measurement precision of absolute range finders based on free-running femtosecond lasers. A dual-wavelength mode-locked laser allows two pulse trains with an offset repetition rate to oscillate in a single laser cavity, and the shared cavity effectively avoids the technical noises that are the common mode to the two pulse trains [18]. Quantum-limited timing jitter is another major contribution to measurement uncertainty. Its effect can be significantly reduced by proper engineering of the mode-locking regime of the femtosecond laser sources [16; 19]. Besides the above experimental approaches, measurement precision can also be improved by post-processing. The most straightforward approach is multiple averaging (MA). Sub-micrometer ranging precision is allowed with hundreds times of averaging [15]. However, MA causes a loss of the update rate since it integrates several distance data points into their arithmetic mean. Moreover, MA will be limited when the measurement target is moving. A good remedy is to extract the acquired distance information by using a digital filter instead of MA. Nevertheless, most digital filters need to know certain priori knowledge of input signals, such as the mathematical models of varying signals, the noise intensity of the data acquiring system, as well as the signal bandwidth. Basic singular spectrum analysis (SSA), a data-driven analysis, established in 1986 [20], synthesizing the ingredients of classical time series analysis, multivariate geometry, multivariate statistics, dynamical systems and signal processing [21], was designed for making an extraction of qualitative information from a noisy signal. A relatively short and noisy signal can be decomposed by basic SSA into a sum of components, each having a certain interpretation, e.g., signal or noise. The basic SSA method has been extending its application to multiple fields such as hyperspectral remote sensing [22; 23], GPS data processing [24] and absolute distance measurement of stationary targets [25]. As an analytical method, the basic SSA method needs to be manually analyzed by analysts after the result is obtained, which leads to an experience-oriented category of signals and noises.