## 1 Introduction  
In recent years, Ultra-Wideband (UWB) radars have attracted a large amount of interest in research due to their wide variety of practical applications and their ability to operate in indoor environments and areas with poor visibility conditions. The most famous applications are the detection, localization and tracking of a moving target because of the interest for rescue, surveillance and security purposes. Some recent works proved that the UWB radar sensor networks can be used for improved accuracy while working within wireless environments with multipath, clutter, line-of-sight (LOS) blockage, excess propagation delays through materials, and other harsh conditions [1; 2]. The basic idea behind UWB technology is to transmit impulses of electro-magnetic wave (EMW). It is not possible to create an ideal impulse in the real world, so UWB technology uses a pulse with a finite amplitude and very short duration, typically \(\sim\)0.5-1.5 ns, as a realistic approximation. This pulse will have a very wide frequency spectrum, hence the name Impulse-Radio UltraWideband (IR-UWB). After the radar transmits a pulse, it starts listening and the returned waveforms are recorded for a fixed interval of time. This interval establishes the effective range of the radar, and the data recorded during one interval is called a \"scan\". Each radar scan will be stored as a column vector of length M, and if N scans are recorded, this will result in a data matrix X of dimension M \(\times\) N called \"Radargram\" as presented in Figure 1.  
The received signal beam includes reflections from both moving and static objects, the noise and direct waves between the transmitting (Tx) and receiving (Rx) antennas. Therefore, the moving-target detection and tracking task is achieved through a number of signal processing phases such as received raw signal preprocessing, background subtraction, target detection, localization and tracking where the output of each step will be the input to the next step as shown in Figure 2. In order to clean our signal and get rid of the noise and cross-talk waves between Tx-Rx, these can be removed or diminished by one suitable bandpass filter as it is explained in [3]. After bandpass-filtering the signal to get rid of the noise, the success in separating the two remaining components of the received signal beam will considerably enhance the accuracy in detection. Different techniques have been developed in this regard, but each one has its drawbacks [4; 5], which will be discussed in the next section. The proposed RPCA algorithm efficiently and robustly recovers the low-rank and sparse parts of a large matrix made up of the sum of these two components where the clutter signal is modeled by the low-rank matrix, while the moving target signal is modeled by the sparse matrix component. However, as stated in the previous section, many RPCA models are implemented using batched data [6; 7; 8], so they require memorization of all samples in order to access every sample in each iteration of the optimization. Storing data first and processing them in a batch manner is not always of great significance, since in most cases we need to record and process frames at the same time. On the other hand, there are a few seminal works on online robust PCA [9; 10; 11; 12]. In [9], an incremental and robust subspace learning method is proposed. The method proposes to integrate the M-estimation into the standard incremental PCA calculation. The author defined an incremental way of solving the RPCA problem, where the PCA model updating is performed directly from the previous eigenvectors and a new observation vector. Thus, each newly coming data point is re-weighted by a pre-defined influence function of its residual to the current estimated subspace. However, the performance is only guaranteed if the updated PCA model at each step of an incremental algorithm is  
Figure 1: Raw data Radargram. Figure 2: Signal processing steps for target detection and tracking. good enough to function as the prototype model.