## 1 Introduction
The main burden is related to the CPU time required to evaluate a single time step which is often much longer than the frequency at which the load changes. The development of powerful system-on-chip and mobile computing units have opened a space for developing several online dynamic load identification algorithms [32; 33; 34]. This paper proposes a dynamic load identification algorithm in the time domain using Kalman filter so that the proposed algorithm can be efficiently implemented for online identification. The worked developed so far is restricted to applications where a priori knowledge about the solution is used to solve the inverse problem online. The main contribution in this work is to try to recover a dynamic load in real time and build the time history of the load as it happens. Kalman filter was first proposed by [PERSON] [35] in 1960. The filter is used in general to evaluate a state vector in the time domain by calculating the minimum-variance unbiased estimation of a predicted value and a measured value. As a recursive algorithm, Kalman filter has the advantages of an iterative algorithm such as a small memory occupation and a reduced number of computations. The algorithm can efficiently and accurately be used to estimate the current state of a system based on the latest measured state. The classical Kalman filter was originally proposed for linear systems. But several algorithms were later developed to adapt Kalman filter for non-linear applications. For example an extended Kalman filter (EKF) was used to linearize the non-linear state-space model [36]. It was shown that using the stator flux and motor speed, the identification based on the EKF is effective for non-linear structures. The untracked Kalman filter was proposed to avoid deriving the Jacoby matrix from the partial derivation of a non-linear system of equations [37; 38]. Compared with the EKF, it is a more accurate non-linear system identification algorithm. The central differential Kalman filter uses the central difference method to linearize a system [39]. The augmented Kalman filter was proposed for dynamic load identification in a combined deterministic-stochastic setting [40; 41]. Meanwhile, the experimental results show that the augmented Kalman filter can be efficiently used for earthquake-related excitation estimates. Furthermore, polluted data or uncertainty in a model are also considered in space with Kalman filter [42, 43]. Although there are some advantages for these identification methods based on Kalman filter in some specific cases, compared to our proposed method, these different methods were only adopted for the discrete systems with few degrees of freedom, without considering the running of the loads in real application, and cannot reconstruct the external load in real time. Different load identification methods were also developed based on the idea of Kalman filter. In order to identify the external excitation acting on a non-linear structural system the extended Kalman filter was combined with the recursive least square method [44] or the unscented Kalman filter is used [38]. The latter algorithm was verified by comparing the results to those found using numerical simulations of a non-linear centralized mass system as well as using experimental results. Moreover, the filter was also used for identifying excitation with a linear time discretization based on the minimum-variance unbiased estimate of the least square method [45]. The proposed algorithm is globally optimal in the minimum-variance unbiased sense. In a different application Kalman filter was used to separate the modal wind load from the measured acceleration response [46]. The modal wind load on a structure were identified by establishing the relevant filter gain matrix and using the noise covariance matrix. Moreover, for excitation identification on a non-linear structure, a method combining the least squares algorithm with adaptive decay factor was proposed [47] where a dual Kalman filter method was developed for identifying excitations.