## 1 Introduction  
In many industry processes, time delay is an unavoidable behavior in their dynamical models. For example, in a chemical industry, analyzers need a certain amount of time to process an analysis, which is used as a part of the control loop [1]. Analyzing and designing a controller for a system with time delays depend on an effective dynamical system model. System identification is an effective way to build mathematical models of dynamical systems from observed input-output data. Conventional identification methods, such as the least squares methods [2], the stochastic gradient methods [3] and the maximum likelihood estimation methods [4], usually require a large number of sampled data and that the model structures, including time delays, are _a priori_ known [5,6]. However, this is not the case in many situations in practice for which the time delays and systems orders have to be estimated together with the parameters. Most of the process industries, such as distillation columns, heat exchangers and reactors, can be modeled as multiple input multiple output (MIMO) or multiple input single output (MISO) systems with long time delays [1]. For a multiple input single output finite impulse response (MISO-FIR) system with many inputs and unknown input time delays, the parameterized model contains a large number of parameters, requiring a great number of observations and a heavy computational burden for identification. Furthermore, the measuring cost is an issue. Especially for chemical processes, it will take a long time to get enough data because of the long analysis time. Therefore, it is a challenging work to find new methods to identify the time delays and parameters of multivariable systems with less computational burden using a small number of sampled data. System models of practical interest, especially the control-oriented models, often require low order, which implies that the systems contain only a few non-zero parameters. Because the time delays and orders are unknown, we can parameterize such an MISO-FIR system by a high-dimensional parameter vector, with only a few non-zero elements. These systems can be termed as sparse systems. On the other hand, a sparse MISO-FIR system contains a long impulse response, but only a few terms are non-zeros. The sparse systems are widely discussed in many fields [7, 8, 9, 10, 11]. For such sparse systems, the identification objective is to estimate the sparse parameter vector and to read the time delays and orders from the structure of the estimated parameter vector. In this paper, we consider the identification of the sparse MISO-FIR systems by using the compressed sensing (CS) recovery theory [12, 13, 14, 15]. CS has been widely applied in signal processing and communication systems, which enables the recovery of an unknown vector from a set of measurements under the assumption that the signal is sparse and certain conditions on the measurement matrices [16, 17, 18, 19]. The identification of a sparse system can be viewed as a CS recovery problem. The sparse recovery problem can be solved by the \(l_{1}\)-norm convex relaxation. However, the \(l_{1}\) regularization schemes are always complex, requiring heavy computational burdens [20, 21, 22]. The greedy methods have speed advantages and are easily implemented. In this literature, a block orthogonal matching pursuit (BOMP) algorithm has been applied to identify the determined linear time invariant (LTI) and linear time variant (LTV) auto-regressive with external (ARX) models without disturbances [9]. In this paper, we will consider identifying the parameters, orders and time delays of the MISO-FIR systems from a small number of noisy measured data. Briefly, the structure of this paper is as follows. Section 2 gives the model description of MISO-FIR systems and describes the identification problem. Section 3 presents a threshold orthogonal matching pursuit (TH-OMP) algorithm based on the compressed sensing theory. Section 4 provides a simulation example to show the effectiveness of the proposed algorithm.