## 1 Introduction  
Nonlinear estimation systems generally exist in civilian and military fields, such as target tracking systems, navigation systems, and communication systems. Nonlinear filtering algorithms have been widely used in these nonlinear estimation systems. For example, a multistatic radar based on nonlinear filter localizes a moving target within a small surveillance area [1]; a nonlinear-filter-based autonomous vehicle navigation system provides good positioning performance for vehicles [2]; the improved control systems based on nonlinear filter are adopted in wireless communication systems [3; 4; 5; 6]. As the above examples show, nonlinear filtering algorithms play an important role in addressing nonlinear estimation problems. In the Bayesian framework, the nonlinear filtering problem is essentially a computational problem of multidimensional integrals, which is typically intractable and hence the numerical approaches are considered [7]. In theory, the particle filter [8; 9; 10; 11] based on the Monte-Carlo approximation for the multidimensional integrals can provide sufficient precision. However, the filter is usually impractical, owing to the enormous computational complexity from it suffers. The marginalized particle filters reduce the computational complexity to a certain degree, but it cannot deal with the problem whose process model and measurement model are both nonlinear. On the contrary, the filters under the Gaussian assumption of posterior probability density can be executed simply and quickly. The extended Kalman filter (EKF) [12; 13], for instance, employs linearization via first-order Taylor series expansion, but it often results in unstable performance, and differentiability of the considered nonlinear functions is also required. In recent years, the deterministically sampled filtershave drawn much attention, such as the central difference Kalman filter (CDKF) [14], the unscented Kalman filter (UKF) [15; 16; 17], and the cubature Kalman filter (CKF) [18]. Among these filters, the UKF uses a set of sigma-points and unscented transformation to capture posterior statistics of the state. The CKF performs with higher accuracy than the EKF and shows better numerical stability and lower computational demands than the UKF with a non-zero scaling parameter in high dimensions [18]. It should be noted that when the system model includes highly nonlinear functions, the unknown high order terms may drastically reduce the accuracy of the covariance estimate [19]. Additionally, the performance of the CKF may be unsatisfactory in high nonlinear conditions, and the way in which to make use of the measurements efficiently should also be taken into account. [PERSON] [20] proposed the fifth and higher-degree CKF to further improve the accuracy, but the number of sample points increases rapidly with the increase of the algebraic degree or the state dimension. Compared with the high-degree CKF, the high-degree simplex cubature Kalman filter (SCKF) [21] uses fewer sample points and shows higher accuracy. Unfortunately, the number of sample points still increases quadratically with the increase of the state dimension. The contribution of this paper is to derive a new class of nonlinear filter with arbitrary order of the Chebyshev-Laguerre (CL) polynomial. In order to regulate the effect of the high order terms, the stochastic orthogonal method [22] is introduced to the third-degree spherical simplex rule, which improves the accuracy of the CKF with only two more sample points. Moreover, the solution to the CL polynomial equation of arbitrary order is discussed [23]. The quadrature points and weights in the radial integral can be subsequently obtained according to the nature of the CL polynomial, and hence the accuracy can be controlled by the order of CL polynomial. The filter is called the orthogonal simplex Chebyshev-Laguerre cubature Kalman filter (OSCL-CKF).