###### Abstract  
Global navigation satellite systems (GNSS) are widely used for the navigation of land vehicles. However, the positioning accuracy of GNSS, such as the global positioning system (GPS), deteriorates in urban areas due to signal blockage and multipath effects. GNSS can be integrated with a micro-electro-mechanical system (MEMS)-based inertial navigation system (INS), such as a reduced inertial sensor system (RISS) using a Kalman filter (KF) to enhance the performance of the integrated navigation solution in GNSS challenging environments. The linearized KF cannot model the low-cost and small-size sensors due to relatively high noise levels and compound error characteristics. This paper reviews two approaches to employing parallel cascade identification (PCI), a non-linear system identification technique, augmented with KF to enhance the navigational solution. First, PCI models azimuth errors for a loosely coupled 2D RISS integrated system with GNSS to obtain a navigation solution. The experimental results demonstrated that PCI improved the integrated 2D RISS/GNSS performance by modeling linear, non-linear, and other residual azimuth errors. For the second scenario, PCI is utilized for modeling residual pseudorange correlated errors of a KF-based tightly coupled RISS/GNSS navigation solution. Experimental results have shown that PCI enhances the performance of the tightly coupled KF by modeling the non-linear pseudorange errors to provide an enhanced and more reliable solution. For the first algorithm, the results demonstrated that PCI can enhance the performance by 77% as compared to the KF solution during the GNSS outages. For the second algorithm, the performance improvement for the proposed PCI technique during the availability of three satellites was 39% compared to the KF solution. Keywords:land vehicle navigation; system identification; inertial sensors; GNSS; Kalman filter; parallel cascade identification +
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model, repeated least squares, correlated residuals, the maximum likelihood method, the Tally principle, and Levin's method. System identification requires the following steps:  
1. Input/output data measurement with appropriate sampling procedures either in the time domain or in the frequency domain. 2. A set of candidate models and to choose a suitable model structure. 3. An estimation method for minimization of fit between model (predicted) output and measured output. The mathematical representation of a system's dynamics is termed modeling. Modeling of the dynamical system is more challenging as the effects of actions take some time to occur. A single system can be described by different models depending upon its applications. A black box approach is based entirely on observed inputs and outputs of the system, as shown in Figure 1. It is widely used for many engineering problems. Using this approach, we can decompose a system into different modules. It is very suitable for linear, time-invariant systems and can also be applied to non-linear systems. However, linear system identification is not able to address many practical time-varying systems, and it becomes necessary to use non-linear system identification techniques [6; 7; 8; 9]. The application of non-linear system identification techniques is justified when linear models are not able to handle the excessive non-linear distortion levels. Non-linear system identification techniques include representation of non-linear systems and estimation of a parametric model. For non-linear systems identification, the model selection and parameter estimation are enormously complicated.