Finally, in Section 5 some conclusions are provided.2.?Nonlinear Static Decoupling2.1. Coupling Error Model and NotationsWe first establish an appropriate coupling error model to capture the relationships between input forces and corresponding coupling errors. In the model, the input forces and output voltages of a 3-axis force sensor in X, Y, Z directions are defined as fx, fy, fz and ux, uy, uz, respectively.For each dimension, output voltages are partitioned into two categories. One category includes the voltages corresponding to input forces in the same dimension, called prime voltages. The other category includes the voltages corresponding to the input forces in the other two dimensions, called coupling errors. We use uxx, uyy, uzz to denote prime voltages and ex, ey, ez to denote coupling errors in X, Y, Z directions, respectively. Prime voltages account for the majority of output voltages. Next, coupling errors are separated into two coupling error elements caused by input forces of different dimensions. Let (exy, exz) represent the coupling error element in X direction, where exy refers to the coupling error element caused by fy, and exz refers to the coupling error element caused by fz. Similarly, we split the coupling error in Y direction into eyx and eyz, and split the coupling error in Z direction into ezx and ezy. We can get:{ux=uxx+exy+exzuy=uyy+eyx+eyzuz=uzz+ezx+ezy(1)Based on the observation of calibration data of multi-axis force sensors in our lab, we make the following scientific research assumptions about coupling errors.The relationship between the prime force and the prime voltage in every dimension is linear;Relationships between disturbing force and thei
Many applications based on vehicle localization, such as navigation systems, fleet management or Electronic Toll Collection (ETC), are a reality today thanks to the so-called Global Navigation Satellite Systems (GNSS) and digital maps. GNSS devices are exploited to estimate the vehicle location, while digital maps are used to refer this location to the road segments where the vehicle drives.However, location-based applications must face serious drawbacks in urban environments, where perhaps safety systems and location-based services become of more necessity. Main drawbacks can be summarized as follows:In urban built-up areas, the satellite signals used by GNSS sensors to estimate the vehicle location are strongly affected by the environment. GNSS signals are reflected, dispersed and attenuated by buildings, other vehicles, trees, etc. [1].While in highways and interurban areas the road layout trends to be simple and the most common approach to define the road shape based on polylines works well [2], in cities the road layout is far more complex and the polylines lack the necessary flexibility to accurately define the road shape.