An observability analysis for profile estimation through vehicle response measurement

To maintain road and railway infrastructure efficiently, the road or rail profile along the longitudinal direction need to be monitored frequently. Profile evaluation through vehicle response measurements potentially provides efficient solutions. However, the applicability of such profile evaluation for various type of vehicle models in terms of effective sensor installation locations is not clarified yet. Observability is a measure of whether the internal states of a system can be estimated through the measurement of its outputs. Hence, the observability rank condition (ORC) analysis of different time invariant linear vehicle models are conducted for the effective placement of the sensors in vehicles to estimate the profile. Since measurement of vehicle's absolute displacement is not practical, accelerations and angular velocities are assumed to be observed variables. Under this assumption, the profile is typically not observable. Therefore, second derivative of the profile is set as the variable to be identified so that non-static components of the profile is obtained as its double integral. The observability of this second derivative of profile is studied through the ORC analysis based on two approaches. The investigation of the ORC allows to determine the appropriate sensor types and their installation locations. This ORC analysis theoretically revealed a sensor type and placement strategy, which can be used as the guideline in the profile estimation through vehicle response measurement.