Kalman Filtering–Based Real-Time Inertial Profiler

Abstract

A legacy inertial profiler treats accelerometer sensor data as ultraclean zero-noise data. This is not true in reality. The inertial displacement of an inertial profiler is calculated by double integration of raw accelerometer sensor data. The integral operation amplifies the noise to form direct-current drifting and a random-walk effect in inertial displacement. Introducing a high-precision real-time kinematic (RTK) global navigation satellite system (GNSS) receiver is helpful in suppressing the direct-current drifting and random-walk effect in inertial displacement. The fusion of GNSS and accelerometer sensor data relies on a Kalman filtering–based algorithm. However, a low-cost inertial profiler normally does not have a high-precision GNSS receiver. Therefore, this paper proposes a new Kalman filtering–based framework in which the laser rangefinder sensor will replace the GNSS as an observer to control the direct-current drifting and random-walk effect. In the new framework, the accelerometer sensor is assumed to be contaminated by noise, the pavement is assumed to be perfectly smooth, and the road profile essentially becomes observation noise. The new framework also incorporates a legacy algorithm based on high-pass filtering (HPF) and a newly proposed Kalman filtering–based algorithm into a unified framework. The legacy HPF-based algorithm is an open-loop mode, and the Kalman filtering–based algorithm is a closed-loop mode. The HPF-based algorithms involve a specifically designed high-pass filter that can cancel the poles of the integral operator on the unit circle, making the new inertial profiler system unconditionally stable. In the new framework, all variables in state vectors are post-HPF, so the chances of variables reaching their upper bounds or saturating next-stage wavelength filters are low. By leveraging the laser measurement as an observer, the closed-loop Kalman filtering–based algorithm can contribute 20 dB greater attenuation to the low-frequency random walk than the open-loop solutions. The new inertial profiler can switch from legacy to Kalman mode when the strong random walk appears in real-time. Combined with a high-precision optical triangulation sensor, the precision of the newly proposed inertial profiler can reach the subcentimeter or even submillimeter level under a large speed range.