Dennis S. Bernstein’s research while affiliated with Concordia University Ann Arbor and other places

Sensor-fault detection is crucial for the safe operation of autonomous vehicles. This paper introduces a novel kinematics-based approach for detecting and identifying faulty sensors, which is model-independent, rule-free, and applicable to ground and aerial vehicles. This method, called kinematics-based sensor fault detection (KSFD), relies on kinematic relations, sensor measurements, and real-time single and double numerical differentiation. Using onboard data from radar, rate gyros, magnetometers, and accelerometers, KSFD identifies a single faulty sensor in real time. To achieve this, adaptive input and state estimation (AISE) is used for real-time single and double numerical differentiation of the sensor data, and the kinematically exact single and double transport theorems are used to evaluate the consistency of the data. Unlike model-based and knowledge-based methods, KSFD relies solely on sensor signals, kinematic relations, and AISE for real-time numerical differentiation. For ground vehicles, KSFD requires six kinematics-based error metrics, whereas, for aerial vehicles, nine error metrics are needed. Simulated and experimental examples are provided to evaluate the effectiveness of KSFD.

In applications that involve sensor data, a useful measure of signal-to-noise ratio (SNR) is the ratio of the root-mean-squared (RMS) signal to the RMS sensor noise. The present paper shows that, for numerical differentiation, the traditional SNR is ineffective. In particular, it is shown that, for a harmonic signal with harmonic sensor noise, a natural and relevant SNR is given by the ratio of the RMS of the derivative of the signal to the RMS of the derivative of the sensor noise. For a harmonic signal with white sensor noise, an effective SNR is derived. Implications of these observations for signal processing are discussed.

This paper extends recursive least squares (RLS) to include time-varying regularization. This extension provides flexibility for updating the least squares regularization term in real time. Existing results with constant regularization imply that the parameter-estimation error dynamics of RLS are globally attractive to zero if and only the regressor is weakly persistently exciting. This work shows that, by extending classical RLS to include a time-varying (fading) regularization term that converges to zero, the parameter-estimation error dynamics are globally attractive to zero without weakly persistent excitation. Moreover, if the fading regularization term converges to zero in finite time, then the parameter estimation error also converges to zero in finite time. Finally, we propose rank-1 fading regularization (R1FR) RLS, a time-varying regularization algorithm with fading regularization that converges to zero, and which runs in the same computational complexity as classical RLS. Numerical examples are presented to validate theoretical guarantees and to show how R1FR-RLS can protect against over-regularization.

Extremum-seeking control (ESC) is widely used to optimize performance when the system dynamics are uncertain. However, sensitivity to sensor noise is an important issue in ESC implementation due to the use of high-pass filters or gradient estimators. To reduce the sensitivity of ESC to noise, this paper investigates the use of adaptive input and state estimation (AISE) for numerical differentiation. In particular, this paper develops extremum-seeking control with adaptive input and state estimation (ESC/AISE), where the high-pass filter of ESC is replaced by AISE to improve performance under sensor noise. The effectiveness of ESC/AISE is illustrated via numerical examples.

The goal of target tracking is to estimate target position, velocity, and acceleration in real time using position data. This paper introduces a novel target-tracking technique that uses adaptive input and state estimation (AISE) for real-time numerical differentiation to estimate velocity, acceleration, and jerk from position data. These estimates are used to model the target motion within the Frenet-Serret (FS) frame. By representing the model in SE(3), the position and velocity are estimated using the invariant extended Kalman filter (IEKF). The proposed method, called FS-IEKF-AISE, is illustrated by numerical examples and compared to prior techniques.

Trajectory prediction is a crucial element of guidance, navigation, and control systems. This paper presents two novel trajectory-prediction methods based on real-time position measurements and adaptive input and state estimation (AISE). The first method, called AISE/va, uses position measurements to estimate the target velocity and acceleration. The second method, called AISE/FS, models the target trajectory as a 3D curve using the Frenet-Serret formulas, which require estimates of velocity, acceleration, and jerk. To estimate velocity, acceleration, and jerk in real time, AISE computes first, second, and third derivatives of the position measurements. AISE does not rely on assumptions about the target maneuver, measurement noise, or disturbances. For trajectory prediction, both methods use measurements of the target position and estimates of its derivatives to extrapolate from the current position. The performance of AISE/va and AISE/FS is compared numerically with the $\alpha$-$\beta$-$\gamma$ filter, which shows that AISE/FS provides more accurate trajectory prediction than AISE/va and traditional methods, especially for complex target maneuvers.