Jacques Waldmann

Line-of-sight rate estimation and linearizing control of an imaging seeker in a tactical missile guided by proportional navigation

Acceleration commands in missiles guided by proportional navigation require the measurement of line-of-sight (LOS) rate. It is often obtained by filtering the output of a 2-DOF rate gyro mounted on the inner gimbal of the seeker. This paper describes the modeling of an imaging seeker and the formulation of an extended Kalman filter (EKF) for the estimation of LOS rate from measurements of relative angular displacement between seeker gimbals and a low-cost strapdown inertial unit. The approach aims at circumventing the need for the rate gyro on the seeker. A linearizing feedback control law for decoupling missile motion from that of the seeker is proposed based on the filter model and its estimates. Additionally, the control law uses visual information from the image sequence for target tracking. Seeker dynamics and control are then integrated into a dynamic model of a cruciform missile equipped with canards and rollerons and guided by proportional navigation in 3D interception tasks. Monte Carlo simulation is employed to evaluate the overall system accuracy subject to different initial conditions and the impact of rolling motion during high-g maneuvers on miss distance. Initial engagement geometry and roll-rate damping at high incidence angles have significant effect.

Observability analysis of inertial navigation errors from optical flow subspace constraint

Observability analysis of the time-varying dynamics yields geometric insights about the unobservable subspace.Camera and IMU jointly rotating in distinct piece-wise constant attitude segments during a straight path yield observable IMU errors.The analysis shows the effect of lateral maneuvers on the observability of misalignment, and velocity error along and orthogonal to the ground velocity.Monte Carlo simulation indicates the fusion of inertial and optical flow data mitigates the position error growth relative to just unaided inertial navigation during GPS outage. Fusion of inertial and vision sensors is an effective aid to inertial navigation systems (INS) during GPS outage. Optical flow-aided inertial navigation circumvents feature tracking, landmark mapping, and state vector augmentation typical of simultaneous localization and mapping (SLAM). This paper focuses on the observability analysis of INS errors from implicit measurements of the optical flow subspace constraint, and derives how observable and unobservable directions are affected by the motion of a camera rigidly coupled to an inertial measurement unit (IMU). Straight motion and piecewise constant (PWC) attitude segments yield the random constant IMU errors observable. The unobservable directions are the three-dimensional (3D) position error, the velocity error along the ground velocity, and the combination of angular misalignment about the local vertical and the velocity error along the horizontal direction orthogonal to the ground velocity. The velocity error along the ground velocity becomes observable with horizontal maneuvering. A Monte Carlo simulation validates the observability analysis, and reveals the feasibility of IMU calibration and the mitigation of navigation error growth with the aid of the optical flow subspace constraint compared with the unaided INS.

A Novel Linear, Unbiased Estimator to Fuse Delayed Measurements in Distributed Sensor Networks with Application to UAV Fleet

This paper proposes a novel methodology to fuse delayed measurements in a distributed sensor network. The algorithm derives from the linear minimum mean square error estimator and yields a linear, unbiased estimator that fuses the delayed measurements. Its performance regarding the estimation accuracy, computational workload and memory storage needs is compared to the classical Kalman filter reiteration that achieves the minimum mean square error in linear and Gaussian systems. The comparison is carried out using a simulated distributed sensor network that consists of a UAV fleet in formation flight in which the GPS measurements and relative positions are exchanged among neighboring network nodes. The novel technique yields similar performance to the reiterated Kalman filtering, which is the optimal linear Gaussian solution, while demanding less storage capacity and computational throughput in the problems of interest.

Feedforward ins aiding: an investigation of maneuvers for in-flight alignment

Navigation in autonomous vehicles involves integrating measurements from on-board inertial sensors and external data collected by various sensors. In this paper, the computer-frame velocity error model is augmented with a random constant model of accelerometer bias and rate-gyro drift for use in a Kalman filter-based fusion of a low-cost rotating inertial navigation system (INS) with external position and velocity measurements. The impact of model mismatch and maneuvers on the estimation of misalignment and inertial measurement unit (IMU) error is investigated. Previously, the literature focused on analyzing the stripped observability matrix that results from applying piece-wise constant acceleration segments to a stabilized, gimbaled INS to determine the accuracy of misalignment, accelerometer bias, and rate-gyro drift estimation. However, its validation via covariance analysis neglected model mismatch. Here, a vertically undamped, three channel INS with a rotating IMU with respect to the host vehicle is simulated. Such IMU rotation does not require the accurate mechanism of a gimbaled INS (GINS) and obviates the need to maneuver away from the desired trajectory during in-flight alignment (IFA) with a strapdown IMU. In comparison with a stationary GINS at a known location, IMU rotation enhances estimation of accelerometer bias, and partially improves estimation of rate-gyro drift and misalignment. Finally, combining IMU rotation with distinct acceleration segments yields full observability, thus significantly enhancing estimation of rate-gyro drift and misalignment.

A Novel Imaging Measurement Model for Vision and Inertial Navigation Fusion with Extended Kalman Filtering

It is well-known that stand-alone inertial navigation systems (INS) have their errors diverging with time. The traditional approach for solving such incovenience is to resort to position and velocity aiding such as global navigation satellite systems (GNSS) signals. However, misalignment errors in such fusion architecture are not observable in the absence of maneuvers. This investigation develops a novel sighting device (SD) model for vision-aided inertial navigation for use in psi-angle error based extended Kalman filtering by means of observations of a priori mapped landmarks. Additionally, the psi-angle error model is revisited and an extended Kalman filter datasheet-based tuning is explained. Results are obtained by computer simulation, where an unmanned aerial vehicle flies a known trajectory with inertial sensor measurements corrupted by a random constant model. Position and velocity errors, misalignment, accelerometer bias, rate-gyro drift and GNSS clock errors with respect to ground-truth are estimated by means of INS/GNSS/SD fusion and tested for statistical consistency.

Forced Singular Perturbations as Theoretical Background to a Split-Coordinate Frame Multirate Strapdown Terrestrial Navigation Algorithm

Forced singular perturbations (FSP) are proposed as a theoretical background to Bar-Itzhacks body−local-level split-coordinate frame multirate scheme intuitively derived for terrestrial strapdown navigation with reduced computations. Forcing the dynamics into distinct time scales caused a degradation of the continuous-time solution, though the loss of accuracy was not significant in comparison with the covered distance. Simulation of ideal sensors undergoing actual operating conditions showed that discretization and use of inertial data in incremental form, however, had a significant impact on navigation acuracy. The interaction between sensor quantization and sensor sampling frequency was investigated. The evaluation of performance in a variety of conditions indicated that the multirate algorithm proposed by Bar-Itzhack, in spite of its elegance and simplicity with reduced computational workload, showed acceptable accuracy in comparison with Savages more complex multirate correction terms to coning, sculling, and scrolling errors.

Saccadic Motion Control for Monocular Fixation in a Robotic Vision Head: A Comparative Study

A comparative evaluation of two methods for visual tracking by saccade control of an active vision head with antropomorphic characteristics conducted at the ITA/INPE Active Computer Vision and Perception Laboratory is presented. The first method accomplishes fixation by detecting motion and controlling gaze direction based on gray-level segmentation. The second method aligns images of different viewpoints in order to apply static camera motion detection. Morphological opening is then employed to compensate for image alignment errors. Results from experiments in a controlled environment show that both approaches are capable of dealing with non-rigid forms and scenes with limited dynamics by operating at about 1 Hz. However, the comparative evaluation shows that image alignment improves tracking robustness to variations in lighting conditions and background texture. The results so far obtained encourage further applications in autonomous robotics and vision-aided robotic rotorcraft navigation.

Observability Analysis for the INS Error Model with GPS/Uncalibrated Magnetometer Aiding

A commercial inertial navigation system (INS) yields time-diverging solutions due to errors in the inertial sensors, which can inhibit long term navigation. To circumvent this issue, a set of non-inertial sensors is used to limit these errors. The fusion between additional data and INS solution is often done by means of an extended Kalman filter using a state-error model. However, the Kalman filter estimates should be used when full observability produces small estimation uncertainty. This paper has analyzed conditions to achieve full observability using as non-inertial sensors a GPS receiver and an uncalibrated magnetometer combined with either a locally horizontal-stabilized IMU or with a strapdown IMU. The magnetometer bias was considered constant and augmented the error-state space. Observability analysis based on concepts of linear algebra provided a geometric insight on the requirements for attaining full observability when assuming piece-wise constant system dynamics. The novel analysis has been validated by covariance analysis of simulation results. Also, simulation results indicate that fusion with uncalibrated magnetometer data without proper processing gives rise to estimation divergence.

Extrapolation of delayed measurements for fusion in a distributed sensor network

The measurement extrapolation (ME) algorithm was devised to fuse delayed measurements in the Kalman filter. It is a suboptimal algorithm that greatly reduces the computational burden of the optimal Reiterated Kalman Filter (RKF). ME can be used in embedded systems that lack the required computational resources to compute the optimal estimate. However, it has not been extended yet to be applied in a distributed sensor network. Furthermore, it is verified here that the original ME algorithm provides a biased estimate, which can degrade the estimation accuracy. Thus, this work proposes to extend ME to fuse delayed measurements received by nodes in a distributed network, and to remove the bias using Bayesian concepts, improving the accuracy of the novel method. The ME computational burden and memory needs are theoretically analyzed and compared to those of the RKF. Finally, simulations of a simplified distributed network are presented to measure the performance of the new algorithm with respect to RKF and to validate the theoretical analysis. The results show that ME can provide an estimate with acceptable accuracy whereas the computational burden is greatly decreased and the memory requirements are only slightly increased compared to RKF.

Theoretical Analysis of the Measurement Transportation Algorithm to Fuse Delayed Data in Distributed Sensor Networks

Distributed sensor networks are capable of robust dynamic system estimation. The shared information in the network can prevent significant degradation or the interruption of the estimation process when a particular network node fails. However, the estimation accuracy can be severely degraded if delayed information is navely fused. The classical algorithm to fuse delayed measurements in a distributed network is the reiterated Kalman filter (RKF), which provides the optimal estimate in linear and Gaussian systems. Nevertheless, this algorithm imposes a huge computational burden and requires considerable memory when the delay is large, thus precluding the use of RKF in embedded systems that lack the needed computational resources. Previously, we proposed a suboptimal algorithm called measurement transportation (MT) that greatly reduces both the memory requirement and computational burden and delivers accuracy comparable to that of the RKF in a simulated UAV network. However, MT was only tested with numerical simulations. Here, we extend the previous investigation with the detailed analysis of MT regarding its accuracy, memory necessity, and computational burden. Cases are shown when the analysis predicts that the accuracy delivered by MT is comparable to that of the RKF and the theoretical results are then validated with a simulated distributed sensor network.