Jang Gyu Lee

Improved Kalman filter design for three-dimensional radar tracking

The problem of three-dimensional (3D) radar tracking is considered. The usual tracking filter design relying on first-order (or linear) approximations leads to poor convergence and erratic filter behavior in highly nonlinear situations. Simple filter algorithms that can overcome these ill effects are developed for two different types of 3D radar measurement. For each type of radar measurement, an accurate expression for the measurement covariance is obtained by evaluating inherent nonlinearities of radar measurements via coordinate transformation. Then algebraic manipulations and reasonable approximations are employed to yield a simple filter formulation based on the expression. The resulting filter equations are similar to the extended Kalman filter (EKF) and provide some useful insights into the behavior of linearized Kalman filters designed with radar measurements. Finally, simulation results show that the proposed approach is very effective in accounting for the measurement nonlinearities.

Design and performance test of an oscillation loop for a MEMS resonant accelerometer

In this paper, the design, analysis and experimental results of the self-sustained oscillation loop for a tunable surface micromachined resonant accelerometer, ACRC-RXL are presented. The fabrication process of the mechanical structure is also illustrated. For the oscillation loop analysis, an operator-theoretical approach is applied based on the describing function technique. Using the analytical results, feedback parameters are designed and the expected loop performance is characterized. Then the accelerometer system is practically implemented using the mechanical structure and signal processing electronics. The experimental results show that the developed accelerometer has a performance of bias stability of about 0.7 mg and a dynamic range over 10 g, which satisfies the navigation-graded sensor performance.

Design of a practical tracking algorithm with radar measurements

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that if cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to nonnegligible nonlinear effects. A new filtering algorithm for improving the tracking performance with radar measurements is developed based on the fact that correct evaluation of the measurement error covariance is possible in the Cartesian coordinate system. The proposed algorithm may be viewed as a modification of the EKF in which the variance of the range measurement errors is evaluated in an adaptive manner. The filter structure facilitates the incorporation of the sequential measurement processing scheme, and this makes the resulting algorithm favorable to both estimation accuracy and computational efficiency. Computer simulation results show that the proposed method offers superior performance in comparison to previous methods. Moreover, our developed algorithm provides some useful insight into the radar tracking problem.

Stability robustness of LQ optimal regulators for the performance index with cross-product terms

Suggested are the guaranteed stability margins of LQ optimal regulators for the performance index with cross-product terms, using modified return difference equality. Sufficient conditions to guarantee the required stability margins are presented as well as the conditions to guarantee the stability margins of standard LQ optimal regulators. An example for LQ optimal control of a DC motor system is given to demonstrate how the weighting matrices can be chosen to guarantee the required stability margins. >

Noise covariances estimation for systems with bias states

This paper presents a new approach to noise covariances estimation for a linear, time-invariant, stochastic system with constant but unknown bias states. The system is supposed to satisfy controllable/observable conditions without bias states. Based on a restructured data representation, the covariance of a new variable that consists of measurement vectors is expressed as a linear combination of unknown parameters. Noise covariances are then estimated by employing a recursive least-squares algorithm. The proposed method requires no a priori estimates of noise covariances, provides consistent estimates, and can also be applied when the relationship between bias states and other states is unknown. The method has been applied to strapdown inertial navigation system initial alignment. Simulation results indicate a satisfactory performance of the proposed method.

Digital rebalance loop design for a dynamically tuned gyroscope using H2 methodology

Abstract Presented in this paper is a wide-bandwidth digital torquing rebalance loop for a dynamically tuned gyroscope (DTG) based on H 2 methodology. The role and the importance of a rebalance loop are explained first. The augmented plant model including gyroscope and integrator is composed. Next, an H 2 -based controller is designed for the augmented plant model. Frequency analyses show that the proposed controller maintains a linear relationship between applied input rate and the output of the controller over a wide operating range and keeps the tilt angle small thereby reducing dynamic errors. To verify the performance of the controller in a real environment, a digital rebalance loop for a DTG is designed, fabricated, and examined. From simulation and experimental results, it is confirmed that the controller is robustly stable and has a wide bandwidth, significantly improving the performance of a DTG.

Comment on "Eigenstructure assignment for linear systems" by A.N. Andry, et al. [Aerospace control]

In the above-titled paper (see ibid., vol.AES-19, p.711-729, Sept. 1983), an achievability subspace is given and used for eigenstructure assignment of linear systems with gain output feedback. The commenter shows that the achievability subspace is not generally achievable. >

Design of digital rebalance loop for a dynamically tuned gyroscope using LQG/LTR method

This paper presents the results of a study on the design of a digital rebalance loop for a dynamically tuned gyroscope (DTG). The dynamic model for a DTG is explained briefly. A digital rebalance loop is designed using an LQG/LTR (linear quadratic Gaussian/loop transfer recovery) methodology. It is important that the output of a rebalance loop should follow exactly the angular rate given externally, as well as the the angles of a DTG should be kept small during the transient state. The performance of the digital LQG/LTR rebalance loop is compared with that of a conventional PID rebalance loop through frequency response, simulation, and experiment. The simulation and experimental results show that the performance of the LQG/LTR rebalance loop is better in that the output of the rebalance loop follows external angular rate more quickly, as well as keeping the angle smaller, compared with the conventional PID rebalance loop. The frequency response also shows that the bandwidth of the proposed rebalance loop is wider than that of the PID loop, which also contributes to the performance improvement.

Comments on "modified extended Kalman filtering and a real-time parallel algorithm for system parameter identification"

In the above said paper by Chui et al. ( ibid. vol.35, no.1, p.100-4 (1990)), a modification of the extended Kalman filter algorithm (MEKF) is introduced and illustrative examples are presented. In this note, we point out that the examples demonstrating the advantage of the MEKF over the conventional EKF are inappropriate. >

An efficient filtering algorithm for improved radar tracking

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that in case cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to non-negligible nonlinear effects. In this paper, a new filtering algorithm for improving the radar tracking performance is developed based on the fact that the correct evaluation of the measurement error covariance can be made possible by doing it with respect to the Cartesian state vector. The resulting filter may be viewed as a modification of the EKF in which the variance of the range measurement errors is re-evaluated at each time step and the measurements are sequentially processed in the order of azimuth and range. Computer simulation results show that the proposed method achieves superior performance than other existing filters while requiring a relatively small computational load.