Garry A. Einicke

Robust extended Kalman filtering

Linearization errors inherent in the specification of an extended Kalman filter (EKF) can severely degrade its performance. This correspondence presents a new approach to the robust design of a discrete-time EKF by application of the robust linear design methods based on the H/sub /spl infin// norm minimization criterion. The results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications.

Longwall mining automation an application of minimum-variance smoothing [Applications of Control]

This article reviews the development of the minimum-variance smoother and describes its use in longwall automation. We describe both continuous- and discrete-time smoother solutions. It is shown, under suitable assumptions, that the two-norm of the smoother estimation error is less than that for the Kalman filter. A simulation study is presented to compare the performance of the minimum-variance smoother with the methods of H.E. Rauch et al. (1965), and D.C. Fraser and J.E. Potter (1969).

Optimal and robust noncausal filter formulations

The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother. The optimal solution involves a cascade of a Kalman predictor and an adjoint Kalman predictor. A robust smoother involving H/sub /spl infin// predictors is also described. Filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error. These bounds lead to a priori estimates for the scalar /spl gamma/ in the H/sub /spl infin// filter and smoother design. The results of simulation studies are presented, which demonstrate that optimal, robust, and extended Kalman smoothers can provide performance benefits.

Performance Analysis of Constrained Loosely Coupled GPS/INS Integration Solutions

The paper investigates approaches for loosely coupled GPS/INS integration. Error performance is calculated using a reference trajectory. A performance improvement can be obtained by exploiting additional map information (for example, a road boundary). A constrained solution has been developed and its performance compared with an unconstrained one. The case of GPS outages is also investigated showing how a Kalman filter that operates on the last received GPS position and velocity measurements provides a performance benefit. Results are obtained by means of simulation studies and real data.

Asymptotic Optimality of the Minimum-Variance Fixed-Interval Smoother

This correspondence investigates the asymptotic performance of the discrete-time and continuous-time, time-varying, minimum-variance, fixed-interval smoothers. Comparison theorems are generalized to provide sufficient conditions for the monotonic convergence of the underlying Riccati equations. Under these conditions, the energy of the estimation errors asymptotically approach a lower bound and attain lscr2 /L2 stability

Riccati Equation and EM Algorithm Convergence for Inertial Navigation Alignment

This correspondence investigates the convergence of a Kalman filter-based expectation-maximization (EM) algorithm for estimating variances. It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of iterations will be monotonically nonincreasing. Further, the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small. Conversely, when the process noise variance becomes negligible, the measurement noise variance estimates asymptotically approach the true values. An inertial navigation application is discussed in which performance depends on accurately estimating the process variances.

The use of fake algebraic Riccati equations for co-channel demodulation

This paper describes a method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system. A fake algebraic Riccati equation is employed in the calculation of the filter gain. The design procedure attempts to produce a stable filter at the expense of optimality. This contrasts with the extended Kalman filter (EKF), which attempts to preserve optimality via its linearization procedure, at the expense of stability. A passivity approach is applied to deduce stability conditions for the filter error system. The performance is compared with an EKF for a co-channel frequency demodulation application.

Bounded Constrained Filtering for GPS/INS Integration

This paper considers estimation problems where inequality constraints are imposed on the outputs of linear systems and can be modeled by nonlinear functions. In this case, censoring functions can be designed to constrain measurements for use by filters and smoothers. It is established that the filter and smoother output estimates are unbiased, provided that the underlying probability density functions are even and the censoring functions are odd. The Bounded Real Lemma is employed to ensure that the output estimates satisfy a performance criterion. A global positioning system (GPS) and inertial navigation system (INS) integration application is discussed in which a developed solution exhibits improved performance during GPS outages when a priori information is used to constrain the altitude and velocity measurements.

EM Algorithm State Matrix Estimation for Navigation

The convergence of an expectation-maximization (EM) algorithm for state matrix estimation is investigated. It is shown for the expectation step that the design and observed error covariances are monotonically dependent on the residual error variances. For the maximization step, it is established that the residual error variances are monotonically dependent on the design and observed error covariances. The state matrix estimates are observed to be unbiased when the measurement noise is negligible. A navigation application is discussed in which the use of estimated parameters improves filtering performance.

An extended AODV protocol for VoIP application in mobile ad hoc network

Most of the routing protocols designed for ad hoc networks assume that IEEE 802.11b is used for lowest-layer communications. In IEEE 802.11 ad hoc mode, the DCF is the basic medium access protocol. In this paper we consider voice calls over mobile ad hoc network based on 802.11b MAC. A new routing metric for searching a stable routing in ad hoc network based on an extended AODV protocol is proposed. The simulation results presented in this work show that the new protocol can improve performance of VoIP over ad hoc network as compared to standard AODV protocol.