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The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.

This paper presents a new position-determination estimator for trilateration location. The proposed estimator takes the measurement bias into consideration and improves the location accuracy of a mobile location system. In case that a mobile station (MS) utilizes signals from a set of base stations for its location, the computed location is largely affected by nonline-of-sight (NLOS) error in signal propagation. A constrained optimization method in a three-stage estimation structure is proposed to estimate and eliminate the measurement bias contained in each pseudorange and mainly caused by the NLOS error. A linear observation model of the bias is formulated, and the interior-point optimization technique optimally estimates the bias by introducing a feasible range of the measurement bias. It is demonstrated that - the new three-stage estimator successfully computes an accurate location of an MS in a realistic environment setting. The location accuracy of the proposed estimator is analyzed and compared with the existing methods through mathematical formulations and simulatious. The proposed estimator efficiently mitigates the effect of a measurement bias and shows that the iterated least square (ILS) accuracy of 118 m [67% distance root-mean-square (DRMS)] can be improved to about 17 m in a typical urban environment. Index Terms--Enhanced-911 (E-911), interior-point optimization method, location-based services, path-delay error, radio navigation, time of arrival (TOA), trilateration, wireless location.

Controllability and observability of discrete linear time-varying systems with norm-bounded parameter uncertainties are analyzed in this note. Like in the continuous case, we propose the sufficient conditions, which ensure controllability and observability of the uncertain system. The proposed conditions allow the evaluation of controllability and observability of the uncertain system without knowledge of specific values of uncertainties. Index Terms--Controllability, discrete time-varying system, observability, robustness.

A nonlinear observer is proposed for a strapdown inertial navigation system (SDINS) in-flight alignment problem using an [H.sub.[infinity]] filter Riccati equation and a freedom parameter. The proposed observer improves the filtering stability, convergence, and performance. The characteristics of the observer are analyzed using a Lyapunov function. Simulation results demonstrate a significant reduction in alignment errors by employing the proposed nonlinear observer. The observer is developed in general such that it can be applied to estimating nonlinear systems other than the SDINS in-flight alignment.

The controllability and the observability of continuous linear time-varying systems with norm-bounded parameter perturbations are analyzed in this paper. The sufficient conditions which ensure the controllability of the perturbed system are presented by using the derived state transition matrix relationship between the nominal system and the perturbed system. The proposed sufficient conditions allow the evaluation of controllability under the norm-bounded parameter perturbations. The robustness of the observability is also studied for continuous linear time-varying systems with norm-bounded parameter perturbations, and the corresponding sufficient conditions are provided. Index Terms: Controllability, observability, parameter perturbations, robustness.

The psi-angle model and the equivalent tilt(ET) model have been widely used for in-flight alignment (IFA) to align and to calibrate a strapdown inertial navigation system (SDINS) on a moving base. However, these models are not effective for a system with large attitude errors because the neglected error terms in the models degrade the performance of a designed filter. In this paper, with an odometer as an external aid, a velocity-aided SDINS is designed for IFA. And equivalent error models applicable to IFA with large attitude errors are derived in terms of rotation vector error and additive and multiplicative quaternion errors. It is found that error models in terms of additive quaternion error (AQE) become linear. Thus the proposed error models reduce unmodeled error terms for a linear filter. From a number of van tests, it is shown that the proposed error models effectively improve the performance of IFA.

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 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.

We propose new equivalent tilt error models which are applicable to the analysis of the terrestrial strapdown inertial navigation systems (SDINS), based on the quaternions. The currently available equivalent tilt error models, like the conventional [Phi] model of the gimbaled inertial navigation systems (GINS), are derived only by the true frame approach. The true frame approach has a computational disadvantage that it produces an error model where the attitude error equation is coupled with its position and velocity error equations. The motivation of this work is to solve this problem. As a result, two kinds of error models are derived. Among them, one is derived by the computer frame approach for practical onboard implementations. Thus, like the conventional GINS [Psi] model, its attitude error equation is decoupled from the position and velocity error equations. The other is derived in order to show the relationship between the true frame approach and the computer frame approach which are applied to the quaternion-based SDINS. Thus, like the GINS [Delta][Theta] model, it can be used to transform the error variables into each other which are calculated by the two different approaches.

A new homing guidance law is proposed to impact a target with a desired attitude angle. It is a variation of the conventional proportional navigation guidance (PNG) law which includes a supplementary time-varying bias. The proposed guidance law does not require a time-to-go estimation and has a simpler form. Analytic conditions for fulfilling the guidance goal are also provided. Simulation results demonstrate that the proposed guidance law has wider haunch envelopes than the previous one and shows a good performance even against a maneuvering target.

A decoupled adaptive tracking filter for maneuvering targets under nonlinear measurement environment is presented. A modified input estimation method is implemented in a line-of-sight Cartesian coordinate system. Since the proposed filter has a decoupled structure, computation is drastically reduced without degrading performance. Also shown is that, due to small cross-correlation between pseudomeasurement noises, accuracy of maneuver detection is improved.

The relationship between quaternion errors and tilt angles from true navigation frame to analytic platform frame is newly derived for strapdown inertial navigation system (SDINS). Using the relationship it is shown that the quaternion error model for attitude and velocity is equivalent to the conventional perturbation error model. Based upon the equivalency, the quaternion errors during a multiposition alignment are determined and analyzed. Furthermore, it is shown that the heading rotation of 180 deg achieves the minimal quaternion error for 2-position ground alignment.

A tree network consisting of communicating processors is considered. The objective is to minimize the processing time by distributing the processing load to other nodes. The effect of the order of load distribution on the processing time is addressed. An algorithm which optimally determines the order of load distribution is developed. It is shown that the order depends only on the channel capacity between nodes but not on the computing capability of each node.

The command to line-of-sight (CLOS) guidance is known to require very high acceleration commands as the distance between a missile and its target becomes closer. Therefore, the CLOS is generally used for midcourse guidance. In order to use the CLOS for homing, an additional feedforward acceleration command (FFC) is necessary. In this correspondence an improved CLOS (ICLOS) technique which includes FFC is proposed. Its performance improvement is demonstrated by applying the technique to a surface-to-air missile (SAM).

Presented in this paper is a complete error covariance analysis for strapdown inertial navigation system (SDINS). We have found that in SDINS the cross-coupling terms in gyrocompass alignment errors can significantly influence the SDINS error propagation. Initial heading error has a close correlation with the east component of gyro bias error, while initial level tilt errors are closely related to accelerometer bias errors. In addition, pseudostate variables are introduced in covariance analysis for SDINS utilizing the characteristics of gyrocompass alignment errors. This approach simplifies the covariance analysis because it makes the initial error covariance matrix to a diagonal form. Thus a real implementation becomes easier. The approach is conformed by comparing the results for a simplified case with the covariance analysis obtained from the conventional SDINS error model.

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.

An adaptive tracking filter for maneuvering targets is proposed using modified input estimation technique. Pseudoresiduals are defined using measurements and the velocity estimate at the hypothesized maneuver onset time. With the pseudoresiduals and a new target model representing transitions of nominal accelerations, a new input estimation method for tracking a maneuvering target is derived. Since the proposed detection technique is more sensitive to maneuvers than previous work, the shorter window length can be employed to detect and compensate target maneuvers. Also shown is the tracking performance of the proposed filter is similar to that of interacting multiple model (IMM) method with 3 models, while computational loads of our method are drastically reduced.

Upper bounds on spectral norm and trace for the solution of continuous algebraic matrix Riccati equations are proposed. The proposed bounds are based on a form of the general analytic solution. It is shown that, in many cases, the spectral norm and the trace bounds are better than other results.

Total least squares (TLS) parameter estimation is an alternative to leaves squares (LS) estimation when there are errors in both data matrix and observation vector. Especially, when some of the columns, not all, of the data matrix A are free of error, we call it a mixed LS-TLS problem. Accordingly, a sequential algorithm for solving a mixed LS-TLS problem is proposed here. The proposed algorithm employs an efficient algorithm to locate the minimum eigenpair, instead of singular value decomposition (SVD) which is computationally exacting. The proposed algorithm is applied to an accelerometer model to identify error parameters which are very important in inertial navigation systems (INS).

It is shown that a mixture of random noises can be represented by a single equivalent ARMA (autoregressive moving average) model that is simple to implement. We applied the scheme to model RLG (ring laser gyroscope) random errors. An identification result from real test data confirms the validity of this approach.

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 (SDINS) initial alignment. Simulation results indicate a satisfactory performance of the proposed method.

In the above note, 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.