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The position estimation errors using the range measurements from the RMS/MTTS system at MacGregor Range are evaluated. The potential reduction of the upward component of the position estimation errors obtained by adding one or more A-stations (measurement sites) attached to a tethered balloon is considered. (Author)

An adaptive, fixed interval smoother for trajectory estimation is described. The fixed interval smoother uses the modified Bryson-Fraser formulation which combines the state estimates of a forward running Kalman filter and a backward running adjoint filter. The square root formulation used for the Kalman filter is described. The procedures used to adapt the Kalman filter to the local noise content of the measurements and to adapt the filter to abrupt changes in target acceleration are discussed. (Author)

The RMS/MTTS instrumentation system located at MacGregor Range is a range measuring, multiple target tracking system. In order to obtain a vehicle trajectory from this system, the range measurement from several receivers are processed by least squares. Since the measured vehicle trajectories are often low altitude, the resulting nonlinear least squares equations are ill-conditioned. In addition, this measurement system is plagued by outliers, sometimes by dense burst of outliers. The combination of ill-conditioning and outliers is lethal and attempts to robustify the nonlinear least squares processing have failed. An alternative is to preprocess each of the range measurement sequences, eliminating the outliers and replacing them if necessary. Each sequence of range measurements is preprocessed by robustly fitting a cubic spline using iteratively reweighted least squares. Due to the nature of spline fitting and the possible dense bursts of outliers, the choice of a good set of initial weights for use in the iteratively reweighted least squares is important to the efficiency of the method. These initial weights are determined using robust, local fitting techniques. Several robust techniques have been tested for this local fitting application. The robust spline preprocessing is illustrated with some especially troublesome data sequences and the relative performance of several robust methods for choosing the initial weights is compared. (Author)

Robust methods provide a fresh approach to the treatment of outliers in filtering and smoothing applications. In deriving the filter and smoother equations via the conditional mean formulation or maximum a posteriori formulation the measurement noise probability density is replaced by a pseudo density which is Gaussian mixture with very heavy tails. The resulting robust filter and smoother are applied to tracking data to obtain improved estimation performance in the presence of outliers. The improvement in estimation performance is evaluated by Monte Carlo using simulated tracking data. The Monte Carlo results indicate the improvement in performance to be somewhat greater than the improvement obtained when using robust filters and smoothers derived from M-estimates. (Author)

Robust methods provide a fresh approach to the treatment of outliers or wild observations in filtering and smoothing applicatons. The robust M-estimates of regression are extended to filtering and fixed lag smoothing by employing a pseudo density of the observatons in the derivations of the filter and fixed lag smoother. These robust methods are applied to tracking data to obtain improved estimation performance in the presence of wild observations. The improvement in estimaton performance is evaluated via Monte Carlo using simulated tracking data. (Author)

The computation of robust M-estimates of regression is considered in detail using the Psi functions of Huber, Andrews, and Hampel. The computation of M-estimates of regression is considered for linear models, linear models with vector observations, and nonlinear models. Examples are given using actual data for each of these different classes of models. Examples are given using actual data for each of these different classes of models. Careful attention is given to the important problem of convergence of M-estimates with redescending Psi functions. A lengthy treatment of this problem is given for the Daniel and Wood data by considering several starting methods for the iterative solution and different breakpoints for the Psi functions. (Author)

Robust Statistics provides a fresh approach to the difficult problem of editing in data reduction. Of prime concern are grossly erroneous measurements which, when undetected, completely destroy automated data reduction procedures causing costly reruns and time delays with human detection of the erroneous measurements. The application of robust statistical methods has been highly successful in dealing with this problem. An introduction to the robust M-estimates and their numerical computation is given. The application of M-estimates to data preprocessing, instrument calibration, N-station cinetheodolites, N-station radar solution, and filtering are described in detail. Numerical examples of these applications using real measurements are given. (Author)

A globally convergent, modified Newton method is developed for the least squares estimation of target from a DME type range measuring system. The resulting algorithm is used to evaluate the effects of truncation error on the accuracy of the position estimates for the RMS/MTTS system located at MacGregor Range.

An algorithm for the triangular decomposition of the sum of a positive definite matrix and a symmetric dyad is described. Several applications of the algorithm to the implementation of a square root Kalman filter are given.

A method is described for the optimal estimation of measurement biases in a Kalman filtering application. The method, which was originally developed by B. Friedland, is based on the decoupling of a large Kalman filter into two smaller filters. One of the smaller filters produces a state estimate which assumes that all measurement biases are zero and the other called the bias filter estimates the measurement biases. The outputs of the two smaller filters are recombined to form the optimal state estimates. Restrictions on the form of the filters which are imposed by the decoupling are discussed. Several extensions of Friedland's original method are presented. Finally, the implementation of the filters via square root filtering techniques is developed.