Critique of some neural network architectures and claims forcontrol and estimation

While there is great potential for successful use of neural network (NN) algorithms in automatic target recognition (ATR) and other pattern identification/classification applications, significant barriers have been encountered that, to date, defy rigorous use of NNs within feedback control designs. The status of several problems and contradictions involving NNs relating to control and estimation theory applications (and to practical failure detection within INS/GPS navigation systems) are summarized here. To give a positive spin and for a balanced perspective, we also mention many novel laudable NN results obtained by invoking the techniques and results of control and estimation theory     

The Proper Computation of the Matrix Pseudoinverse and its Impact in MVRO Filtering

There have been two new algorithms of fairly recent origin offered for the calculation of the matrix pseudoinverse. Unfortunately, nonpathological counterexamples can be constructed, as offered herein, that demonstrate the questionable nature of these two algorithms; however, a resolution is offered here to help prevent possible uncritical propagation of the questionable algorithms. As a rigorous alternative, a well-established technique (endorsed by numerical analysts) is reviewed for calculating the correct matrix pseudoinverse using a computer. Additionally, this technique possesses existent independently verified/validated and assessible software code for a convenient implementation. However, historical loose ends in calculating the associated condition number are singled out here as cause for concern and as a topic for future resolution and refinement. Finally, as the primary motivation for considering these issues, an application example is offered from estimation theory in the implementation and analysis of a minimum variance reduced-order (MVRO) filter having proper performance that critically hinges on the correct computation of the matrix pseudoinverse. While examples of applying MVRO to navigation applications were provided almost a decade ago, a clear indication of the somewhat restrictive conditions of applicability were wanting and so are elucidated here since there appears to be a resurgence of interest in this analytic technique. Another contribution is in providing a tally of the drawbacks to be incurred in using MVRO as well as its previously publicized benefits.     

Further comments on “Optimal sensor selection strategy fordiscrete-time estimators” [and reply]

The fundamental TPBVP usually underlying true “optimal sensor selection strategy” is revisited to obtain practical real-time mechanizations as a solution to an exclusively initial value problem     

Fallacies in computational testing of matrix positivedefiniteness/semidefiniteness

The status of computational tests for establishing matrix positive semidefiniteness and positive definiteness is reviewed. Two pervasive real-time tests that have been used for many years in varied applications to ensure that computed covariances encountered in Kalman filter applications are positive definite and discussed. Structural representations of covariance matrices are reviewed as a prelude to constructing a counterexample and demonstrating that it refutes these real-time tests. It is maintained that the latter are bogus approaches despite the fact that they are pervasive. It is suggested that such bogus tests arose as an attempt to fill the need for a quick check (over the entire mission time) of the massive number of matrices computationally encountered in real-time applications     

Analytic example of a Schweppe likelihood-ratio detector

A low-dimensional test problem with a known solution is used to verify various computer implementations of F.C. Schweppe's likelihood detector (1965). In this case a closed-form solution is provided for a Schweppe likelihood detector in terms of an intermediate Kalman filter, as utilized in its implementation, for detecting the presence of a two-state signal model in Gaussian white noise. The associated error probabilities are also evaluated following a procedure that utilizes optimized Chernoff-like bounds for a tight approximation. A methodology is demonstrated for appropriately setting the decision threshold for this example as a tradeoff against allowable observation time. By using this or similar examples, certain qualitative and quantitative aspects of the software implementation can be checked for conformance to anticipated behavior as an intermediate benchmark, prior to modular replacement of the various high-order matrices appropriate to the particular application     

Automatic recognition of ISAR ship images

Inverse synthetic aperture radar (ISAR) produces images of ships at sea which human operators can be trained to recognize. Because ISAR uses the ship's own varying angular motions (roll, pitch, and yaw) for cross-range resolution, the viewing aspect and cross-range scale factor are continually changing on time scales of a few seconds. This and other characteristics of ISAR imaging make the problem of automatic recognition of ISAR images quite distinct from the recognition of optical images. The nature of ISAR imaging of ships, and single-frame and multiple-frame techniques for segmentation, feature extraction, and classification are described. Results are shown which illustrate a capability for automatic recognition of ISAR ship imagery     

THE ELECTRON DRIFT INSTRUMENT FOR CLUSTER

The Electron Drift Instrument (EDI) measures the drift of a weak beam of test electrons that, when emitted in certain directions, return to the spacecraft after one or more gyrations. This drift is related to the electric field and the gradient in the magnetic field, and these quantities can, by use of different electron energies, be determined separately. As a by-product, the magnetic field strength is also measured. The present paper describes the scientific objectives, the experimental method, and the technical realization of the various elements of the instrument.     

Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration     

Decentralized Filtering and Redundancy Management for Multisensor Navigation

Failure detection and redundancy management is discussed for avionics applications of integrated navigation involving coordinated use of multiple simultaneous sensor subsystems such as GPS, JTIDS, TACAN, VOR/DME, ILS, an inertial navigation system (INS), and possibly even Doppler AHRS. A brief high level survey is provided to assess the status of those techniques and methodologies advertized as already available for handling the challenging real-time failure detection, redundancy management, and Kalman filtering aspects of these systems with differing availabilities, differing reliabilities, differing accuracies, and differing information content/sampling rates. Following the status review, a new failure detection/redundancy management approach is developed based on voter/monitoring at both the raw data and at the filtered-data level, as well as using additional inputs from hardware built-in-testing (BIT) and from specialized tests for subsequent failure isolation in the case of ambiguous indications. The technique developed involves use of Gaussian confidence regions to reasonably account for the inherent differences in accuracy between the various sensor subsystems. Online estimates of covariances from the Kalman filter are to be used for this purpose (when available). A technique is provided for quantitatively evaluating both the probability of detecting failed component subsystems and the probability of false alarm to be incurred, which is then to be traded off as the basis for rational selection of the thresholds used in the automated decision process. Moreover, the redundancy management procedure is demonstrated to be amenable to pilot or navigation operator prompting and override, if necessary.     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.