Characterization of Kalman filter residuals in the presence ofmismodeling

The mean and covariance of a Kalman filter residual are computed for specific cases in which the Kalman filter model differs from a linear model that accurately represents the true system (the truth model). Multiple model adaptive estimation (MMAE) uses a bank of Kalman filters, each with a different internal model, and a hypothesis testing algorithm that uses the residuals from this bank of Kalman filters to estimate the true system model. At most, only one Kalman filter model will exactly match the truth model and will produce a residual whose mean and standard deviation have already been analyzed. All of the other filters use internal models that mismodel the true system. We compute the effects of a mismodeled input matrix, output matrix, and state transition matrix on these residuals. The computed mean and covariance are compared with simulation results of flight control failures that correspond to mismodeled input matrices and output matrices     

A Note on the Ambiguity of Troposcatter Aircraft Interference Patterns

Earlier investigators of troposcatter propagation phenomena have suggested that aircraft-created interference patterns observed at the receiving site can be used to measure aircraft motion within and near the common volume region. A simplified signal and scattering model is used to show that these interference signatures are ambiguous unless prior knowledge of the aircraft trajectory is available.     

Interrelationship of single-filter and multiple-model adaptivealgorithms

An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model     

Multiple-model adaptive estimation using a residual correlationKalman filter bank

We propose a modified multiple model adaptive estimation (MMAE) algorithm that uses the time correlation of the Kalman filter residuals, in place of their scaled magnitude, to assign conditional probabilities for each of the modeled hypotheses. This modified algorithm, denoted the residual correlation Kalman filter bank (RCKFB), uses the magnitude of an estimate of the correlation of the residual with a slightly modified version of the usual MMAE hypothesis testing algorithm to assign the conditional probabilities to the various hypotheses that are modeled in the Kalman filter bank within the MMAE. This concept is used to detect flight control actuator failures, where the existence of a single frequency sinusoid (which is highly time correlated) in the residual of an elemental filter within an MMAE is indicative of that filter having the wrong actuator failure status hypothesis. This technique results in a delay in detecting the flight control actuator failure because several samples of the residual must be collected before the residual correlation can be estimated. However, it allows a significant reduction of the amplitude of the required system inputs for exciting the various system modes to enhance identifiability, to the point where they may possibly be subliminal, so as not to be objectionable to the pilot and passengers     

Performance enhancement of a multiple model adaptive estimator

We describe performance improvement techniques for a multiple model adaptive estimator (MMAE) used to detect and identify control surface and sensor failures on an unmanned flight vehicle. Initially failure identification was accomplished within 4 s of onset, but by removing the “β dominance” effects, bounding the hypothesis conditional probabilities, retuning the Kalman filters, increasing the penalty for measurement residuals, decreasing the probability smoothing, and increasing residual propagation, the identification time was reduced to 2 s     

COMPTEL observations of gamma-ray bursts

The COMPTEL experiment on GRO images 0.7 – 30 MeV celestial gamma-radiation that falls within its 1 steradian field of view. During the first fifteen months in orbit, preliminary localizations from BATSE triggers indicated that about 1 in 6 cosmic events could have fallen within COMPTEL's field of view. We summarize work on the brightest of these gamma-ray bursts and present new position constraints for GRB 911118 and GRB 920622.