Optimum FFT-based frequency acquisition with application toCOSPAS-SARSAT

In the case of a single sinusoid or multiple well-separated sinusoids, a coarse estimator consisting of a windowed Fourier transform followed by a fine estimator which is an interpolator is a good approximation to an optimal frequency acquisition and measurement algorithm. The design tradeoffs are described. It is shown that for the fine-frequency estimator a good method is to fit a Gaussian function to the fast-Fourier-transform (FFT) peak and its two neighbors. This method achieves a frequency standard deviation and a bias in the order of only a few percent of a bin. In the case of short-time stationarity, for a moderate number of averages and for an adaptive threshold detector, only between 0.5 and 1 dB is lost when averaging is traded off for FFT length, in contrast to the asymptotic result of 1.5 dB. The COSPAS-SARSAT satellite system for emergency detection and localization is used to illustrate the concepts. The algorithm is analyzed theoretically, and good agreement is found with test results     

Multiposition alignment of strapdown inertial navigation system

The authors demonstrate that the stationary alignment of strapdown inertial navigation system (SDINS) can be improved by employing the multiposition/technique. Using an observability analysis, it is shown that an optimal two-position alignment not only satisfies complete observability conditions but also minimizes alignment errors. This is done by analytic rank testing of the stripped observability matrix and numerical calculation of the error covariance. It is also shown that an optimal three-position alignment accelerates the convergence of the alignment error compared with two-position alignment     

The organic matter of comet Halley as inferred by joint gas phase and solid phase analyses

During encounters with comet Halley, the experiment PICCA onboard GIOTTO measured the gas phase organic ion composition of the coma and the experiment PUMA onboard VEGA-1 measured the dust composition. Joining both results, we obtain a consistent picture of the parent organic matter from which dust and gas is produced. One recognizes a complex unsaturated polycondensate, which splits during coma-formation into the more refractory C=C,C-N-containing dust part, and the more volatile C=C,C-O-containing gas part. The responsible exothermal chemical reactions, which are triggered by the sunlight, may play a major role in the dynamics of coma formation.This paper is a shortened and upgraded version of Krueger, F.R., Korth, A., and Kissel, J.: 1989, in S. Chang (ed.) Proc. of the ROSETTA Conf., Milpitas CA, January 1989, submitted.     

Optimum gain control for A/D conversion using digitized I/Q data inquadrature sampling

Calculation of optimum gain for minimum distortion due to A/D (analog-to-digital) conversion requires the estimation of the input signal strength. To use a common AGC (automatic gain control) for both the I/Q (in-phase and quadrature) signals, it is efficient to estimate the input signal strength using the quantized A/D output from both channels. Assuming a Gaussian input, the relationship between σ of the input of the A/D converter and E(|x|+|y|) and E(max(|x|,|y|)+1/2 min (|x|,|y|)) for t quantized I/Q output x and y is derived. Numerical results obtained using the derived expression and the statistical data obtained through simulation show excellent agreement. It is concluded that, because of its simplicity, the cubic equation obtained by fitting the numerical results should be useful     

Comments on `Tracking a maneuvering target using input estimation''

P.L. Boglar (see ibid., vol.AES-23, no.3, p.298-310, May 1987) developed a recursive formulation of the Chan, Hu, and Plant (CHP) algorithm, and the results of the simulation verified the performance improvements. The commenter claims that Bogler obtained an incorrect recursive formulation of input estimation because he incorrectly used the formulation of the Kalman filter. The commenter presents calculations that aim to demonstrate this claim     

Augmenting the Linear Variance Equation

A technique is developed to convert the covariance analysis ofcertain time-varying linear systems into time-invariant form, thusallowing an arbitrary time step for the solution of the differentialequations. The result is accomplished by augmenting the linearvariance equation and augmenting the state vector if necessary. Themethod is illustrated with an example showing the covariancepropagation of ring laser gyro errors in a strapdown inertial systeminto navigation errors during turns.     

Carrier Tracking by Smoothing Filter Improves Symbol SNR

The potential benefit of using a smoothing filter to estimate a carrier phase over use of phase-locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of an all-digital coherent demodulation receiver. These are residual carrier PLL, sideband-aided residual carrier PLL, and finally sideband aided with Kalman smoother. The average symbol SNR after losses due to carrier phase estimation is computed for different total power SNRs, symbol rates, and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.7 dB over sideband-aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to residual carrier loop is often in excess of 1 dB.     

Instrument Failure Detection in Partially Observable Systems

Instrument failure detection using the dedicated observer scheme (DOS) depends on partial state observability through each instrument which is monitored. For instrument fault detection by the DOS technique, a quantitative measure of partial state observability is established for each instrument and used to determine a necessary condition on the output structure of the system. This measure, called the internal redundancy of the instrument, indicates the complexity of the logic required for failure detection, and it also indicates where some hardware redundancy can be introduced into the system to improve the fault detection capability of the DOS. The principles developed are applied to a simulation of the pitch axis autopilot of the A7 jet aircraft.     

Adaptive Tracking Filter for Maneuvering Targets

A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.     

Measurement of Distributed Targets with the Random Signal Radar

A model of a distributed target as a collection of independent, Poisson distributed point scatterers or scattering centers in a range-velocity target space is introduced and is characterized by a deterministic function called the ?scatterer density function.? This function is the density of the point scatterers in the range-velocity space and can be estimated in a relatively straightforward manner by any radar having adequate resolution in both range and velocity and no ambiguities in the region occupied by the distributed target. The use of the random signal radar with a correlator receiver is considered here and the statistical properties of the correlator output, when the return signal is from a distributed target, are derived. It is shown that the spectral density is simply related to the scatterer density function. The technique is illustrated by an example in which the target is a tornado modeled as a cylinder with constant angular velocity. The example suggests that is a possible to remotely estimate the radar cross section per unit volume as a function of distance from the center of the tornado.