Tracking the Frequency Translation of a Sum of Orthogonal Sinusoids

The maximum likelihood approach is used to derive a method for estimating and tracking the frequency translation of a signal consisting of a sum of orthogonal sinusoids corrupted by additive white noise. The likelihood function is reduced to an equivalent statistic expressed in terms of the squared magnitude of the finite Fourier transform of the received signal. A function that generates an error signal for a frequency translation tracking loop is derived, and a method of generating the error signal using the discrete Fourier transform (DFT) of the received signal weighted by a linear ramp is suggested. Two noise-free examples are presented.     

Analysis of Detection Probability for the Acoustooptic Receiver

A numerical method is described for analyzing the performance of an acoustooptic receiver. The method provides output waveforms, probability density functions for samples of the output, and detection probabilities for output samples. The approach is general in that input pulse envelope shapes, pulse offset frequencies, and output rilter magnitude responses are arbitrary. The basic analysis is also independent of the shape of the optical beam and of the photodiode windows.     

Small Aperture Angle Measurement for Active Echo Location Systems

The problem of bearing estimation for active systems is examined from the point of view of the generalized wideband ambiguity function (GAF). The maximum likelihood (ML) estimator is derived and its local and global properties are discussed. A structure is proposed which searches the three-dimensional ambiguity surface in two stages first, in range-Doppler, and then, in bearing with the goal of reducing search complexity when utilizing highly resolvent waveforms. Comparisons are made between the ML estimators and structures utilizing phase information which generate closed form estimators. The beneficial results of full bandwidth utilization are discussed in terms of both local and global properties of the GAF.     

Clutter Map CFAR Analysis

An analysis of the probability of target detection for a clutter map CFAR using digital exponential filtering has been performed. General performance equations are derived. The probability of detection versus signal-to-noise ratio is plotted for a false alarm probability of 1.E-06 for several weight values. The CFAR loss is plotted for a detection probability of 0.9 and false alarm probabilities of 1.E-06 and 1.E-08.     

Instantaneous Frequency Estimation Using Adaptive Linear Predictor Weights

A computationally efficient scheme for estimating the digital instantaneous frequencies of narrowband inputs is introduced. The frequency estimates are obtained by searching for minima of the inverse input power spectrum. This spectrum is estimated at each input sample from the weights of an adaptive linear predictor which uses the LMS (least mean square) algorithm to update its weights. The related minima are sought via an iterative search algorithm, referred to as the iterative frequency estimator. This algorithm is computationally more efficient than available methods, and also provides a higher resolution. Simulation results are included; these include tracking of random message sequences in FM signals, and the formant frequency estimation of speech.     

Modeling Random Gyro Drift Rate by Data Dependent Systems

A new modeling procedure is presented in which a mathematical model for random gyro drift rate is obtained directly from the original observations without requiring any theoretical conjectures or preprocessing of the data. The adequate model so obtained confirms the presence of a random walk component causing the "steady state" drift and a stochastic component of the nature of correlated noise. It also provides a quantitative measure of the relative contribution of each component, useful in determining the quality of the gyro in guidance over extended periods.     

A Nonlinear Tracker Using Attitude Measurements

The subject of this paper involves tracking the present position of a maneuvering aircraft as well as predicting its future position. A tracking filter is developed that uses aircraft attitude angles (yaw, pitch, roll) in addition to the usual radar measurements. Computer simulation of tracker performance when tracking violently maneuvering aircraft indicates that a dramatic improvement is obtained by using attitude information. The approach taken is to develop a 12-or 15-state extended Kalman filter that models both translational and rotational degrees of freedom. By measuring and estimating attitude it is possible to approximately determine the magnitude and direction of the force system acting on the vehicle and therefore determine vehicle linear acceleration. Knowledge of acceleration is then used to improve the estimate of present and future position of the vehicle being tracked. Simulation of a T-38 aircraft performing a 5 g turn indicates that the new tracker produces maximum trajectory prediction errors that are 36 percent of the errors experienced by more conventional trackers.     

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.     

Experimental Detection of Anomalous Mode-C Reports Using Radar Data

A new methodology to scan automated radar terminal system (ARTS-III) data for aircraft tracks exhibiting probable mode-C encoder/transponder faults is described. The tracks of more than 8000 climbing or descending aircraft, recorded at the Seattle-Tacoma terminal area, were analyzed using this method. Based on this sample, the probability of the previously recognized "stuck C-bit" error is estimated to be 0.44 percent (0.31-0.61 percent, 95 percent confidence). In addition, a new, more subtle error, here termed the "deficient response," was discovered which is estimated to occur with a probability of 0.77 percent (0.59-0.98 percent, 95 percent confidence). Subsequent tests found this new error to have much less impact on traffic alert and collision avoidance system (TCAS) performance than does the stuck C-bit error.     

Normalized LMS Algorithm Degradation Due to Estimation Noise

The steady-state weight vector derived by either the least mean square (LMS) or normalized least mean square (NLMS) algorithms has random deviations from the optimum values. These deviations increase the steady-state residue power. A previous paper derived the LMS weight noise effects for a multiple sidelobe canceller (MSLC) application. This paper describes the NLMS weight noise effects. It is shown that for a thermal noise environment, the weight noise effect for the LMS algorithm is insignificant but is quite significant for the NLMS algorithm. Calculations for example noise plus interference environments imply that the NLMS weight noise effects are always larger than that for LMS.