Expressions in Closed Form for the Angular Accuracy of a Scanning Radar

Closed-form expressions are given for the standard deviation of the error in estimating angle (usually azimuth) in a scanning radar. The formulas apply to Swerling's lower bound and to the error using a pulse-to-pulse two-pole filter. They apply to non-fluctuating and Swerling II targets and hold for all signal-to-noise ratios. Comparison with graphical results in the literature shows that the average deviation obtained using the formulas is less than 4 percent.     

Stability of Gyro in a Vehicle Spinning with Uncertain Angular Velocity

The analysis of a single-axis rate gyroscope mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using circle criterion, it is shown that the gimbal motion is globally asymptotically stable if Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. A simple analytical relation for the selection of gyro parameters for stability is derived.     

Maximum Likelihood Elevation Angle Estimates of Radar Targets Using Subapertures

The maximum likelihood estimates of the elevation angles of two closely spaced targets within the beamwidth is considered. For an array divided into three subapertures, a simple, closed form solution is found whose accuracy compares favorably to the maximum likelihood estimate which uses all the individual elements. Simulation results are presented for the case of a radar target located over a smooth reflecting surface.     

The Effect of Differential Time Delays in the LMS Feedback Loop

The effect of differential time delay in the feedback loops of an LMS adaptive array is examined. Differential time delay is shown to have two effects on array performance. First, it causes the weights to oscillate during weight transients. Second, it degrades the output signal-to-interference-plus-noise ratio (SINR) from the array. Weight oscillation occurs when the phase shifts in the LMS loop are not matched at the signal carrier frequency. SINR degradation depends on signal bandwidth: the wider the bandwidth, the larger the degradation.     

Three Mile Island? Lessons for America

The great fear of a nuclear castastrophe is the prime lesson learned from the Three Mile Island accident. This fear is real and creates a major risk to our society. Although the probability of a major release of radioactivity occurring at a given plant in a given year is low, the rapidly increasin number of plants around the world increases the probability that such a catastrophe will occur someplace in the next few years. When a major release does occur, people will demand an end to the use of energy from nuclear power. We are at grave risk in not having an alternative, in not providing a choice in time. The alternatives are clearly defined. But we need to see that the resources are made available to develop them.     

Concatenated Sequences for Spread Spectrum Systems

Concatenated sequences are suggested and developed for use in spread spectrum (SS) systems. Special receiver realization is discussed and it is shown that the concatenated sequences offer great advantage in reducing the size of the matched filter correlators (MFC) in the SS receiver. Experimental systems have been built using concatenated sequences and their performance is reported here. It has been shown that a processing gain of 60 is obtainable with a 15 × 4 concatenated sequence which requires three tapped delay lines (TDL), two of length 15 and one of 4. Thus a total of only 34 delay units (with a nonlinear interface network, only 19 delay units) are required. Teleprinter signals can be transmitted over telephone channels using a bandwidth (BW) expansion of 60 with an input signal-to-noise ratio (SNR) of only -5.1 dB, resulting in a character- error-rate of 1 in 103. Techniques have been developed to reduce the sidelobe levels in the aperiodic autocorrelation functions (ACF) of the pseudonoise (PN) codes. For 15 length and 7 length PN sequences, sidelobes are reduced by 9 dB and 9.4 dB, respectively, using transversal filters. Application of the SS systems to the problem of multiaccessing and antijamming are discussed.     

Gravity Sensors and the Principle of Equivalence

The tensor characteristics of the inertial fields created by acceleration and rotation, and the gravitational fields created by masses are discussed. Although it is sometimes thought that it is impossible to distinguish between gravitational and inertial effects because of Einstein's principle of equivalence, these effects do have different, detectable tensor characteristics. The principle of equivalence is only strictly applicable at a point, while the instruments to measure these tensor fields exist over a finite region. The inertial field created by acceleration is a uniform vector field and has no gradients, while the inertial field created by rotation has a uniform cylindrically symmetric tensor gradient but none of higher order. The gravitational field created by a mass is highly nonuniform with essentially no limit to the number of higher order gradients. These differences make it theoretically possible to independently measure gravitation, rotation, and acceleration effects; to do so, some form of differential force sensor with tensor response characteristics must be used. The standard technique is static, using differential accelerometers to sense the spatial gradient characteristics of the fields. A more promising technique is dynamic; by rotation of the differential sensor, the static spatial variations are transformed into temporal variations with various frequency components. It is then possible to distinguish between the various fields by frequency filtering.     

Leading Edge Estimation Errors

The leading edge estimator (LEE) of a pulse signal is defined as the instant at which a filtered version of the received noisy signal passes a preset threshold. A rigorous analysis for a rectangular pulse model of the signal results in an exact probability density function for the LEE, valid within the time interval of the leading edge of the filtered pulse. Possible occurrence of the threshold crossing outside of this interval is considered to be an anomalous estimate, since it leads to a gross error in comparison with the regular cases. It is found that the density function of the LEE error is asymmetrical and therefore biased, that the probability PA of anomalous estimation increases with the filter bandwidth, thus setting a well definable limit to the latter and that, for prespecified PA, the minimum bias and variance are proportional, respectively, to R-1 and R-2, minima being obtained by allowing for the largest bandwidth compatible with PA. On the other hand, for given bandwidth the variance decreases only as R-1. Here R is the signal-to-noise energy ratio. Results are presented in form of parameterized graphs.     

Cross Sections and Radar Equation for Nonlinear Scatterers

The nonlinear system concepts of nonlinear transfer functions are extended to nonlinear cross sections which may be used to quantitatively describe the characteristics of a nonlinear scatter. The concept of nonlinear cross sections is used to generalize the radar equation for nonlinear scattering objects.     

Adaptive False Alarmrm Regulation in Double Threshold Radar Detection

In practical situations the false alarm probability in double threshold radar detection, sometimes known as binary integration with sliding window detection, is dependent on the nonstationarity and azimuthal correlation of the clutter which is present. Control of the false alarm probability can be achieved, to a certain extent, by the adjustment of the second threshold in the detection process. In this study two adaptive control techniques which are based on the statistical characteristics of the data are compared. Comparing the results for a technique based on first-order statistics with one based on second-order statistics, it is shown that the second-order, or correlation sensitive, technique can give a reduction of 30 to 45 percent in the false alarm probability with no corresponding loss in the detection probability. An interesting aspect of the results is the fact that the effects of the size of the sample area and the bias in the correlation estimator are clearly evident.