P.R. Mahapatra

A jerk model for tracking highly maneuvering targets

A model of target motion in three-dimensional space that includes position derivatives up to the third order is developed. Compared with available models, which include terms at the most up to the second derivative, the model introduced in this work, called the jerk model, can more accurately describe agile target maneuvers which are likely to contain significant higher order derivatives. A compatible 4-state Kalman filter to perform tracking in conjunction with the jerk model is also presented, and an initialization procedure for the filter is provided. The improved performance of the jerk model over a lower order model is illustrated through numerical simulation.

The proportional navigation dilemma-pure or true?

Two generic classes of proportional navigation (PN) laws are compared in detail. One class consists of pursuer-velocity-referenced systems, which include pure proportional navigation (PPN) and its variants; the second category consists of line-of-sight- (LOS-) referenced systems such as true proportional navigation (TPN), generalized true proportional navigation (GTPN), and generalized guidance laws. The existing closed-form solutions are discussed in detail, and the classical linear and quasilinear analytical solutions are summarized. A critical comparison is then made with regard to the definition, implementation, and analytical aspects of the guidance laws, including the method, the nature of solution, and an appraisal of the behavior of the pursuer motion resulting from the laws. It is established that, in spite of some restricted advantages in the solvability of the equations of motion, the LOS-referenced PN schemes suffer from serious limitations in terms of implementation and trajectory behavior. Among the major drawbacks are forward velocity variation requirement, relatively large control effort requirement, restrictions on initial engagement conditions to ensure intercept, lack of robustness, and possibility of unbounded acceleration. It is concluded that PPN is a better guidance law in a practical sense than TPN and its generalizations. >

Two Methods of Ambiguity Resolution in Pulse Doppler Weather Radars

A comparison is made of the performance of a weather Doppler radar with a staggered pulse repetition time and a radar with a random (but known) phase. As a standard for this comparison, the specifications of the forthcoming next generation weather radar (NEXRAD) are used. A statistical analysis of the spectral moment estimates for the staggered scheme is developed, and a theoretical expression for the signal-to-noise ratio due to recohering-filtering-recohering for the random phase radar is obtained. Algorithms for assignment of correct ranges to pertinent spectral moments for both techniques are presented.

Practical Algorithms for Mean Velocity Estimation in Pulse Doppler Weather Radars Using a Small Number of Samples

Doppler weather radars with fast scanning rates must estimate spectral moments based on a small number of echo samples. This paper concerns the estimation of mean Doppler velocity in a coherent radar using a short complex time series. Specific results are presented based on 16 samples. A wide range of signal-to-noise ratios are considered, and attention is given to ease of implementation. It is shown that FFT estimators fare poorly in low SNR and/or high spectrum-width situations. Several variants of a vector pulse-pair processor are postulated and an algorithm is developed for the resolution of phase angle ambiguity. This processor is found to be better than conventional processors at very low SNR values. A feasible approximation to the maximum entropy estimator is derived as well as a technique utilizing the maximization of the periodogram. It is found that a vector pulse-pair processor operating with four lags for clear air observation and a single lag (pulse-pair mode) for storm observation may be a good way to estimate Doppler velocities over the entire gamut of weather phenomena.

Accurate solution of proportional navigation for maneuvering targets

An accurate solution is presented of the nonlinear differential equations describing motion under proportional navigation when the target is laterally maneuvering. A quasilinearization (QL) approach is used, followed by a perturbation technique to obtain closed-form solutions for trajectory parameters. An explicit expression for the pursuer lateral acceleration is derived and shown to contain contributions due to initial heading error and target maneuver, with a coupling between the two effects. The solution is shown to be a substantial and consistent generalization or an earlier accurate solution for nonmaneuvering targets and also of classical linear solutions for maneuvering targets. The generalized QL solution presented provides very accurate estimates of pursuer lateral acceleration over a much broader range of engagement geometries and target maneuvers than presently available closed-form solutions. >

Mixed coordinate tracking of generalized maneuvering targets using acceleration and jerk models

In a recent paper the authors introduced an all-Cartesian formulation of a jerk model for tracking highly maneuvering targets. Here a more complex but realistic case is considered, where target motion modeling and tracking are carried out in the 3-D Cartesian frame using measurements obtained in a spherical system. The transformation of the measurements into the Cartesian system results in nonlinear measurement equations. We solve the problem using an extended Kalman filter (EKF) approach, and also treat the earlier acceleration model similarly for comparison of results.

Multisensor Observation of an Atmospheric Undular Bore

Abstract A detailed and unique multisensor observation of an undular bore is presented. The data include those from rawinsonde, satellite, two Doppler radars, and a tall instrumented tower. Noteworthy are Doppler radar images that resolve the waves characteristics and capture a good part of its spatial extent. The basic parameters of the wave train are established from the observations.

Sensors and systems to enhance aviation safety against weather hazards

The authors describe the physics of adverse weather, the basics of Doppler engineering, and a host of advanced sensing systems-some with the ability to autonomously identify and track storm conditions-for all stages of airplane travel. Three major new Doppler radar systems are discussed: the next generation weather radar, the terminal Doppler weather radar, and the airport surveillance radar with a dedicated weather channel. Other relatively simple new instruments for aviation weather support include the low level wind shear alert system, the Doppler wind profilers, the automated weather observation system, and the automated surface observation system. These systems are designed to perform higher level functions such as detection, characterization, and hazard potential estimation of aviation-significant weather phenomena, as well as their communication and display automatically. >

Recent radar observations of asteroid 1566 Icarus

Abstract We report Doppler-only radar observations of Icarus at Goldstone at a transmitter frequency of 8510 MHz (3.5 cm wavelength) during 8–10 June 1996, the first radar detection of the object since 1968. Optimally filtered and folded spectra achieve a maximum opposite-circular (OC) polarization signal-to-noise ratio of about 10 and help to constrain Icarus physical properties. We obtain an OC radar cross section of 0.05 km 2 (with a 35% uncertainty), which is less than values estimated by Goldstein, 1969 and by Pettengill et al., 1969 , and a circular polarization (SC⧸OC) ratio of 0.5±0.2. We analyze the echo power spectrum with a model incorporating the echo bandwidth B and a spectral shape parameter n , yielding a coupled constraint between B and n . We adopt 25 Hz as the lower bound on B , which gives a lower bound on the maximum pole-on breadth of about 0.6 km and upper bounds on the radar and optical albedos that are consistent with Icarus tentative QS classification. The observed circular polarization ratio indicates a very rough near-surface at spatial scales of the order of the radar wavelength.

Emitter Location Independent of Systematic Errors in Direction Finders

A scheme is suggested for the passive location of radio emitter position by using a mobile direction finder. The vehicle carrying the direction finder is made to maneuver such that the apparent direction of arrival is held constant. The resulting trajectory of the vehicle is a logarithmic spiral. The true direction of arrival can be obtained by monitoring the parameters of the spiral trajectory without using the value of the direction fimder reading. Two specific algorithms to eliminate direction finder bias are presented and their sensitivity to random errors in measurement assessed.