Cascaded detector for multiple high-PRF pulse Doppler radars

A postdetection design methodology for a multiple high-pulse-repetition frequency (PRF) pulse Doppler radar has been developed. The postdetection processor consists of an M out of N detector where range and target ambiguities are resolved, followed by a square-law detector which enhances the minimum signal-to-noise (S/N) power-ratio per pulse burst performance. For given probabilities of false alarm and detection, formulas are derived from which the three thresholds associated with the cascaded detector can be found. Fundamental tradeoffs between the minimum S/N required, number of ghosts, and the number of operations (NOPs) that the cascaded detector must perform are identified. It is shown that the NOPs and the number of ghosts increase and the minimum S/N required decreases as the binary M out of N detector passes more detections to the square-law detector     

Digital system design in the presence of single event upsets

The authors consider the effects of single event upsets (SEUs) on digital systems, and show techniques for designing reliable systems with current levels of SEU protection. Three main systems are discussed: main memory, logic, and cache memory. A design for the main and cache memory subsystems that are SEU protected is also described. With SEU defined in bit days p, and using single error correction, it is shown that for all subsystems considered, an effective upset rate which is proportional to the product of p² and the time between corrections, or scrub time, can be obtained. Data for memory chip size and performance derived from the gallium-arsenide (GaAs) pilot lines funded by the Defense Advanced Research Projects Agency (DARPA) throughout the 1980s are used     

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     

Identification of rational transfer function from frequencyresponse sample

A method for identifying a transfer function, H(z)=A(z)/B(z), from its frequency response values is presented. Identifying the transfer function involves determining the unknown degrees and coefficients of the polynomials A(z) and B( z), given the frequency response samples. The method for finding the parameters of the transfer function involves solving linear simultaneous equations only. An important aspect of the method is the decoupled manner in which the polynomials A(z) and B(z) are determined. The author presents two slightly different derivations of the linear equations involved, one based on the properties of divided differences and the other using Vandermonde matrices or, equivalently, Lagrange interpolation. A matrix synthesized from the given frequency response samples is shown to have a rank equal to the number of poles in the system     

A parallel square-root algorithm for modified extended Kalmanfilter

A parallel square-root algorithm and its systolic array implementation are proposed for performing modified extended Kalman filtering (MEKF). The proposed parallel square-root algorithm is designed based on the singular value decomposition (SVD) and the Faddeev algorithm, and a very large scale integration (VLSI) systolic array architecture is developed for its implementation. Compared to other square root Kalman filtering algorithms, the proposed method is more numerically stable. The VLSI architecture described has good parallel and pipelining characteristics in applying to the MEKF and achieves higher efficiency. For n-dimensional state vector estimations, the proposed architecture consists of O(2n²) processing elements and uses O ((s+17)n) time-steps for a complete iteration at each instant, in contrast to the complexity of O((s+6) n³) time-steps for a sequential implementation, where s≈log n     

The autocorrelation of m-sequences over nonprime finitefields

Nonbinary m-sequences (maximal length sequences) for spread-spectrum communication systems that have a two-level autocorrelation are presented. The autocorrelation function of an m -sequence over the Galois field of q elements GF(q), where q=p^k, for p a prime and k an integer greater than 1, is developed and shown to be bilevel when the elements of GF(q) are expressed as elements of a vector space over the pth roots of unity     

Distribution of general noncentral positive definite quadratic formin K-dimensions

The authors present a series solution using Hermite polynomials to the long-standing problem of computing the probability P that positive definite noncentral quadratic form d(x) of a Gaussian random vector x∈R satisfies d( x)⩽r² for any given r∈R. This problem has wide applications in radar, tracking, air traffic control, etc. The fast-converging series solution presented is very accurate and can be performed rapidly using the recursion relations for Hermite polynomials     

Tracking multitarget in cluttered environment

A method for multitarget tracking and initiating tracking in a cluttered environment is proposed. The algorithm uses a sliding window of length uT (T is the sampling time) to keep the measurement sequence at time k. Instead of solving a large problem, the entire set of targets and measurements is divided into several clusters so that a number of smaller problems are solved independently. When a set of measurements is received, a new set of data-association hypotheses is formed for all the measurements lying in the validation gates within each cluster from time K-u+1 to K. The probability of each track history is computed, and, choosing the largest of these histories, the target measurement is updated with an adaptive state estimator. A covariance-matching technique is used to improve the accuracy of the adaptive state estimator. In several examples, the algorithm successfully tracks targets over a wide range of conditions     

Optimal speckle reduction in polarimetric SAR imagery

Speckle is a major cause of degradation in synthetic aperture radar (SAR) imagery. With the availability of fully polarimetric SAR data, it is possible to use the three complex elements (HH, HV, VV) of the polarimetric scattering matrix to reduce speckle. The optimal method for combining the elements of the scattering matrix to minimize image speckle is derived, and the solution is shown to be a polarimetric whitening filter (PWF). A simulation of spatially correlated, K-distributed, fully polarimetric clutter is then used to compare the PWF with other, suboptimal speckle-reduction methods. Target detection performance of the PWF, span, and single-channel |HH|² detectors is compared with that of the optimal polarimetric detector (OPD). A novel, constant-false-alarm-rate (CFAR) detector (the adaptive PWF) is as a simple alternative to the OPD for detecting targets in clutter. This algorithm estimates the polarization covariance of the clutter, uses the covariance to construct the minimum-speckle image, and then tests for the presence of a target. An exact theoretical analysis of the adaptive PWF is presented; the algorithm is shown to have detection performance comparable with that of the OPD     

Finding the best set of K paths through a trellis withapplication to multitarget tracking

A solution is presented to the problem of finding the best set of K completely unmerged paths through a trellis with M _i⩾K states at depth i in the trellis, i=0, 1, 2, . . ., N. Here, `best set' means that the sum of the metrics of all K paths in the set is minimized, and `completely unmerged' means that no two paths pass through a common state. The solution involves using the Viterbi algorithm on an expanded trellis. This result is then used to separate the tracks of K targets optimally in a simplified model of a multitarget radar system. The model includes measurement errors and false alarms, but it does not include the effects of missing detections or merged measurements     

On the uniform sampling of a sinusoidal signal

It is generally accepted that a monochromatic signal such as sin 2πWt (W>0) must be sampled at a uniform rate greater than the ostensible Nyquist rate of 2W samples per to effect a reconstruction of the signal. It is shown that a sinusoid of frequency W Hz is completely determined by its samples taken at the uniform rate of 2r samples per second, where r>0 is arbitrary subject only to the restriction that W ≠kr for any positive integer k. In particular, a pure sinusoid may be sampled uniformly without loss of information at arbitrarily small rates     

Nonparametric rank detectors on quantized radar video signals

Uniform randomization of ties is required for defining distribution-free ranks of independent and identically distributed quantized samples. Formulas of rank probabilities are given and applied to radar detection under quantized video samples. For some detectors, and assuming Gaussian noise, the asymptotic loss L_∞(q) is calculated versus the normalized quantization step q, and the loss L(q) is estimated by Monte Carlo simulations. Both of these resulted in monotonic functions of q (0<q<1.1) that are independent of the other parameters. Furthermore, L(q)≈L_∞(q )⩽0.45 dB, as q<0.8. The quantization step q is normalized with respect to the noise standard deviation     

Convergence bounds of an SMI/Gram-Schmidt canceler in colored noise

The performance of the sampled matrix inversion (SMI) adaptive algorithm in colored noise is investigated using the Gram-Schmidt (GS) canceler as an analysis tool. Lower and upper bounds of average convergence are derived, indicating that average convergence slows as the input time samples become correlated. When the input samples are uncorrelated, the fastest SMI algorithm convergence occurs. When the input samples are correlated then the convergence bounds depend on the number of channels N, the number of samples per channels K , and the eigenvalues associated with K×K correlation matrix of the samples in a given channel. This matrix is assumed identical for all channels     

Periodic ambiguity function of CW signals with perfect periodicautocorrelation

A periodic ambiguity function (PAF) is discussed which describes the response of a correlation receiver to a CW signal modulated by a periodic waveform, when the reference signal in the receiver is constructed from an integral number N, of periods T, of the transmitted signal. The PAF is a generalization of the periodic autocorrelation function, to the case of non-zero Doppler shift. It is shown that the PAF of N periods is obtained by multiplying the PAF of a single period by the universal function sin(Nπν T)/N sin(πνT), where ν is the Doppler shift, to phase-modulated signals which exhibit perfect periodic autocorrelation when there is no Doppler shift. The PAF of these signals exhibits universal cuts along the delay and Doppler axes. These cuts are functions only of t, N and the number M, the modulation bits in one period     

Estimation of radar detection and false alarm probability

The accuracy with which detection and false alarm probabilities can be estimated with a limited amount of measured radar data is addressed. A simple simulation method for estimating the statistical performance of a radar detection system is presented. Confidence limits and a rule of thumb for accuracy for the estimated probabilities are presented along with procedures for calculating them. It is concluded that the minimum value of N used in a detection radar signal simulation should be 10/P_FA when the simple simulation method is used, where P_FA is the probability of false alarm, and that a value closer to 100/P _FA is preferable     

Position and force control of coordinated multiple arms

A technique is presented for controlling multiple manipulators which are holding a single object and therefore form a closed kinematic chain. The object, which may or may not be in contact with a rigid environment, is assumed to be held rigidly by n robot end-effectors. The derivation is based on setting up constraint equations which reduce the 6×n degrees of freedom of n manipulators each having six joints. Additional constraint equations are considered when one or more degrees of freedom of the object is reduced due to external constraints. Utilizing the operational space dynamic equations, a decoupling controller is designed to control both the position and the interaction forces of the object with the environment. Simulation results for the control of a pair of two-link manipulators are presented     

Performances of order statistics CFAR

A previous analysis of order-statistics constant-false-alarm-rate (OS-CFAR) radar receiving a single pulse from a Rayleigh fluctuating target in a Rayleigh background is extended to a Rayleigh-plus-dominant target. The analysis includes effects of a multitarget environment. A detailed comparison of OS-CFAR, cell-averaging (CA) CFAR, and censored CA-CFAR is provided for a Rayleigh target in the presence of strongly interfering targets. The false-alarm analysis of OS-CFAR is extended to the more general case of a Weibull background. The deterioration of the CFAR property of OS as the shape factor, C, of a Weibull probability density function changes from Rayleigh (C=2) to a longer-tailed one (C<2) is evaluated. The analytic comparison between CA-CFAR and OS-CFAR is extended to an integration of pulses reflected from a Swerling II target. The OS-CFAR performance (with and without interfering targets) yields an integral equation that is solved numerically     

False alarm control using Doppler estimation

A technique which uses maximum-likelihood estimates (MLEs) of target Doppler and target amplitude is developed for rejecting clutter residues. Multiple estimates are made and consistency checks are applied to the estimates. Simulation results indicate that for large clutter-to-noise ratios (C/N⩾55 dB) the probability of false alarm from clutter residues is reduced from 1.0 to below 0.01     

Detection performance in K-distributed and correlatedRayleigh clutters

Performance prediction for a detection system employing noncoherent integration is carried out for a chi-square family of fluctuating targets in K-distributed clutter plus noise. The detection performance for Swerling 11 targets in the K-distributed clutter plus noise is compared with that in exponentially correlated Rayleigh clutter. The results show that the performance prediction based on N pulses integrated in clutter plus noise using the K-distributed clutter model may be approximately equivalent to that using the exponentially correlated Rayleigh-distributed clutter model     

Design of high-efficiency series-resonant converters aboveresonance

Power losses in series-resonant converters (SRCs) operated above resonance are examined for the purpose of developing design guidelines leading to SRC designs with the highest possible operating efficiencies. Loss expressions are formulated and analyzed as functions of normalized voltage conversion ratio M and normalized output current J for the controlled transistor switches, antiparallel diodes, bridge diodes, and resonant capacitor. Overall losses range from a low of nearly 9% to a maximum of about 17%. Operating efficiencies corresponding to these losses range from a high of 92% to a low of 85%. Operation at the maximum efficiency of 92% occurs at values of M close to unity and is not highly dependent on J. However, in a practical closed-loop regulated SRC, operation with M too close to unity could provide an insufficient design margin, given component tolerances or other variations