Binary integration of fluctuating targets

The detection performance of a binary integrator (M-out-of-N detector) against nonfluctuating, slowly fluctuating, and quickly fluctuating targets is given. Since the solution for the slowly fluctuating target is numerically intensive, a simpler approximate solution is developed. This approximation is very accurate and is valid even when the noise power varies from pulse to pulse within a single antenna scan     

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     

Adaptive canceler and pulse compressor interactions

Performance results for the sidelobe level of a compressed pulse that has been preprocessed through an adaptive canceler are obtained. The adaptive canceler is implemented using the sampled matrix inversion algorithm. Because of finite sampling, the quiescent compressed pulse sidelobe levels are degraded due to the preprocessing of the main channel input data stream (the uncompressed pulse) through an adaptive canceler. It is shown that if N is the number of input canceler channels (main and auxiliaries) and K is the number of independent samples per channel, then K/N can be significantly greater than one in order to retain sidelobes that are close to the original quiescent sidelobe level (with no adaptive canceler). Also it is shown that the maximum level of degradation is independent of whether pulse compression occurs before or after the adaptive canceler if the uncompressed pulse is completely contained within the K samples that are used to calculate the canceler weights. This same analysis can be used to predict the canceler noise power level that is induced by having the desired signal present in the canceler weight calculation     

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     

Performance of receivers with linear detectors

The false-alarm and detection probabilities of a receiver summing M independent outputs of a linear detector are calculated by numerical saddlepoint integration. The saddlepoint approximation is also considered. Both constant-amplitude and Rayleigh-fading signals are treated, and the relative efficiency of the quadratic and the linear detectors for these is calculated for a broad range of values of M . The numerical integration method is the more efficient, the smaller the false-alarm probability or the false-dismissal probability, that is, under just those conditions for which the terms in the Gram-Charlier series oscillate most violently and the series becomes least reliable. The simpler saddlepoint approximation yields values that in those same regions have been found close enough to the exact probabilities to be adequate for most engineering purposes. The larger the number M of samples, the more efficient methods are     

CW alternatives to the coherent pulse train-signals and processors

Continuous wave (CW) signals phase modulated by a periodic waveform, and their corresponding receivers, are discussed. The combined response in delay and Doppler is almost identical to the (ideal) response of the coherent pulse train. The receivers are matched to an integral number N of modulation periods of the transmitted signal. CW implies a duty cycle of 100%. However, the signal duration need not be longer than N+2 periods. The CW signals have the advantage that their peak power is equal to the average power. Their disadvantages are more complicated receiver processing and the need for two antennas     

Detection probabilities for correlated Rayleigh fading signals

Both the method of saddlepoint integration and its associated saddlepoint approximation are applied to calculating the probability of detecting correlated Rayleigh-fading signals in Gaussian noise by means of a detector that integrates M samples of the output of a quadratic rectifier. The quadrature components of the signal samples are modeled as an autoregressive moving-average process, and specific results are exhibited for a first-order Markov process. By these methods the fluctuation loss can be computed for much larger values of M and for larger values of the detection probability than previously. Values calculated by the saddlepoint approximation prove to be close enough to the exact values to be useful over a broad range of signal parameters     

Efficient algorithms for finding the K best paths througha trellis

A set of algorithms is presented for finding the best set of K mutually exclusive paths through a trellis of N nodes, with worst-case computation time bounded by N³log n for a fixed-precision computation. The algorithms are based on a transformation of the K-path trellis problem into an equivalent minimum-cost network flow (MCNF) problem. The approach allows the application of efficient MCNF algorithms, which can obtain optimal solutions orders of magnitude faster than the algorithm proposed by J.K. Wolf et al. (1989). The resulting algorithms extend the practicality of the trellis formulation (in terms of required computations) to multiobject tracking problems with much larger numbers of targets and false alarms. A response by Wolf et al. is included     

Tracking multiple targets with correlated measurements andmaneuvers

The problem of tracking N targets with correlation in both measurement and maneuver statistics is solved by transforming to a coordinate frame in which the N targets are decoupled. For the case of N identical targets, the decoupling is shown to coincide with a transformation to a set of nested center-of-mass coordinates. Absolute and differential tracking accuracies are compared with suboptimal results to show the improvement that is achieved by properly exploiting the correlation between targets     

Explicit solutions for some simple decentralized detection problems

A decentralized detection problem is considered in which a number of identical sensors transmit a finite-valued function of their observations to a fusion center which makes a final decision on one of M alternative hypotheses. The authors consider the case in which the number of sensors is large, and they derive (asymptotically) optimal rules for determining the messages of the sensors when the observations are generated from a simple and symmetrical set of discrete distributions. They also consider the tradeoff between the number of sensors and the communication rate of each sensor when there is a constraint on the total communication rate from the sensors to the fusion center. The results suggest that it is preferable to have several independent sensors transmitting low-rate (coarse) information instead of a few sensors transmitting high-rate (very detailed) information. They also suggest that an M-ary hypothesis testing problem can be viewed as a collection of M(M-1)/2 binary hypothesis testing problems. From this point of view the most useful messages (decision rules) are those that provide information to the fusion center that is relevant to the largest possible numbers of these binary hypothesis testing problems     

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     

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     

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     

CFAR data fusion center with inhomogeneous receivers

Detection systems with distributed sensors and data fusion are increasingly used by surveillance systems. A system formed by N inhomogeneous constant false alarm rate (CFAR) detectors (cell-averaging (CA) and ordered statistic (OS) CFAR detectors) is studied. A recursive formulation of an algorithm that permits a fixed level of false alarms in the data fusion center is presented, to set the optimum individual threshold levels in the CFAR receivers and the optimum `K out of N' decision rule in order to maximize the total probability of detection. The algorithm also considers receivers of different quality or with different communication channel qualities connecting them with the fusion center. This procedure has been applied to several hypothetical networks with distributed CA-CFAR and OS-CFAR receivers and for Rayleigh targets and interference, and it was seen that in general the fusion decision OR rule is not always the best     

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     

Multiple target angle tracking using sensor array outputs

The use of the output of an array of sensors to track multiple independently moving targets is reported. The output of each sensor in the array is the sum of signals received from each of the targets. The results of direction-of-arrival estimation by eigenvalue analysis are extended to derive a recursive procedure based on a matrix quadratic equation. The solution of this matrix quadratic equation is used to provide updated target positions. A linear approximation method for estimating the solution of the matrix equation is presented. The algorithm is demonstrated by the simulated tracking of two targets. The main advantage of the algorithm is that a closed-form solution for updating the target angle estimates has been obtained. Also, its application is straightforward, and the data association problem due to uncertainty in the origin of the measurements is avoided. However, it requires the inversion of an N×N as well as other linear operations, so that the computational burden becomes substantial as N becomes very large     

Collapsing losses of peak signal integrators

Collapsing losses are computed for systems in which the peak return of K samples of noise plus one sample of signal-plus-noise are integrated over N looks. The statistical approach, collapsing losses, and an application are described. The peak integrator is found to have substantially lower collapsing losses than conventional systems in which the average, not the peak, is integrated     

Detection probability for partially correlated chi-square targets

The probability of detection of the sum of N square-law-detected pulses is derived for the case where the signal fluctuation obeys chi-square statistics with four degrees of freedom. P. Swerling's (1960) case III and IV represent the cases where the signal is completely correlated and completely decorrelated, respectively, from pulse to pulse. An exact expression for probability of detection is derived for the condition of partial signal correlation. The results given are compared with the approximate technique commonly used to handle partial signal correlation     

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     

Optimal serial distributed decision fusion

The problem of distributed detection involving N sensors is considered. The configuration of sensors is serial in the sense that the Jth sensor decides using the decision it receives along with its own observation. When each sensor uses the Neyman-Pearson test, the probability of detection is maximized for a given probability of false alarm, at the Nth stage. With two sensors, the serial scheme has a performance better than or equal to the parallel fusion scheme analyzed in the literature. Numerical examples illustrate the global optimization by the selection of operating thresholds at the sensors