Waveform libraries: Measures of effectiveness for radar scheduling

Our goal was to provide an overview of a circle of emerging ideas in the area of waveform scheduling for active radar. Principled scheduling of waveforms in radar and other active sensing modalities is motivated by the nonexistence of any single waveform that is ideal for all situations encountered in typical operational scenarios. This raises the possibility of achieving operationally significant performance gains through closed-loop waveform scheduling. In principle, the waveform transmitted in each epoch should be optimized with respect to a metric of desired performance using all information available from prior measurements in conjunction with models of scenario dynamics. In practice, the operational tempo of the system may preclude such on-the-fly waveform design, though further research into fast adaption of waveforms could possibly attenuate such obstacles in the future. The focus in this article has been on the use of predesigned libraries of waveforms from which the scheduler can select in lieu of undertaking a real-time design. Despite promising results, such as the performance gains shown in the tracking example presented here, many challenges remain to be addressed to bring the power of waveform scheduling to the level of maturity needed to manifest major impact as a standard component of civilian and military radar systems.Douglas Cochran, Sofia Suvorova, Stephen D. Howard and Bill Mora

Bounds on Multiple Sensor Fusion

We consider the problem of fusing measurements from multiple sensors, where the sensing regions overlap and data are non-negative---possibly resulting from a count of indistinguishable discrete entities. Because of overlaps, it is, in general, impossible to fuse this information to arrive at an accurate estimate of the overall amount or count of material present in the union of the sensing regions. Here we study the range of overall values consistent with the data. Posed as a linear programming problem, this leads to interesting questions associated with the geometry of the sensor regions, specifically, the arrangement of their non-empty intersections. We define a computational tool called the fusion polytope and derive a condition for this to be in the positive orthant thus simplifying calculations. We show that, in two dimensions, inflated tiling schemes based on rectangular regions fail to satisfy this condition, whereas inflated tiling schemes based on hexagons do.Comment: 23 page

Target Track Initiation Comparison and Optimization

This paper proposes a procedure for comparison of target tracking filters in cluttered environment, using simulated experiments. Important simulation issues, including track generation and retention across simulation runs and true track definition are discussed. False track discrimination is identified as an important target tracking filter performance measure. This measure has two components; confirmed true track statistics and confirmed false track statistics. In order to meaningfully compare false track discrimination capabilities of target tracking filters, we suggest optimizing true track statistics, while using false track statistics as the optimization constrains. The optimization procedure is described, and the importance of correct parameter selection is illustrated

Optimal Policy for Scheduling of Gauss-Markov Systems

This paper considers the problem of multi-step scheduling the measurement of several Gauss-Markov systems. Such a problem occurs, for example, in the allocation of the time of a single beam phased-array radar system among several targets. The problem is put into a mathematical framework and is solved for the case of two one-dimensional systems for which the cost function is the sum of the variances of the estimates of the states of the two systems

Golay Complementary Waveforms in Reed–Müller Sequences for Radar Detection of Nonzero Doppler Targets

Golay complementary waveforms can, in theory, yield radar returns of high range resolution with essentially zero sidelobes. In practice, when deployed conventionally, while high signal-to-noise ratios can be achieved for static target detection, significant range sidelobes are generated by target returns of nonzero Doppler causing unreliable detection. We consider signal processing techniques using Golay complementary waveforms to improve radar detection performance in scenarios involving multiple nonzero Doppler targets. A signal processing procedure based on an existing, so called, Binomial Design algorithm that alters the transmission order of Golay complementary waveforms and weights the returns is proposed in an attempt to achieve an enhanced illumination performance. The procedure applies one of three proposed waveform transmission ordering algorithms, followed by a pointwise nonlinear processor combining the outputs of the Binomial Design algorithm and one of the ordering algorithms. The computational complexity of the Binomial Design algorithm and the three ordering algorithms are compared, and a statistical analysis of the performance of the pointwise nonlinear processing is given. Estimation of the areas in the Delay–Doppler map occupied by significant range sidelobes for given targets are also discussed. Numerical simulations for the comparison of the performances of the Binomial Design algorithm and the three ordering algorithms are presented for both fixed and randomized target locations. The simulation results demonstrate that the proposed signal processing procedure has a better detection performance in terms of lower sidelobes and higher Doppler resolution in the presence of multiple nonzero Doppler targets compared to existing methods

Bayesian Detection of a Sinusoidal Signal With Randomly Varying Frequency

The problem of detecting a sinusoidal signal with randomly varying frequency has a long history. It is one of the core problems in signal processing, arising in many applications including, for example, underwater acoustic frequency line tracking, demodulation of FM radio communications, laser phase drift in optical communications and, recently, continuous gravitational wave astronomy. In this paper we describe a Markov Chain Monte Carlo based procedure to compute a specific detection posterior density. We demonstrate via simulation that our approach results in an up to 25 percent higher detection rate than Hidden Markov Model based solutions, which are generally considered to be the leading techniques for these problems