A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

The parametric adaptive matched filter (PAMF) for space-time adaptive processing (STAP) is introduced via the matched filter (MF), multichannel linear prediction, and the multichannel LDU decomposition. Two alternative algorithmic implementations of the PAMF are discussed. Issues considered include sample training data size and constant false alarm rate (CFAR). Detection test statistics are estimated for airborne phased array radar measurements, and probability of detection is estimated using simulated phased array radar data for airborne surveillance radar scenarios. For large sample sizes, the PAMF performs close to the MF; performance degrades slightly for small sample sizes. In both sample size ranges, the PAMF is tolerant to targets present in the training set.

Parametric adaptive matched filter for airborne radar applications

The exact statistics of the estimated reflection coefficients for an autoregressive process are difficult to determine. However, since almost all the common methods for estimating the reflection coefficients are maximum likelihood estimates for large data records, the asymptotic distribution of the estimates is multivariate Gaussian with a covariance matrix given by the Cramer-Rao bound. A recursive means of computing the covariance matrix bound is described. Simulation results show that the asymptotic expressions are accurate for large data records. However, for relatively short data records, the asymptotic expressions are accurate only for spectra with a small dynamic range.

On the statistics of the estimated reflection coefficients of an autoregressive process

The authors consider the problem of detecting range-distributed targets in the presence of structured disturbance modelled as an autoregressive Gaussian process with unknown parameters. The focus is on two different scenarios. The first assumes that all the data vectors from the cells under test share the same covariance matrix (homogeneous environment). The second refers to the case of data vectors characterised by completely different covariances (heterogeneous environment). Four detectors exploiting the asymptotic generalised likelihood ratio criterion are devised and assessed. Remarkably, they ensure the constant false alarm rate (CFAR) property with respect to the disturbance power level, and two of them are asymptotically CFAR with respect to the disturbance covariance matrix. Finally the performance assessment, based also on real radar data, has shown that these detectors achieve, in general, satisfactory detection performances.

Model-based adaptive detection of range-spread targets

The problem of detecting a known signal in colored Gaussian noise of unknown covariance is addressed. The noise is modeled as an autoregressive process of known order but unknown coefficients. By employing the theory of generalized likelihood ratio testing, a detector structure is derived and then analyzed for performance. It is proven that for large data records the detection performance is identical to that of an optimal prewhitener and matched filter, and therefore the detector itself is optimal. Simulation results indicate that the data record length necessary for the asymptotic results to apply can be quite small. Thus, the proposed detector is well suited for practical applications.

Asymptotically optimal detection in unknown colored noise via autoregressive modeling

A new adaptive filter to reject clutter is derived using autoregressive spectral analysis techniques. The adaptive filter performs open. Ioop processing, resulting in a shorter transient response, and is therefore suitable for radar waveforms containing only a small number of samples. A number of examples including application to ballistic missile defense are presented to demonstrate the performance capabilities of the new adaptive filter.

P.K. Rajasekaran

Papers

Adaptive Clutter Filtering Using Autogressive Spectral Estimation