An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
For the passive estimation of directions of arrivals (DOAs) of transmitting sources from an antenna array, high resolution estimators can be achieved from maximum likelihood or signal subspace based concepts, provided that certain model assumptions are satisfied. For the signal subspace class of methods, the sources are nearly always regarded as being stationary during the observation interval of the array data. If this is the case, and if all the other model assumptions are valid, then the DOA can be estimated to arbitrary accuracy in the presence of noise by observing the data over a sufficiently long time interval. When sources are in fact moving relative to the receiving array, errors are induced in signal subspace methods. These depend on the extent of the source motion. Hence there is a trade-off between decreasing noise errors and increasing motion errors as the observation time is increased, and some optimum observation period exists. In some cases, however, even the performance at the optimum observation interval may be unsatisfactory, and alternative approaches are desirable. Signal subspace concepts break down when sources are moving, and maximum likelihood methods for moving sources are computationally expensive. To overcome these problems three novel algorithms have been developed for the joint estimation of source position and velocity from a batch of array data for sources moving with constant angular velocity. These allow increased accuracy in the source position determination, and provide unbiased velocity estimates. The performance of the estimators is compared to the Cramer-Rao lower bound.
The one-dimensional bearing estimation problem of linearly periodic arrays with sensor position errors has been tackled by the Toeplitz approximation method (TAM), iterative TAM, modified TAM, and iterative MTAM without calibrating the sensor positions. This paper extends these methods to the two-dimensional situation using a uniform planar array with sensor position errors to estimate the 2-D angle-of-arrivals (AOAs), azimuth and elevation angles of the emitting sources. Based on the block Toeplitz property and eigenstructure of the ideal covariance matrix observed by the unperturbed array, we extend the methods to alleviate the effect caused by the random perturbations in sensor position. The Music algorithm incorporating a 2-D AOA searching is applied for bearing estimation. Further, the 1-D processing approach presented earlier for solving the 2-D AOA estimation problem can also be applied to reduce the computational burden of 2-D AOA searching.
Estimation of differential delay-Doppler parameters in passive sonar and radar applications is addressed. Without assuming Gaussianity it is shown that the conventional ambiguity function is asymptotically chi-squared and yields consistent delay-Doppler estimates for narrowband signals observed in uncorrelated sensor noises. Related asymptotic covariance expressions and their computable forms are also derived. It is further shown that the performance of the ambiguity function degrades severely when the sensor noises are correlated. To deal with such noises a novel third-order ambiguity function is proposed and is shown to be consistent and theoretically immune to Gaussian and symmetrically distributed disturbances. Further, to take into account the errors due to variances of sample statistics, alternative delay-Doppler estimators are defined to minimise a cumulant matching criterion and related issues are discussed. The case of wideband signals is also addressed and, finally, extensions to kth-order ambiguity functions are proposed. Computer simulations are performed to confirm the theory. Throughout the paper the analysis treats both deterministic and stochastic signals on a common framework. Connections with active sonar and radar problems are also shown as a special case.
The authors have developed two simplified adaptive eigen-subspace methods which robustly converge to the noise subspace only if the number of sources is less than the number of sensors. The first simplification, achieved by introducing an orthogonal factor, reduces the computational complexity and preserves the parallel structure of the inflation method (Yang and Kaveh, 1988). The convergence performances and initialisation behaviours perform better than other adaptive eigen-subspace algorithms when the number of sources is unknown. Further simplification is achieved using a unitary transformation approach (Huarng and Yeh, 1991). This leads to an adaptive real eigen-subspace algorithm which further reduces the computational complexity and also resolves the paired multipath problem. Simulations for evaluations of the proposed and the existing algorithms are also included in this paper.
A stable alternative is described for the 'standard' systolic MVDR beamforming algorithm of McWhirter and Shepherd, which suffers from numerical instability. The alterative algorithm is similar to covariance-type recursive least squares algorithms, and is therefore readily implemented on an RLS systolic array.
The VIA-ESPRIT algorithm is a computationally efficient method for direction of arrival (DOA) estimation. This algorithm uses virtual interpolated arrays (VIA) to apply ESPRIT type techniques to arbitrary array geometries. This paper presents a performance analysis of VIA-ESPRIT. Expressions for the bias and the variance of the estimation errors are derived. Simulation results verify the theoretically predicted performance.
Carrier wave interference (CWI) has been shown to be a serious problem which affects the operation of all Loran-C receivers in Europe, and aviation and land-mobile receivers in the US and Canada. The designers of Loran-C systems for use in Europe have been obliged to pay considerable attention to CWI in predicting coverage. The paper contains a unified analysis of the effects of the phase-decoding and averaging operations of receivers on CWI and provides a quantitative assessment of receiver performance under CWI conditions. The analysis covers synchronous, near-synchronous and asynchronous interference. It shows that, in contrast to asynchronous interference, synchronous and near-synchronous CWI are attenuated by phase decoding and averaging within periods of two group repetition intervals and that longer periods of averaging do not improve performance. Front-end filtering is incorporated into the analysis by considering not only the attenuation of interference that it provides but also the delay and distortion it causes to Loran-C signals. Both the phase-tracking and the cycle-selection functions of receivers are examined. The results of the analysis, which are confirmed by computer simulation, are presented in a form that will be of direct use to the designers of Loran-C receivers and systems
Fractal theory is applied to the analysis of real radar signals which are scattered from rough sea surfaces. The databases formed by sampling the radar signals include the two general cases, i.e. both forward-scattered and backscattered signals. The signals for the two cases were recorded using two entirely different radar systems and at two entirely differently geographic locations. The box counting method is used to estimate the fractal dimension of the scattered signals. To corroborate this result, a computation of the fractal dimension is based on the index α in the power spectrum relation, P(f) ∞f−α. The estimates derived from both methods are consistent. It is observed that the forward-scattered and back-scattered radar signals have very similar fractal dimensions, i.e. 1.746 ± 0.033 for the 9.6 GHz forward-scattered signals, 1.753 ± 0.024 for the 8.6 GHz forward-scattered signals, and 1.758 ± 0.015 for the 9.39 GHz back-scattered signals. Finally, it is shown that there is a detectable variation in the fractal dimension when a target is present. Based on this variation, it is therefore possible to detect the presence of a target by observing the fractal dimension of the radar returns.
The paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resort to their hypothesised value. By using estimates of the directional vectors obtained via blind identification, i.e. without knowing the array manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors etc., so that neither array calibration nor physical modelling is necessary. Rather suprisingly, ‘blind beamformers’ may outperform ‘informed beamformers’ in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption on which blind identification relies is the statistical independence of the sources, which is exploited using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalisation of fourth-order cumulant matrices; its implementation is described, and its performance is investigated by numerical experiments.
A delayed N-path structure for high-speed adaptive linear phase FIR digital filtering is presented. The corresponding adaptive algorithm is derived. The resulting throughput rate of the present system can be 2N2 times that of a conventional adaptive FIR digital filter. Simulation results obtained in using the proposed high-speed structure for adaptive noise cancellation and adaptive system modelling are also given
High-performance synthetic aperture radars (SARs) for mapping demand massive digital signal processing powers. The fall in the cost of computing devices has recently passed the point at which such processors can be afforded and SARs are now being used in a range of applications. The analogous inverse synthetic aperture radar (ISAR), which enables moving targets to be imaged by stationary or moving radars, is also becoming widely used. The unifying principle underlying SARs and ISARs is presented and the common parameters defining the performances of both types of radar are derived. A novel technique is described which enables the radar to measure the random angular spin of a ship at sea, thereby permitting it to be imaged deterministically by ISAR. Results are presented from a representative selection of ISARs and SARs ranging from the imaging of model targets by ISARs operating at scaled-up frequencies through to the mapping of the surface of Venus by a satellite SAR. The paper concludes with a review of likely future developments of these types of radar and suggests that further major advances are possible.
The problem of detecting an unknown, random, stationary, non-Gaussian signal that is common to two spatially separated sensors, is considered. The signal is assumed to have a non-vanishing bispectrum. The measurement noise sequences at the two sensors are either mutually independent with arbitrary cumulant spectra, or dependent with vanishing bispectra. Two statistical tests are presented for signal detection when the noise statistics are unknown. The performance of the tests is illustrated by computer simulation examples.
When measurements are available in the polar or spherical co-ordinate system the tracking algorithm becomes nonlinear. The authors consider the problem of tracking a target moving at a constant velocity in a straight-line trajectory when the measurements are available in polar co-ordinates. A new algorithm involving co-ordinate transformation, linearisation and approximation is presented. The transformed measurements are preprocessed and provided to a Kalman filter which yields the final state estimates. Simulation results are presented to demonstrate the superior performance of the new algorithm for the nonlinear problem.
Concern is with phenomena that are moving and developing in time. Indistinguishable particles are displaced independently, with successive displacements possibly correlated. One wishes to estimate the joint probability distribution of those displacements. It is shown how this may be done via estimates of higher-order cumulant densities and spectra. The results simplify in the case that the original placements of the particles are homogeneous Poisson. Surprisingly then the cumulant density is essentially the probability density.
The authors consider the detection and classification of multiple non-Gaussian linear sources by superposition of their waveforms available from a single sensor whose measurements are possibly corrupted by additive Gaussian noise. It is shown that by using multiple frequency lags of the trispectrum of single sensor measurements, it is possible to form a trispectral matrix C that possesses the same structure as the array covariance matrix of narrowband multisensor measurements. Consequently, techniques that are applicable to narrowband array processing can be adapted for the analysis of single sensor data; the rank of C reveals the number of sources, and a multiple signal characterisation (MUSIC)-like method can be used for source classification using a directory of candidate source spectra. Simulations are included to illustrate the proposed methods.
A floating point roundoff error analysis in the estimation of higher-order statistics, moments or cumulants of real stationary processes from single data records is provided. Closed form expressions or upper bounds are derived for the mean and variance of the quantisation noise introduced in the estimation of the all-zero and all-tau (diagonal slice) moments, power, skewness and kurtosis. Numerical and simulation results show that the roundoff noise can significantly affect the moment and cumulant estimates, especially when long data records are employed for the purpose of reducing the estimation variance. The obtained results can provide guidelines in choosing a processor with the appropriate register length (in number of bits) in applications that require the calculation of higher-order statistics.
The authors address the problems encountered in the realisation of a practical time delay beamformer for the reception of acoustic data transmitted through the water. They outline a solution that employs significantly less hardware than that used by other reported schemes, and does so without sacrificing beam pattern integrity. Results obtained from outdoor tests are also presented
