Amplitude estimation of a signal with known waveform in the presence of steering vector uncertainties

In this correspondence, we address the problem of estimating the amplitude of a signal with known waveform received on an array of sensors and we consider the case where there exist uncertainties about the spatial signature of the signal of interest. Closed-form expressions for the Cramer–Rao bound are derived and the respective influence of the uncertainties and the number of snapshots is studied. The maximum likelihood estimator (MLE) of the signal of interest amplitude along with the covariance matrix of the interferences and noise is also derived and an iterative algorithm is presented to obtain the ML estimates

Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

Joint Cramér-Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems

Symmetric Normal Mixture GARCH

Normal mixture (NM) GARCH models are better able to account for leptokurtosis in financial data and offer a more intuitive and tractable framework for risk analysis and option pricing than student’s t-GARCH models. We present a general, symmetric parameterisation for NM-GARCH(1,1) models, derive the analytic derivatives for the maximum likelihood estimation of the model parameters and their standard errors and compute the moments of the error term. Also, we formulate specific conditions on the model parameters to ensure positive, finite conditional and unconditional second and fourth moments. Simulations quantify the potential bias and inefficiency of parameter estimates as a function of the mixing law. We show that there is a serious bias on parameter estimates for volatility components having very low weight in the mixing law. An empirical application uses moment specification tests and information criteria to determine the optimal number of normal densities in the mixture. For daily returns on three US Dollar foreign exchange rates (British pound, euro and Japanese yen) we find that, whilst normal GARCH(1,1) models fail the moment tests, a simple mixture of two normal densities is sufficient to capture the conditional excess kurtosis in the data. According to our chosen criteria, and given our simulation results, we conclude that a two regime symmetric NM-GARCH model, which quantifies volatility corresponding to ‘normal’ and ‘exceptional’ market circumstances, is optimal for these exchange rate data.Volatility regimes, conditional excess kurtosis, normal mixture, heavy trails, exchange rates, conditional heteroscedasticity, GARCH models.

An Exploratory Analysis Of A Time Synchronization Protocol For UAS

This dissertation provides a numerical analysis of a Receiver Only Synchronization (ROS) protocol which is proposed for use by Unmanned Aircraft Systems (UAS) in Beyond Visual Line of Sight (BVLOS) operations. The use of ROS protocols could reinforce current technologies that enable transmission over 5G cell networks, decreasing latency issues and enabling the incorporation of an increased number of UAS to the network, without loss of accuracy. A minimum squared error (MSE)-based accuracy of clock offset and clock skew estimations was obtained using the number of iterations and number of observations as independent parameters. Although the model converged after only four iterations, the number of observations needed was considerably large, of no less than about 250. The noise, introduced in the system through the first residual, the correlation parameter and the disturbance terms, was assumed to be autocorrelated. Previous studies suggested that correlated noise might be typical in multipath scenarios, or in case of damaged antennas. Four noise distributions: gaussian, exponential, gamma and Weibull were considered. Each of them is adapted to different noise sources in the OSI model. Dispersion of results in the first case, the only case with zero mean, was checked against the Cramér-Rao Bound (CRB) limit. Results confirmed that the scheme proposed was fully efficient. Moreover, results with the other three cases were less promising, thus demonstrating that only zero mean distributions could deliver good results. This fact would limit the proposed scheme application in multipath scenarios, where echoes of previous signals may reach the receiver at delayed times. In the second part, a wake/sleep scheme was imposed on the model, concluding that for wake/sleep ratios below 92/08 results were not accurate at p=.05 level. The study also evaluated the impact of noise levels in the time domain and showed that above -2dB in time a substantial contribution of error terms disturbed the initial estimations significantly. The tests were performed in Matlab®. Based on the results, three venues confirming the assumptions made were proposed for future work. Some final reflections on the use of 5G in aviation brought the present dissertation to a close

Estimation from quantized Gaussian measurements: when and how to use dither

Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than one-third. When that ratio is also greater than 0.822/K^0.930 for the number of measurements K > 20, estimators we present are more efficient than the midrange.https://arxiv.org/abs/1811.06856Accepted manuscrip