Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Minimum-Error-Probability CFO Estimation for Multiuser MIMO-OFDM Systems

We consider carrier frequency offset (CFO) estimation in the context of multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems over noisy frequency-selective wireless channels with both single- and multiuser scenarios. We conceived a new approach for parameter estimation by discretizing the continuous-valued CFO parameter into a discrete set of bins and then invoked detection theory, analogous to the minimum-bit-error-ratio optimization framework for detecting the finite-alphabet received signal. Using this radical approach, we propose a novel CFO estimation method and study its performance using both analytical results and Monte Carlo simulations. We obtain expressions for the variance of the CFO estimation error and the resultant BER degradation with the single- user scenario. Our simulations demonstrate that the overall BER performance of a MIMO-OFDM system using the proposed method is substantially improved for all the modulation schemes considered, albeit this is achieved at increased complexity.

Achievable rate and error performance of an amplify and forward multi-way relay network in the presence of imperfect channel estimation

In this paper, we investigate the impact of channel estimation error on the achievable common rate and error performance of amplify and forward (AF) multi-way relay networks (MWRNs). Assuming lattice codes with large dimensions, we provide the analytical expressions for the end-to-end SNR at the users and obtain upper bounds on the achievable common rate for an AF MWRN. Moreover, considering binary phase shift keying (BPSK) modulation as the simplest case of lattice codes, we obtain the average bit error rate (BER) for a user in an AF MWRN. The analysis shows that the average BER is a linearly increasing function and the achievable common rate is a linearly decreasing function of the channel estimation error. On the other hand, the average BER decreases and the achievable common rate increases with increasing correlation between the true and the estimated channel. Also, we observe that the AFprotocol is robust against increasing number of users in terms of error performance. We show that when the decoding user has better channel conditions compared to other users, AF relaying gives a better error performance and common rate. Finally, simulation results are provided to verify the validity of our analysis.

Distribution state estimation based on particle swarm and doubly loop mutant optimization (DLM-PSO)

This paper presents a novel algorithm based on particle swarm optimization (PSO) to estimate the states of electric distribution networks. In order to improve the performance, accuracy, convergence speed, and eliminate the stagnation effect of original PSO, a secondary PSO loop and mutation algorithm as well as stretching function is proposed. For accounting uncertainties of loads in distribution networks, pseudo-measurements is modeled as loads with the realistic errors. Simulation results on 6-bus radial and 34-bus IEEE test distribution networks show that the distribution state estimation based on proposed DLM-PSO presents lower estimation error and standard deviation in comparison with algorithms such as WLS, GA, HBMO, and original PSO.

From a tree to a stand in Finnish boreal forests: biomass estimation and comparison of methods

There is an increasing need to compare the results obtained with different methods of estimation of tree biomass in order to reduce the uncertainty in the assessment of forest biomass carbon. In this study, tree biomass was investigated in a 30-year-old Scots pine (Pinus sylvestris) (Young-Stand) and a 130-year-old mixed Norway spruce (Picea abies)-Scots pine stand (Mature-Stand) located in southern Finland (61º50' N, 24º22' E). In particular, a comparison of the results of different estimation methods was conducted to assess the reliability and suitability of their applications. For the trees in Mature-Stand, annual stem biomass increment fluctuated following a sigmoid equation, and the fitting curves reached a maximum level (from about 1 kg/yr for understorey spruce to 7 kg/yr for dominant pine) when the trees were 100 years old. Tree biomass was estimated to be about 70 Mg/ha in Young-Stand and about 220 Mg/ha in Mature-Stand. In the region (58.00-62.13 ºN, 14-34 ºE, ≤ 300 m a.s.l.) surrounding the study stands, the tree biomass accumulation in Norway spruce and Scots pine stands followed a sigmoid equation with stand age, with a maximum of 230 Mg/ha at the age of 140 years. In Mature-Stand, lichen biomass on the trees was 1.63 Mg/ha with more than half of the biomass occurring on dead branches, and the standing crop of litter lichen on the ground was about 0.09 Mg/ha. There were substantial differences among the results estimated by different methods in the stands. These results imply that a possible estimation error should be taken into account when calculating tree biomass in a stand with an indirect approach.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

Subspace intersection method of high-resolution bearing estimation in shallow ocean using acoustic vector sensors

The subspace intersection method (SIM) provides unbiased bearing estimates of multiple acoustic sources in a range-independent shallow ocean using a one-dimensional search without prior knowledge of source ranges and depths. The original formulation of this method is based on deployment of a horizontal linear array of hydrophones which measure acoustic pressure. In this paper, we extend SIM to an array of acoustic vector sensors which measure pressure as well as all components of particle velocity. Use of vector sensors reduces the minimum number of sensors required by a factor of 4, and also eliminates the constraint that the intersensor spacing should not exceed half wavelength. The additional information provided by the vector sensors leads to performance enhancement in the form of lower estimation error and higher resolution.

Instantaneous frequency and bandwidth estimation using filterbank arrays

Accurate estimation of the instantaneous frequency of speech resonances is a hard problem mainly due to phase discontinuities in the speech signal associated with excitation instants. We review a variety of approaches for enhanced frequency and bandwidth estimation in the time-domain and propose a new cognitively motivated approach using filterbank arrays. We show that by filtering speech resonances using filters of different center frequency, bandwidth and shape, the ambiguity in instantaneous frequency estimation associated with amplitude envelope minima and phase discontinuities can be significantly reduced. The novel estimators are shown to perform well on synthetic speech signals with frequency and bandwidth micro-modulations (i.e., modulations within a pitch period), as well as on real speech signals. Filterbank arrays, when applied to frequency and bandwidth modulation index estimation, are shown to reduce the estimation error variance by 85% and 70% respectively. © 2013 IEEE.

Dynamic State Estimation of Power Systems with Quantization Eects: A Recursive Filter Approach

In this paper, a recursive filter algorithm is developed to deal with the state estimation problem for power systems with quantized nonlinear measurements. The measurements from both the remote terminal units and the phasor measurement unit are subject to quantizations described by a logarithmic quantizer. Attention is focused on the design of a recursive filter such that, in the simultaneous presence of nonlinear measurements and quantization effects, an upper bound for the estimation error covariance is guaranteed and subsequently minimized. Instead of using the traditional approximation methods in nonlinear estimation that simply ignore the linearization errors, we treat both the linearization and quantization errors as norm-bounded uncertainties in the algorithm development so as to improve the performance of the estimator. For the power system with such kind of introduced uncertainties, a filter is designed in the framework of robust recursive estimation, and the developed filter algorithm is tested on the IEEE benchmark power system to demonstrate its effectiveness.