Auxiliary Estimator Research Articles

Depth-Enhanced Deep Learning Approach For Monocular Camera Based 3D Object Detection

Automatic 3D object detection using monocular cameras presents significant challenges in the context of autonomous driving. Precise labeling of 3D object scales requires accurate spatial information, which is difficult to obtain from a single image due to the inherent lack of depth information in monocular images, compared to LiDAR data. In this paper, we propose a novel approach to address this issue by enhancing deep neural networks with depth information for monocular 3D object detection. The proposed method comprises three key components: 1)Feature Enhancement Pyramid Module: We extend the conventional Feature Pyramid Networks (FPN) by introducing a feature enhancement pyramid network. This module fuses feature maps from the original pyramid and captures contextual correlations across multiple scales. To increase the connectivity between low-level and high-level features, additional pathways are incorporated. 2)Auxiliary Dense Depth Estimator: We introduce an auxiliary dense depth estimator that generates dense depth maps to enhance the spatial perception capabilities of the deep network model without adding computational burden. 3)Augmented Center Depth Regression: To aid center depth estimation, we employ additional bounding box vertex depth regression based on geometry. Our experimental results demonstrate the superiority of the proposed technique over existing competitive methods reported in the literature. The approach showcases remarkable performance improvements in monocular 3D object detection, making it a promising solution for autonomous driving applications.

Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression

Uncertainty quantification is critical for deploying deep neural networks (DNNs) in real-world applications. An Auxiliary Uncertainty Estimator (AuxUE) is one of the most effective means to estimate the uncertainty of the main task prediction without modifying the main task model. To be considered robust, an AuxUE must be capable of maintaining its performance and triggering higher uncertainties while encountering Out-of-Distribution (OOD) inputs, i.e., to provide robust aleatoric and epistemic uncertainty. However, for vision regression tasks, current AuxUE designs are mainly adopted for aleatoric uncertainty estimates, and AuxUE robustness has not been explored. In this work, we propose a generalized AuxUE scheme for more robust uncertainty quantification on regression tasks. Concretely, to achieve a more robust aleatoric uncertainty estimation, different distribution assumptions are considered for heteroscedastic noise, and Laplace distribution is finally chosen to approximate the prediction error. For epistemic uncertainty, we propose a novel solution named Discretization-Induced Dirichlet pOsterior (DIDO), which models the Dirichlet posterior on the discretized prediction error. Extensive experiments on age estimation, monocular depth estimation, and super-resolution tasks show that our proposed method can provide robust uncertainty estimates in the face of noisy inputs and that it can be scalable to both image-level and pixel-wise tasks.

Visual identification of some regularities in packet network traffic

Modern heterogeneous packet networks generate network traffic with a complex structure. In this article, the object of study is a time series. The total number of User Datagram Protocol (UDP) packets has reached 250242. According to analysts, the growth trend of traffic, including real-time applications, will continue and the volume of data will grow, which may lead to the formation of packet queues when processed by network devices. In this case, there may be losses in case of long queues. To solve this problem, a power spectrum assessment was carried out. The AR maximum entropy estimator has been shown to be more sensitive than the auxiliary Fourier estimator. Accounting for non-stationarity by spectral methods is possible only through estimation in a sliding time window. Nine diagrams of spectral-temporal analysis of the original series, its increments, and the mixed series of increments were obtained: with default parameters, with small and large windows. Diagrams related to the original series reflect the dynamics of changes in data transmission intensity in the network; they show higher temporal resolution, indicating the presence of high-frequency components (noise) and the presence of low-frequency components (trend). Diagrams with increments describe signals of periodic components; changing the length of the window did not reflect the presence of noise or trend signs. Diagrams with mixed increments show that frequency components are uniformly distributed. The uniqueness of this work lies in the real measured data, and a distinctive feature of the obtained results is the visual examination of the complex traffic structure, allowing for the resolution of the investigated problem. Practical application of the results obtained can be applied in Quality of Service (QoS) management, resource planning, and network performance optimization

Calibration of Uncertainty in Sea Ice Concentration Retrieval With an Auxiliary Prediction Interval Estimator

Calibration of Uncertainty in Sea Ice Concentration Retrieval With an Auxiliary Prediction Interval Estimator

Transformer guided geometry model for flow-based unsupervised visual odometry

Existing unsupervised visual odometry (VO) methods either match pairwise images or integrate the temporal information using recurrent neural networks over a long sequence of images. They are either not accurate, time-consuming in training or error accumulative. In this paper, we propose a method consisting of two camera pose estimators that deal with the information from pairwise images and a short sequence of images, respectively. For image sequences, a transformer-like structure is adopted to build a geometry model over a local temporal window, referred to as transformer-based auxiliary pose estimator (TAPE). Meanwhile, a flow-to-flow pose estimator (F2FPE) is proposed to exploit the relationship between pairwise images. The two estimators are constrained through a simple yet effective consistency loss in training. Empirical evaluation has shown that the proposed method outperforms the state-of-the-art unsupervised learning-based methods by a large margin and performs comparably to supervised and traditional ones on the KITTI and Malaga dataset.

On stability and convergence of optimal estimation for networked control systems with dual packet losses without acknowledgment

This paper studies the optimal state estimation problem for networked control systems with control and observation packet losses but without packet acknowledgment (ACK). The packet ACK is a signal sent by the actuator to inform the estimator whether control packets are lost or not. Systems with packet ACK are usually called transmission control protocol (TCP)-like systems, and those without ACK are named user datagram protocol (UDP)-like systems. For UDP-like systems, the optimal estimator is derived and it is consisted of an exponentially increasing number of terms. By developing an auxiliary estimator, it is shown that there exists a critical observation packet arrival rate determining the stability of the expected EC (EEC), and it is identical to its counterpart for TCP-like systems. It is revealed that whether there is packet ACK or not has no effect on the stability of the EEC. Furthermore, under some conditions the EEC converges exponentially.

On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

AbstractThis paper deals with higher order asymptotic properties for three indirect inference estimators. We provide conditions that ensure the validity of locally uniform, with respect to the parameter, Edgeworth approximations. When these are of sufficiently high order they also form integrability conditions that validate locally uniform moment approximations. We derive the relevant second order bias and MSE approximations for the three estimators as functions of the respective approximations for the auxiliary estimator. We confirm that in the special case of deterministic weighting and affinity of the binding function, one of them is second order unbiased. The other two estimators do not have this property under the same conditions. Moreover, in this case, the second order approximate MSEs imply the superiority of the first estimator. We generalize to multistep procedures that provide recursive indirect inference estimators which are locally uniformly unbiased at any given order. Furthermore, in a particular case, we manage to validate locally uniform Edgeworth expansions for one of the estimators without any differentiability requirements for the estimating equations. We examine the bias-MSE results in a small Monte Carlo exercise.

Optimal Estimation in UDP-Like Networked Control Systems With Intermittent Inputs: Stability Analysis and Suboptimal Filter Design

We investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator. Most existing results for this setup are concerned with the design of controller, while the optimal estimation and its performance evaluation have been rarely treated. In this paper, we show that, unlike many other cases such as intermittent observations or TCP-like systems, the system state follows a Gaussian mixture distribution with exponentially increasing terms, which leads to a Gaussian sum filter-based optimal estimation. We develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices. It is revealed that the stability is independent of the packet loss rate, and is not affected by the lack of acknowledgment. A suboptimal filtering algorithm with improved computational efficiency is then developed. Numerical examples and simulations are employed to illustrate the theoretical results.

A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction

Summary In this paper, we define a set of indirect inference estimators based on moment approximations of the auxiliary estimators. Their introduction is motivated by reasons of analytical and computational facilitation. Their definition provides an indirect inference framework for some classical bias correction procedures. We derive higher-order asymptotic properties of these estimators. We demonstrate that under our assumption framework, and in the special case of deterministic weighting and affinity of the binding function, these are second-order unbiased. Moreover, their second-order approximate mean square errors do not depend on the cardinality of the Monte Carlo or bootstrap samples that our definition might involve. Consequently, the second-order mean square error of the auxiliary estimator is not altered. We extend this to a class of multistep indirect inference estimators that have zero higher-order bias without increasing the approximate mean square error, up to the same order. Our theoretical results are also validated by three Monte Carlo experiments.

Active fault detection for open loop stable LTI SISO systems

Active fault detection for a stable open-loop LTI SISO system is considered. The optimal active fault detection setup is developed around an estimator based architecture. The auxiliary signal and estimator are then designed in order to maximize detection performance. Equations are derived which relate the estimator design to the nominal residual signal covariance. The relationship between the auxiliary input and the system performance degradation constraint is considered. The effect of estimator gain and excitation signal frequency on the dual Youla-Jabr-Bongiorno-Kucera parameter is investigated. Finally, the effect of the excitation signal frequency on detector performance is investigated, and a minimum targeted detection time parameter is introduced. This set of equations are then used to minimise the fault detection time for fixed performance constraints and minimum targeted detection time.

Optimal Estimation for Networked Control Systems with Intermittent Inputs without Acknowledgement

This paper investigates the optimal estimation problem for networked control systems, where the control packets are randomly dropped without acknowledgement to the estimator. Most existing results for this setup are concerned with the design of controller, while the optimal estimation and its performance evaluation have not been fully studied. This paper shows, unlike many other cases such as intermittent observations or TCP-like systems, the system state follows a Gaussian mixture distribution with exponentially increasing terms. The optimal estimation is obtained by Gaussian sum filtering, while the computation is time- consuming. By constructing an auxiliary estimator, a fast and stable filtering algorithm is proposed to improve computational efficiency.

Maximal Asymptotic Biases of M-Estimators of Location with Preliminary Scale Estimates

We consider the problem of finding the maximal asymptotic bias of an M-estimator of a location parameter, using a preliminary estimate of the unknown scale parameter, when the error distribution is assumed to lie in an ϵ-contamination neighborhood of a fixed symmetric unimodal distribution. The least favorable contaminating distribution is shown to put all its mass at ∞ under some fairly general conditions. A particular case considered is that of the auxiliary scale estimator being a location-invariant and scale-equivariant version of a trimmed variance.

Data record-based criteria for the selection of an auxiliary vector estimator of the mmse/mvdr filter

When the auxiliary vector (AV) filter generation algorithm utilizes sample average estimated input data statistics, it provides a sequence of estimates of the ideal minimum mean-square error or minimum-variance distortionless-response filter for the given signal processing/receiver design application. Evidently, early nonasymptotic elements of the sequence offer favorable bias/variance balance characteristics and outperform in mean-square filter estimation error the unbiased sample matrix inversion (SMI) estimator as well as the (constraint) least-mean square, recursive least-squares, "multistage nested Wiener filter", and diagonally-loaded SMI filter estimators. Selecting the most successful (in some appropriate sense) AV filter estimator in the sequence for a given data record is a critical problem that has not been addressed so far. We deal exactly with this problem and we propose two data-driven selection criteria. The first criterion minimizes the cross-validated sample average variance of the AV filter output and can be applied to general filter estimation problems; the second criterion maximizes the estimated J-divergence of the AV filter output conditional distributions and is tailored to binary phase-shift-keying-type detection problems.

On Bias Compensated Recursive Least-Squares Algorithm for FIR Adaptive Filtering

It is known that recursive least squares (RLS) algorithm or least mean square (LMS) algorithm leads to biased FIR filter coefficients in the presence of input and output noise. In this paper, a new type of bias compensated recursive least squares (BCRLS) algorithm is proposed to produce consistent results for adaptive FIR filtering in the input and output noise case. The proposed algorithm introduces an auxiliary estimator to estimate unknown input noise variance. Owing to this, the bias of the RLS solution due to the input noise can be compensated to yield the consistent filter coefficients. Computational simulations indicate that the proposed algorithm is very efficient

Robust Simulation-Based Estimation of ARMA Models

This article proposes a new approach to the robust estimation of a mixed autoregressive and moving average (ARMA) model. It is based on the indirect inference method that originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed is based on an auxiliary autoregressive representation whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate. The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM estimators. An essential feature of the introduced estimator, compared to existing robust estimators for ARMA models, is its theoretical tractability that allows us to show consistency and asymptotic normality. Moreover, it is possible to characterize the influence function and the breakdown point of the estimator. In a small sample Monte Carlo study it is found that the new estimator performs fairly well when compared with existing procedures. Furthermore, with two real examples, we also compare the proposed inferential method with two different approaches based on outliers detection.

Estimation of the parameters of autoregressive signals from colored noise-corrupted measurements

This paper is concerned with identification of autoregressive (AR) model parameters using observations corrupted with colored noise. A novel formulation of an auxiliary least-squares estimator is introduced so that the autocovariance functions of the colored observation noise can be estimated in a straightforward manner. With this, the colored-noise-induced estimation bias can be removed to yield the unbiased estimate of the AR parameters. The performance of the proposed unbiased estimation algorithm is illustrated by simulation results. The presented work greatly extends the author's previous methods that were developed for identification of AR signals observed in white noise.

Mixed estimation of old‐age mortality

The estimation of the mortality of the “oldest old”; is subject to considerable random error, but important prior information exists that can be used to make the estimates more robust. Mixed estimation is a method of incorporating auxiliary information into the statistical estimation of linear models. We extend the method to cover general maximum likelihood estimation, and show that the mixed estimator can be represented approximately as a weighted average of the purely data based estimator and the auxiliary estimator. The methods can be applied to the analysis of the old‐age mortality via logistic and Poisson regression. A major advantage of the mixed estimator is the simplicity with which it can incorporate partial prior information. Moreover, no special software is needed in the fitting. We show how the targeting methods of Coale and Kisker can be represented as mixed estimation in a natural way that is more flexible than the original proposal. We also derive empirical estimates of the target information based on pooled data from several countries with high quality data. We consider the mortality of Finland at ages 80 +, study the reliability of the evidence of mortality crossover, and derive estimates of life expectancy at age 100.

Maximum asymptotic variances of mndash;estimators of location with auxiliary scale estimator under symmetric contamination

The model for the error distribution is , where F0 is a known distribution symmetric about 0, ∊ is a fixed proportion of contamination, and G is an unknown symmetric distribution. The two auxiliary scale estimators are Huber proposal 2 estimator and interquantile range of sample distribution [d](F). In Huber proposal 2 case, we first obtain the breakdown points for the estimator and also the range : of . For each fixed , the maximum asymptotic variance subject to is obtained by putting some of the contaminating mass at 0 and the rest of mass at [d] [d]. The original infinite-dimensional problem is then reduced to a one-dimensional problem of finding the value of [d] for which V([d]) is maximized. The result obtained is that this maximum is always attained at [d]max. When ψ is monotone and the scale estimator is S(F), for fixed , the maximum variance V(s) subject to S(F) = s is attained by placing the contaminating mass at . A sufficient condition under which V(s) is maximized at Smaxis given. However,...