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Airborne Distributed Coherent Aperture Radar (ADCAR) is one of the most promising next-generation radars to significantly improve target detection and discrimination abilities. However, time and phase synchronization among unit radars should be done before an ADCAR is intended to cohere on a potential target. To address this problem, a time and phase synchronization technique using clutter observations is proposed in this paper. Clutter returns from different azimuths and elevations on the surface of the earth are employed to calibrate system uncertainties. Two stages are mainly considered: a scene registration among range-Doppler units from different transmit/receive pairs is performed to enhance the clutter coherence in the first stage, followed by a joint estimation of those synchronization errors in the second stage. To relieve the computational burden, a novel Separable and Sequential Estimation (SSE) method is provided to separate the unknowns at the sacrifice of a range-Doppler unit. Moreover, performance analyses including the clutter coherence ability, estimation lower bound, and signal coherence loss are also performed. Finally, simulation results indicate that ADCAR time and phase synchronization is realized by using our methods.

This article proposes the orthogonal series method for the cumulative distribution function estimation based on a random number of observations Nt, which may be recorded in time (0,t]. We give the ...

In this paper, a novel training beam sequence design for multiuser millimeter wave tracking systems is proposed. For each receiver, a single-path channel model is firstly investigated, where we introduce a maximum a posteriori (MAP) criterion to estimate the time-varying angle of departure (AoD), followed by an extended Kalman filter to update the stale complex path gain. We then employ training beam sequence design to minimize the estimated AoD’s average mean squared error (AMSE), which however has no explicit expression. We firstly derive a closed-form upper bound for the AMSE and then simplify this upper bound into a tractable form, based on which a nonlinear optimization problem (NLP) is formulated. By solving this NLP optimally using its corresponding Karush-Kuhn-Tucker conditions, we obtain an efficient training beam sequence. The proposed MAP criterion and its associated training beam sequence design are further extended to multi-path scenarios, where a joint estimation of the multiple paths is firstly discussed, followed by a sequential estimation as a low-complexity alternative. Numerical results demonstrate the superiority of our proposed scheme over the existing benchmark methods, especially in the case when the receivers’ channels change rapidly.

Time signals are measured experimentally throughout sciences, technologies and industries. Of particular interest here is the focus on time signals encoded by means of magnetic resonance spectroscopy (MRS). The great majority of generic time signals are equivalent to auto-correlation functions from quantum physics. Therefore, a quantum-mechanical theory of measurements of encoded MRS time signals is achievable by performing quantum-mechanical spectral analysis. When time signals are measured, such an analysis becomes an inverse problem (harmonic inversion) with the task of reconstruction of the fundamental frequencies and the corresponding amplitudes. These complex-valued nodal parameters are the building blocks of the associated resonances in the frequency spectrum. Customarily, the MRS literature reports on fitting some ad hoc mathematical expressions to a set of resonances in a Fourier spectrum to extract their positions, widths and heights. Instead, an alternative would be to diagonalize the so-called data matrix with the signal points as its elements and to extract the resonance parameters without varying any adjusting, free constants as these would be absent altogether. Such a data matrix (the Hankel matrix) is from the category of the evolution matrix in the Schrödinger picture of quantum mechanics. Therefore, the spectrum of this matrix, i.e. the eigenvalues and the corresponding amplitudes, as the Cauchy residues (that are the squared projections of the full wave functions of the system onto the initial state) are equivalent to the sought resonance parameters, just mentioned. The lineshape profile of the frequency-dependent quantum-mechanical spectral envelope is given by the Heaviside partial fraction sum. Each term (i.e. every partial fraction) in this summation represents a component lineshape to be assigned to a given molecule (metabolite) in the tissue scanned by MRS. This is far reaching, since such a procedure allows reconstruction of the most basic quantum-mechanical entities, e.g. the total wave function of the investigated system and its ’Hamiltonian’ (a generator of the dynamics), directly from the encoded time signals. Since quantum mechanics operates with abstract objects, it can be applied to any system including living species. For example, time signals measured from the brain of a human being can be analyzed along these lines, as has actually been done e.g. by own our research. In this way, one can arrive at a quantum-mechanical description of the dynamics of vital organs of the patient by retrieving the interactions as the most important parts of various pathways of the tissue functions and metabolism. Of practical importance is that the outlined quantum-mechanical prediction of the frequency spectrum coincides with the Padé approximant, which is in signal processing alternatively called the fast Padé transform (FPT) for nonderivative estimations. Further, there is a novelty called the derivative fast Padé transform (dFPT). The FPT and dFPT passed the test of time with three fundamentally different time signals, synthesized (noise-free, noise-contaminated) as well as encoded from phantoms and from patients. Such systematics are necessary as they permit robust and reliable benchmarkings of the theory in a manner which can build confidence of the physician, while interpreting the patient’s data and making the appropriate diagnosis. In the present study, we pursue further this road paved earlier by applying the FPT and dFPT (both as shape and parameter estimators) to time signals encoded by in vivo proton MRS from an ovarian tumor. A clinical 3T scanner is used for encoding at a short echo time (30 ms) at which most resonances have not reached yet their decay mode and, as such, could be detected to assist with diagnostics. We have two goals, mathematical and clinical. First, we want to find out whether particularly the nonparametric dFPT, as a shape estimator, can accurately quantify. Secondly, we want to determine whether this processor can provide reliable information for evaluating an ovarian tumor. From the obtained results, it follows that both goals have met with success. The nonparametric dFPT, from its onset as a shape estimator, transformed itself into a parameter estimator. Its quantification capabilities are confirmed by reproducing the components reconstructed by the parametric dFPT. Thereby, fully quantified information is provided to such a precise extent that a large number of sharp resonances (more than 160) appear as being well isolated and, thus, assignable to the known metabolites with no ambiguities. Importantly, some of these metabolites are recognized cancer biomarkers (e.g. choline, phosphocholine, lactate). Also, broader resonances assigned to macromolecules are quantifiable by a sequential estimation (after subtracting the formerly quantified sharp resonances and processing the residual spectrum by the nonparametric dFPT). This is essential too as the presence of macromolecules in nonoderivative envelopes deceptively exaggerates the intensities of sharper resonances and, hence, can be misleading for diagnostics. The dFPT, as the quantification-equipped shape estimator, rules out such possibilities as wider resonances can be separately quantified. This, in turn, helps make adequate assessment of the true yield from sharp resonances assigned to metabolites of recognized diagnostic relevance.

In wireless links between ground stations and UAVs (Unmanned Aerial Vehicles), wireless signals may be attenuated by obstructions such as buildings. A three-dimensional RSS (Received Signal Strength) map (3D-RSS map), which represents a set of RSSs at various reception points in a three-dimensional area, is a promising geographical database that can be used to design reliable ground-to-air wireless links. The construction of a 3D-RSS map requires higher computational complexity, especially for a large 3D area. In order to sequentially estimate a 3D-RSS map from partial observations of RSS values in the 3D area, we propose a graph Laplacian-based sequential smooth estimator. In the proposed estimator, the 3D area is divided into voxels, and a UAV observes the RSS values at the voxels along a predetermined path. By considering the voxels as vertices in an undirected graph, a measurement graph is dynamically constructed using vertices from which recent observations were obtained and their neighboring vertices, and the 3D-RSS map is sequentially estimated by performing graph Laplacian regularized least square estimation.

Structural health monitoring of complex structures is often limited by restricted accessibility to locations of interest within the structure and availability of operational loads. In this work, a novel output-only virtual sensing scheme is proposed. This scheme involves the implementation of the modal expansion in an augmented Kalman filter. The performance of the proposed scheme is compared with two existing methods. Method 1 relies on a finite element model updating, batch data processing, and modal expansion (MUME) procedure. Method 2 employs a recursive sequential estimation algorithm, which feeds a substructure model of the instrumented system into an augmented Kalman filter (AKF). The new scheme referred to as Method 3 (ME-AKF), implements strain estimates generated via Modal Expansion into an AKF as virtual measurements. To demonstrate the applicability of the aforementioned methods, a rollercoaster connection was instrumented with accelerometers, strain rosettes, and an optical sensor. A comparison of estimated dynamic strain response at unmeasured locations using three alternative schemes is presented. Although acceleration measurements are used indirectly for model updating, the response-only methods presented in this research use only measurements from strain rosettes for strain history predictions and require no prior knowledge of input forces. Predicted strains using all methods are shown to sufficiently predict the measured strain time histories from a control location and lie within a 95% confidence interval calculated based on modal expansion equations. In addition, the proposed ME-AKF method shows improvement in strain predictions at unmeasured locations without the necessity of batch data processing. The proposed scheme shows high potential for real-time dynamic estimation of the strain and stress state of complex structures at unmeasured locations.

The global approaches solve SfM problems by independently inferring relative motions, followed be a sequential estimation of global rotations and translations. It is a fast approach but not optimal because it relies only on pairs and triplets of images and it is not a joint optimisation. In this publication we present a methodology that increases the quality of global solutions without the usual computational burden tied to the bundle adjustment. We propose an efficient structure approximation approach that relies on relative motions known upfront. Using the approximated structure, we are capable of refining the initial poses at very low computational cost. Compared to different benchmark datasets and software solutions, our approach improves the processing times while maintaining good accuracy.

We review the main concepts underlying the determination of terrestrial reference frames (TRFs) through a recursive algorithm based on Kalman Filtering and Rauch-Tung-Striebel (RTS) smoothing which is currently adopted at Jet Propulsion Laboratory (JPL) to compute sub-secular frame products (JTRFs). We contextualize the TRF determination in the state-space framework and we emphasize connections between frame state, its observability through space-geodetic frame inputs and the similarity transformation which is central to frame definition. We elaborate on the notion of sub-secular frame, enabled by our approach, in constrast to standard TRF products which, secular by construction, are designed to represent the long-term mean physical properties of the frame. Comparisons of JTRF solutions to standard products such as the International Terrestrial Reference Frame (ITRF) suggest high-level consistency in a long-term sense with time derivatives of the Helmert transformation parameters connecting the two TRFs below 0.18 mm/yr. We discuss advantages and limitations of JPL approach to TRF determination and outline lines of inquiries that are currently being researched as part of JTRF development plan.

The asynchronous optimal estimation problem is studied for linear discrete–time stochastic systems subject to a uniform state updating rate and random nonuniform measurement sampling rates. For the case where there are samples within a state updating period, a modified measurement equation from the original system is established for synchronization. Based on the established state–space model, an optimal sequential filter (SF) is developed in terms of the linear minimum variance (LMV) within a state updating period (SUP). It is noted that the SF is more suitable for dealing with the estimation problem of asynchronous sampling systems than other algorithms. Moreover, the proposed SF possesses the same estimation accuracy as that of the augmented batch filter (ABF), as well as a reduced computational cost. The equivalence of their estimation accuracy is strictly proven. Finally, the multisensor case is discussed. The effectiveness of the proposed algorithms is verified with simulation research.

In this paper, we address the signal estimation problem for a linear combination of multiple structured models, which is widely employed in the passive and/or active sensing systems to characterize the behaviors, for example, jamming and multipath propagation, in radar and communication societies. An iterative sequential estimation (ISE) algorithm is presented to obtain simultaneously the multiple structured signals. At each iteration, employing the estimated signals at the previous step, the optimal linear filters, based on mean-squared error criteria, are designed to minimize the output average power for every element of each signal. Finally, we evaluate the performance of the proposed ISE method compared with the least-square and compressed sensing algorithms via numerical simulations. The results highlight the presented algorithm shows a better signal estimation performance at low SNR and plays a trade-off between the computational complexity and the signal estimation performance.

We study the problem of distributed sequential estimation of common states and measurement noise covariance matrices of hidden Markov models by networks of collaborating nodes. We adopt a realistic assumption that the true covariance matrices are possibly different (heterogeneous) across the network. This setting is frequent in many distributed real-world systems where the sensors (e.g., radars) are deployed in a spatially anisotropic environment, or where the networks may consist of sensors with different measuring principles (e.g., using different wavelengths). Our solution is rooted in the variational Bayesian paradigm. In order to improve the estimation performance, the measurements and the posterior estimates are communicated among adjacent neighbors within one network hop distance using the information diffusion strategy. The resulting adaptive algorithm selects neighbors with compatible information to prevent degradation of estimates.

Recently, extensive researches focus on the joint estimation of carrier frequency and direction-of-arrival, whereas the heavy computation burden and affordable hardware cost are always required therein. To alleviate the problem, we propose a relaxed coprime array based two-stage estimator, which can sequentially detect the frequencies and direction-of-arrival for multiple targets. Guided by the closed-form robust algorithm, this relaxation yields a higher array sparsity compared with existing sparse arrays. Specifically, the first stage aims to achieve the classification of the frequency and angle remainders arising from temporal-spatial undersampling, which is realized by combining spectrum correction with pattern clustering. By incorporating the closed-form robust Chinese Remainder Theorem into the remainder classification result, we obtain all the frequencies and direction-of-arrival in the second stage. Both performance analysis and numerical results were conducted to verify the effectiveness of the proposed estimator in the multi-target case.

We describe a control loop over a sequential online algorithm. The control loop either computes or uses the sequential algorithm to estimate the temporal percentiles of any univariate input data sequence. It transforms an input sequence of numbers into output sequence of histograms. This is performed without storing or sorting all of the observations. The algorithm continuously tests whether the input data is stationary, and reacts to events that do not appear to be stationary. It also indicates how to interpret the histograms since their information content varies according to whether a histogram was computed or estimated. It works with parameter-defined, fixed-size small memory and limited CPU power. It can be used for a statistical reduction of a numerical data stream and, therefore, applied to various Internet of Things applications, edge analytics or fog computing. The algorithm has a built-in feasibility metric called applicability. The applicability metric indicates whether the use of the algorithm is justified for a data source: it works for an arbitrary univariate numerical input, but it is statistically feasible only under some requirements, which are explicitly stated here. We also show the results of a performance study, which was executed on the algorithm with synthetic data.

In the context of sequential estimation of radio range-based indoor position tracking, Bayesian smoothing framework is promising as involving past, present and future observations. The performance and practicability of a smoothing method greatly depend on how many and how future observations are incorporated. Aiming at real-time locating systems, the authors propose one time-step smoothing form on sequential Monte Carlo methods, including four popular Bayesian smoothers and a novel one time-step smoothed filtering (SF) algorithm. The smoothing algorithms are evaluated through two-dimensional position tracking on a real-world indoor test-bed. The authors present results that the proposed SF improves tracking performance requiring very limited computation and memory, which is applicable for real-time indoor position tracking. Moreover, the one time-step smoothing form is validated to mitigate ranging errors and smooth positioning trajectories.

The discrete polynomial-phase transform (DPT) method estimate chirp rate and central frequency of LFM signal based on sequential estimation of polynomial phase parameters. DPT method which has been developed by an iterative approach as Improved DPT method uses nonlinear least squares (NLS) technique to estimate phase parameters of the LFM signal. NLS have high computational load. In order to promote the precision of estimation and reduce the computational load in Improved DPT method, combined technique is proposed and used which provides an initial estimation of frequency interval based on NLS criterion in single-exponential mode and using random basis functions method.

This letter proposes a computationally efficient sequential estimation of integer carrier frequency offset (IFO) and sidelink identity (SID) in the long term evolution-device-to-device system. To detect the IFO without a priori knowledge on the SID information, the proposed detection method utilizes the conjugate property between two primary sidelink synchronization sequences. This design facilitates joint detection of the IFO and SID so that it can be detected sequentially. Simulation results indicate that the proposed sequential detection scheme has good performance and reduces computational complexity significantly compared to existing detection methods.

Line spectral estimation (LSE) with multiple measurement vector (MMV) is studied utilizing the Bayesian variational inference. Motivated by the recent grid-less variational line spectral estimation (VALSE) method, we develop the MMV VALSE (MVALSE). The MVALSE shares the advantages of the VALSE method, such as automatically estimating the model order, noise variance, weight variance, and providing the uncertainty of the frequency estimates. The MVALSE can be viewed as applying the VALSE with single measurement vector to each snapshot, and combining the intermediate data appropriately. Furthermore, the MVALSE is developed to perform sequential estimation. Numerical results demonstrate the effectiveness of the MVALSE method, compared to the state-of-the-art MMV methods.

We study the problem of estimating the source of a network cascade. The cascade initially starts from a single vertex and spreads deterministically over time, but only a noisy version of the propagation is observable. The goal is then to design a stopping time and estimator that will estimate the source well while ensuring the number of affected vertices is not too large. We rigorously formulate a Bayesian approach to the problem. If vertices can be labelled by vectors in Euclidean space (which is natural in spatial networks), the optimal estimator is the conditional mean estimator, and we derive an explicit form for the optimal stopping time under minimal assumptions on the cascade dynamics. We study the performance of the optimal stopping time on lattices, and show that a computationally efficient but suboptimal stopping time which compares the posterior variance to a threshold has near-optimal performance.

This chapter describes the sequential estimation method for the case wherein the observations are obtained sequentially in the general state-space model. While various methods have been proposed as solutions, this book introduces the particle filter. Regarding the implementation of the particle filter, this book mentions both the scratching and library-based approaches.

In this article we describe a new Hermite series based sequential estimator for the Spearman rank correlation coefficient and provide algorithms applicable in both the stationary and non-stationary settings. To treat the non-stationary setting, we introduce a novel, exponentially weighted estimator for the Spearman rank correlation, which allows the local nonparametric correlation of a bivariate data stream to be tracked. To the best of our knowledge this is the first algorithm to be proposed for estimating a time varying Spearman rank correlation that does not rely on a moving window approach. We explore the practical effectiveness of the Hermite series based estimators through real data and simulation studies demonstrating good practical performance. The simulation studies in particular reveal competitive performance compared to an existing algorithm. The potential applications of this work are manifold. The Hermite series based Spearman rank correlation estimator can be applied to fast and robust online calculation of correlation which may vary over time. Possible machine learning applications include, amongst others, fast feature selection and hierarchical clustering on massive data sets., Revised article incorporating comments by the reviewers, associate editor and editor of the Journal of Multivariate Analysis (accepted manuscript). Changes include a modified title and a significantly shortened article

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A “Netlist” implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

We consider the problem of locating the source of a network cascade, given a noisy time-series of network data. Initially, the cascade starts with one unknown, affected vertex and spreads deterministically at each time step. The goal is to find an adaptive procedure that outputs an estimate for the source as fast as possible, subject to a bound on the estimation error. For a general class of graphs, we describe a family of matrix sequential probability ratio tests (MSPRTs) that are first-order asymptotically optimal up to a constant factor as the estimation error tends to zero. We apply our results to lattices and regular trees, and show that MSPRTs are asymptotically optimal for regular trees. We support our theoretical results with simulations.

In this paper, we develop, analyze, and implement a new recursive method to conservatively account for non-Gaussian measurement errors with an uncertain correlation structure in Kalman filters (KFs). Under the assumptions of symmetric overbounding, the method guarantees a CDF overbound on the entire KF estimation error distribution. First, we leverage previous work on symmetric overbounding and frequency-domain overbounding to show how to transform a measurement domain CDF overbound into a position domain overbound. The second part of the paper evaluates the proposed method through Monte Carlo simulation for a GPS-based position estimation problem. Specifically, we show that while frequency domain overbounding produces a position domain overbound for Gaussian noise with an uncertain correlation structure, combination with symmetric overbounding is required to ensure position domain overbounding for non-Gaussian correlated noise.

In this paper, a sequential approach is proposed to estimate the relative transfer functions (RTF) used in developing a generalized sidelobe canceller (GSC). The latency in calibrating microphone arrays for GSC, often suffered by conventional approaches involving batch operations, is significantly reduced in the proposed sequential method. This is accomplished by an immediate generation of the RTF from initial input segments and subsequent updates of the RTF as the input stream continues. From the experimental results via the mean square error (MSE) criterion, it has been shown that the proposed method exhibits improved performance over the conventional batch approach as well as over recently introduced least mean squares approaches.

Asynchronism among the local radars is one of the most important challenges for multi-target tracking (MTT) in multi-static radar systems. In order to address this challenge in the framework of random finite set (RFS) based on Bayesian inference, we propose a decentralized probability hypothesis density (PHD) filter based on the asynchronous periodical sequential estimation (APSE). First, starting from a multi-target Bayesian filter, we derive the multi-target density update expressions for the APSE solution in the RFS framework. Next, we develop the PHD recursion expressions of the APSE solution, named as APSE-PHD, and describe the Gaussian mixture (GM) implementation of the APSE-PHD. Simulation results for a challenging tracking scenario confirm that the proposed APSE-PHD algorithm is effective for MTT in the asynchronous multistatic radar system and outperforms the existing PHD-based algorithm.

In this paper, we propose a metric (Euclidean) rectification method for a target spatial plane showed up in a single viewpoint image. Our approach is realized from a homography matrix calculated without using four points correspondence, unlike general well-known metric rectification methods. The method first estimates a projection matrix for the pre-defined world coordinate system on a specific plane regarded as the base one, and then sequentially estimates adjacent spatial planes appeared in the input image, using our previous method.1 Once our method can estimate the target plane, the world coordinate system on the base plane is moved to on the estimated target plane, and it is regarded as the new world coordinate system. By doing this, it can be showed that the homography matrix for the target plane is calculated only from the original projection matrix and the transformation parameters between the old and the new world coordinate systems (rotation and translation). Finally, metric rectification can be realized using the calculated homography matrix; i.e., the proposed method can obtain 3D information such as length and angle on a plane where four-point correspondence is not easily determined, only using a single view image. Experimental results showed the validity and effectiveness of our approach.

The JTRF2014 realization of terrestrial reference frame has adopted a weekly time series representation that can track dominant non-linear station motions including periodic and random variations. The realization is based on the Kalman filter and smoother algorithms whose time sequential nature would also be suitable for continuous updating of an existing frame as soon as new geodetic data become available. As a part of preparation for the next reference frame realization, we have been examining alternative filter and smoother algorithms based on the square-root information filter (SRIF), known generally for improved numerical accuracy of the covariance matrix represented by a square-root matrix. The new algorithms offer a number of other advantages over the conventional filter/smoother algorithms used in JTRF2014. Namely, the new approach allows us to (1) avoid using some fictitious covariance matrix to initialize the filter, (2) avoid the random-walk constraints for the Helmert parameter sequences, and (3) handle cross-temporal EOP data such as the week-long segments reported by the SLR and DORIS networks. We have also been enhancing the stochastic models of the station position motion to be used by the filter and smoother, including models for non-tidal deformation., EGUsphere

Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on the expected number of bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. For a class of continuous Markov processes satisfying regularity conditions, we find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. We show that the optimal encoding policy transmits a $1$-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it to decide the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function. Furthermore, we show that the optimal causal code also minimizes the mean-square cost of a continuous-time control system driven by a continuous Markov process and controlled by an additive control signal.

Background subtraction is an important computer vision scheme for segmenting moving objects from a video. The imminent IoT era imposes severe constraints on camera systems in terms of area, speed, power, and accuracy. This chapter presents a new background subtraction scheme which is based on Poisson noise model, where we use a Poisson mixture model (PMM) for modeling dynamic backgrounds. Furthermore, we have used a method for sequential estimation of parameters of the PMM which does not allow the parameters to fluctuate with random noise. Resultantly, our method achieves a reduction of 17.76% and 8.16% in percent of wrong classification compared to the hardware implementations of Gaussian Mixture Models and Pixel-based Adaptive Segmented (PBAS) methods, respectively. The proposed scheme is also very fast, low power, and requires very little logic resources. The memory bandwidth requirement of the proposed scheme is 6.66%, 41.36%, and 90.48% lower compared to state-of-the-art FPGA implementation of GMM, ViBe, and PBAS algorithms, respectively. The proposed background subtraction scheme achieves a significant speed up compared to FPGA implementations of GMM (by 42.68%), ViBe (by 115%), and PBAS (by 142.2%) schemes. Similarly, the energy consumption of the proposed method is 76.39% and 99.9% less compared to GMM and PBAS, respectively. In summary, the advantages of the proposed method in accuracy, speed, and energy consumption combined together make it especially suitable for embedded applications.

The non-orthogonal multiple access (NOMA) scheme has been considered as one of the methods for performing large capacity, high-speed communications in fifth-generation mobile communications system (5G). We propose a chaos NOMA scheme that realizes physical layer security and reliable communication. However, in conventional studies, the decoding of chaos NOMA uses joint maximum likelihood sequential estimation (MLSE), which simultaneously estimates the signals of all superposed users, and the decoding complexity increases exponentially with the number of superimposed users. Therefore, in this paper, we propose a low complexity decoding scheme for chaos NOMA using a combination of successive interference cancellation (SIC), which is a typical decoding method for NOMA, and partial MLSE. Through numerical simulations, we show that complexity is significantly reduced with the joint MLSE, and that the transmission performance is still better than that of the conventional NOMA scheme.

Because GLONASS employs frequency division multiple access technique, the inter-frequency biases (IFBs) generate in the double difference observations from different types of receivers. Therefore, it is significant to eliminate the IFBs for GLONASS high-precision positioning. The size of the phase IFBs rate is generally millimeter or centimeter, the IFBs of L1 and L2 are almost equivalent, and possess a certain linear relationship with the frequency number, which is conducive to the separation of the IFBs and the ambiguities. In this paper, two methods of phase IFBs correction are adopted to compare, including pre-calibration and real-time estimation. In the pre-calibration, the function model of the widelane observation residuals and the IFBs rate is established, and the IFBs rate is estimated by sequential estimation; in the real-time estimation, the GLONASS mathematical model considering IFBs is constructed, and the IFBs rate is estimated by Kalman filter. In the data preprocessing, the triple difference observations are used to construct slip test statistics for cycle slip detection. The LAMBDA method is used to fix the ambiguity. The experimental results show that the two methods can effectively estimate GLONASS IFBs rate and both the fixed rate and positioning accuracy are improved evidently after the IFBs elimination. The filtering method is more stable and suitable for real-time solution.

Estimation with assigned risk is a classical statistical problem, and the theory is well developed for the case of directly observed (no missing) data. In this article a more complicated problem of estimation of the spectral density in presence of missing data is considered. First, the corresponding theory of sequential estimation with minimal expected stopping time is developed. Then it is shown that a two‐stage estimator may be used and it yields the minimal stopping time. Sample size of the first stage may be deterministic and in order smaller than a minimal stopping time, and then the first stage defines the size of the second stage. Furthermore, the estimator adapts to unknown smoothness of an underlying spectral density and to an underlying missing mechanism.

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is able to use any valid approximation to the filtering and prediction densities of the state process. It computes the posterior distribution of the static parameters on a discrete grid that tracks the support dynamically. For inference of the state process, the Kalman filter and its extensions as well as cubature filtering have been used. It is illustrated with several examples including the stochastic volatility model and the challenging Kitagawa model and is compared to both online and offline methods. It is shown to provide a good trade off between speed and performance.

We investigate a robust sequential estimation algorithm of particle filters, which combine multiple features of visual objects, in order to obtain reliable evidential information from independent sources of sensor data. Most of particle filter algorithms are based on conditional density propagation in Bayesian inference rules. In this paper, it is modified by the conjunctive rule of independent features. Therefore, the proposed algorithm is more reliable since it demonstrates the solution to both efficiency depletion and over-sampling in particle filters.

This study deals with the target detection problem embedded in multiple range jamming which is usually employed to mask the useful signal or deceive the radar systems. Exploiting the observation that the waveform of the range jamming would be not identical to the probing signal of the radar system, the authors propose a coupled sequential estimation algorithm to obtain simultaneously the range profiles of target and jamming. Each iteration of the proposed algorithm designs a set of linear filters for each range bin based on the minimisation of the output average power by utilising the obtained range profiles of target and jamming at the last iteration. The proposed algorithm is capable of eliminating the jamming in the target range profiles and shares very low range sidelobes. The numerical simulations are provided to prove the effectiveness of the proposed algorithm also in comparison with the matched filter.

A novel multiple-graph technique has been proposed for the preliminary assessment of the ground conditions in the Himalayan region. This technique has been developed based on the sequential estimation of three quantities, viz. rock mass strength , competency factor and the ground condition. Rock mass strength is estimated from rock mass quality ( Q ). Moreover, two empirical ground classifications have been suggested, based on many case histories , for separately defining ground condition in soft rocks and hard rocks. A graphical work flow chart and practical illustration of this method has been presented using two sets of examples. The proposed technique is an efficient tool for quick estimation of the ground condition in the primary phase of design of tunnels and also during the excavation of tunnels.

In this article, we consider the problem of multivariate Bayesian sequential estimation of the unknown mean vector. We propose a robust sequential procedure without using the prior informat...

This paper deals with the relatively new field of sequence-based estimation in which the goal is to estimate the parameters of a distribution by utilizing both the information in the observations and in their sequence of appearance. Traditionally, the Maximum Likelihood (ML) and Bayesian estimation paradigms work within the model that the data, from which the parameters are to be estimated, is known, and that it is treated as a set rather than as a sequence. The position that we take is that these methods ignore, and thus discard, valuable sequence -based information, and our intention is to obtain ML estimates by “extracting” the information contained in the observations when perceived as a sequence. The results of Oommen (November 2007) introduced the concepts of Sequence Based Estimation (SBE) for the Binomial distribution, where the authors derived the corresponding MLE results when the samples are taken two-at-a-time, and then extended these for the cases when they are processed three-at-a-time, four-at-a-time etc. This current paper generalizes these results for the multinomial case. The strategy we invoke involves a novel phenomenon called “Occlusion” that has not been reported in the field of estimation. The phenomenon can be described as follows: By occluding (hiding or concealing) certain observations, we map the estimation problem onto a lower-dimensional space, i.e., onto a binomial space. Once these occluded SBEs have been computed, we demonstrate how the overall Multinomial SBE (MSBE) can be obtained by mapping several lower-dimensional estimates, that are all bound by rigid probability constraints, onto the original higher-dimensional space. In each case, we formally prove and experimentally demonstrate the convergence of the corresponding estimates. The estimation methods proposed here have also been tested on real-life datasets from the UCI repository (Frank and Asuncion, 2013), and the accuracies obtained have been remarkable. We also discuss how various MSBEs can be fused to yield a superior MSBE, and present some potential applications of MSBEs. Our new estimates have great potential for practitioners, especially when the cardinality of the observation set is small.

This paper is focused on the problem of the detection of multiple scatterers in synthetic aperture radar (SAR) tomography. The method presented exploits the a priori information that at most $K_{{\rm{max}}}$ different scatterers are present in the same range-azimuth resolution cell. In particular, a simplified version of a generalized-likelihood ratio test (GLRT) detector, based on support estimation (Sup-GLRT), is proposed. The Sup-GLRT is a constant false alarm rate sequential test that detects the presence of scatterers, one after another, and estimates their positions, detecting the support of the unknown signal. The proposed simplified test denoted as Fast-Sup-GLRT detector, despite still being a multistep statistical hypothesis test, exploits, at each step i , an approximated maximum-likelihood estimate of the signal support of cardinality i −1, based on the sequential estimation of i −1 supports of cardinality one. The introduced approximation allows a considerable reduction of the computational complexity, which from the combinatorial trend of Sup-GLRT passes to the linear one of Fast-Sup-GLRT, without significantly impairing the detection probability. The performance of the proposed approach is analyzed using TerraSAR-X system parameters, with particular reference to the elevation superresolution achievable for an assigned probability of false alarm and with a given number of acquisitions. Numerical results on simulated and real data are presented and discussed.

This is Part II of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we considered a state-space model where the state was an ARMA process of known order and where the parameters of the process could be known or unknown. In this paper, we extend our work from Part I by considering the same type of models, with the added complexity that the ARMA processes are now of unknown order. Instead of working on a scheme that first tracks the state by operating with different assumed models, and then selects the best model by using a predefined criterion, we present a method that directly estimates the state without the need of knowing the model order. We derive the transition density of the state for unknown ARMA model order, and propose a particle filter based on that density and the empirical Bayesian methodology. We demonstrate the performance of the proposed method with computer simulations and compare it with the methods from Part I.

Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those arising in turbulence, in which effective low-dimensional representation of the desired probability distribution is challenging. Nonetheless recent advances have shown considerable success in filtering based on certain carefully chosen simplifications of the underlying system, which allow closed form filters. This leads to filtering algorithms with significant, but judiciously chosen, model error. The purpose of this article is to analyze the effectiveness of these simplified filters, and to suggest modifications of them which lead to improved filtering in certain time-scale regimes. We employ a Markov switching process for the true signal underlying the data, rather than working with a fully resolved DNS PDE model. Such Markov switching models haven been demonstrated to provide an excellent surrogate test-bed for the turbulent bursting phenomena which make filtering of complex physical models, such as those arising in atmospheric sciences, so challenging.\ud \ud

Recent developments are summarized concerning Sequest and Sequem, sequential procedures for estimating nonextreme and extreme steady-state quantiles of a simulation output process. The procedures deliver point and confidence-interval (CI) estimators of a given quantile, where each CI approximately satisfies given requirements on its coverage probability and its absolute or relative precision. The public-domain Sequest software now includes both procedures. The software is applied to a user-supplied dataset exhibiting warm-up effects, autocorrelation, and a multimodal marginal distribution. For the simulation analysis method of standardized time series (STS), we also sketch an elementary proof of a functional central limit theorem (FCLT) that is needed to develop STS-based quantile-estimation procedures when the output process satisfies a conventional density-regularity condition and either (i) a geometric-moment contraction condition and an FCLT for a related binary process, or (ii) conventional strong-mixing conditions.

In this paper, we consider a challenging problem of accurate instantaneous frequency (IF) estimation of multi-component non-linear frequency modulated (FM) signals, which may have distinct amplitude levels, in the presence of burst missing data samples. We propose a technique, in which the signal components are sequentially estimated from the strongest component to the weaker ones. First, the time-frequency (TF) representation of the received signal is obtained after applying a signal-adaptive TF kernel. Then, the IF of the strongest signal component is estimated to reconstruct its waveform, and its contribution is removed from the signal through orthogonal projection. The procedure is successively implemented for weaker signal components until the residual becomes negligible. The refined estimation of the signal components is independent of the missing data positions. The proposed technique successfully resolves signal components with distinct amplitude levels and achieves concentrated TF representations by mitigating the undesired effects of cross-terms and artifacts due to the burst missing data samples. Simulation results confirm the effectiveness of the proposed approach.

The accurate estimation of time difference of arrival (TDOA) and frequency difference of arrival (FDOA) can be very important in passive location. However, when relative time companding (RTC) or relative doppler companding (RDC) occurs, the conventional cross ambiguity function (CAF) method fails to achieve a good performance. This paper concerns the RTC/RDC problem and proposes a two-step estimation method for joint TDOA, FDOA and doppler rate parameters. The first step obtains a sequential estimation using short-CAFs and the second step obtains the final estimation using least square method. Theoretical analysis and simulation results final shows the effectiveness of the proposed method.

We consider the purely sequential procedure for estimating the scale parameter of a gamma distribution with known shape parameter, when the risk function is bounded by the known preassigned number. In this paper, we provide asymptotic formulas for the expectation of the total sample size. Also, we propose how to adjust the stopping variable so that the risk is uniformly bounded by a known preassigned number. In the end, the performances of the proposed methodology are investigated with the help of simulations and also by using a real data set.

Among the evaluation indicators of the remaining useful life of on-board power batteries, accurate capacity estimation is one of the dominant factors for the reliability of electric vehicles. During the battery lifespan, taking into account that a large amount of charging data can provide periodical updates for empirical model, a sequential capacity estimation framework combining data-driven method and empirical model is put forward. The feature variables of incremental capacity are extracted as the training data set of back propagation neural network, framing the online estimation model; simultaneously the Arrhenius fading model is employed for continuous estimation. However, open-loop Arrhenius model suffers from on-board parameter mismatch. To further improve convergence and precision, sequential estimation algorithm is proposed in this paper: the estimation of model parameter adopting the particle filter leads to a closed-loop parameter update; afterwards the updated capacity is fused once again with online identification by the extended Kalman filter. Finally, the results of experiments under alternating temperature indicate that the error of sequential capacity estimation converges to within 2.5%. In addition, the results of robustness analysis prove the stability of the sequential capacity estimation strategy.

Summary Kalman filter is a sequential estimation scheme that combines predicted and observed data to reduce the uncertainty of the next prediction. Because of its sequential nature, the algorithm cannot be efficiently implemented on modern parallel compute hardware nor can it be practically implemented on large-scale dynamical systems because of memory issues. In this paper, we attempt to address pitfalls of the earlier low-memory approach described in and extend it for parallel implementation. First, we describe a low-memory method that enables one to pack covariance matrix data employed by the Kalman filter into a low-memory form by means of certain quasi-Newton approximation. Second, we derive parallel formulation of the filtering task, which allows to compute several filter iterations independently. Furthermore, this leads to an improvement of estimation quality as the method takes into account the cross-correlations between consequent system states. We experimentally demonstrate this improvement by comparing the suggested algorithm with the other data assimilation methods that can benefit from parallel implementation. Copyright © 2016 John Wiley & Sons, Ltd.

Multi-arm group sequential clinical trials are efficient designs to compare multiple treatments to a control. They allow one to test for treatment effects already in interim analyses and can have a lower average sample number than fixed sample designs. Their operating characteristics depend on the stopping rule: We consider simultaneous stopping, where the whole trial is stopped as soon as for any of the arms the null hypothesis of no treatment effect can be rejected, and separate stopping, where only recruitment to arms for which a significant treatment effect could be demonstrated is stopped, but the other arms are continued. For both stopping rules, the family-wise error rate can be controlled by the closed testing procedure applied to group sequential tests of intersection and elementary hypotheses. The group sequential boundaries for the separate stopping rule also control the family-wise error rate if the simultaneous stopping rule is applied. However, we show that for the simultaneous stopping rule, one can apply improved, less conservative stopping boundaries for local tests of elementary hypotheses. We derive corresponding improved Pocock and O'Brien type boundaries as well as optimized boundaries to maximize the power or average sample number and investigate the operating characteristics and small sample properties of the resulting designs. To control the power to reject at least one null hypothesis, the simultaneous stopping rule requires a lower average sample number than the separate stopping rule. This comes at the cost of a lower power to reject all null hypotheses. Some of this loss in power can be regained by applying the improved stopping boundaries for the simultaneous stopping rule. The procedures are illustrated with clinical trials in systemic sclerosis and narcolepsy. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

In this study, the authors consider the coupled sequential detection and estimation of weak targets for track-before-detect algorithm in long range early warning radar. They present a new strategy and develop a coupled cost function consisting of detection, position estimation and tracking estimation loss. In the proposed procedure, the sequential stopping and detection rules are simplified. Moreover, they derive the lower bounds of the detection and estimation probabilities, which can be used to design the suitable related parameter values. Finally, several numerical simulations of the new strategy and the comparisons are presented and discussed.