Estimation and Filtering Theory

This paper presents a frame work for hardware acceleration for post video processing system implemented on FPGA. The deblocking filter algorithms ported on SOC having Altera NIOS-II soft core processor.SOC designed with the help of SOPC builder .Custom instructions are chosen by identifying the most frequently used tasks in the algorithm and the instruction set of NIOS-II processor has been extended. Deblocking filter new instruction added to the processor that are implemented in hardware and interfaced to the NIOS-II processor. New instruction added to the processor to boost the performance of the deblocking filter algorithm. Use of custom instructions the implemented tasks have been accelerated by 5.88%. The benefit of the speed is obtained at the cost of very small hardware resources.

A high order signal model is proposed in which the states are Kronecker tensor products of probability distributions. This model enables an optimal linear filter to be specified. A minimum residual error variance criterion may be used to select the number of discretizations and Kronecker products. The filtering of LIDAR data from a coal shiploader environment is investigated. It is demonstrated that the proposed method can outperform conventional Kalman and hidden Markov model filters.

Multi-sensor networks can alleviate the need for high-cost, high-accuracy, single-sensor tracking in favor of an abundance of lower-cost and lower-accuracy sensors to perform multi-sensor tracking. The use of a multi-sensor network gives rise to the need for a fusion step that combines the outputs of all sensor nodes into a single probabilistic state description. When considering Gaussian uncertainties, the well-known covariance intersection technique may be used. In the more general, non-Gaussian case, covariance intersection is not sufficient. This paper examines a fusion method based on logarithmic opinion pools and develops algorithms for multi-sensor data fusion as well as investigates weight selection schemes for the opinion pool. The proposed fusion rules are applied to the tracking of a space object using multiple ground-based optical sensors. Non-Gaussian orbit determination methods are applied to each sensor individually, and the fusion rule is applied to the combined outputs of each sensor node. It is shown that the multi-sensor fusion rule leads to an increase of nearly two orders of magnitude in the position tracking accuracy as compared to the traditional single-sensor tracking method.

Convolving the output of Discontinuous Galerkin computations with symmetric Smoothness-Increasing Accuracy-Conserving (SIAC) filters can improve both smoothness and accuracy. To extend convolution to the boundaries, several one-sided spline filters have recently been developed. This paper interprets these filters as instances of a general class of position-dependent (PSIAC) spline filters that can have non-uniform knot sequences and skip B-splines of the sequence. PSIAC filters with rational knot sequences have rational coefficients. For prototype knot sequences , such as integer sequences that may have repeated entries, PSIAC filters can be expressed in symbolic form. Based on the insight that filters for shifted or scaled knot sequences are easily derived by non-uniform scaling of one prototype filter, a single filter can be re-used in different locations and at different scales. Computing a value of the convolution then simplifies to forming a scalar product of a short vector with the local output data. Restating one-sided filters in this form improves both stability and efficiency compared to their original formulation via numerical integration. PSIAC filtering is demonstrated for several established and one new boundary filter.

The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5 ± 0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.

A  simple  UV-Visible  spectrophotometric  method  has  been
developed for the determination of Atorvastatin in its pure form as
well as pharmaceutical dosage form using Methyl Orange reagent.
The  method  is  based  on  the  measurement  of  absorbance  of
Atorvastatin in methanol at 410 nm. The Beer’s law is obeyed
over  the  linear  range  50-300μg  /ml  of  Atorvastatin.  All  the
variables were studied to optimize the reaction conditions. No
interference  was  observed  in  the  presence  of  common
pharmaceutical excipients. The validity of the method was tested
by analyzing the drug in its pharmaceutical preparations. Good
recoveries were also obtained. Assay for the tablet preparation was
performed using UV-Visible spectrophotometric method and the
results were found to be within acceptable limits.

"This book provides several flight-validated formulations and algorithms, fortified by thousands of hours working with real GPS and inertial data.  The material, not yet widely used only due to its originality, is beginning to appear in classrooms and (soon) in operational systems.  Considerable improvement is offered in multiple areas, including:
• transition from pre-GNSS nmi/hr to today's cm/sec for inertial
  navigation
• full usage for “fractured” (intermittent and permanently
  ambiguous) carrier phase
• rigorous integrity for separate SVs, with integrity validation
  extended in several ways
• unprecedented robustness and situation awareness
• state-of-the-art performance with low cost IMUs
• usage of raw data from GPS (carrier phase and pseudorange)
  & from IMU (gyro and accelerometer increments)
• "cookbook" steps to obtain nav (position/velocity/attitude)
  estimates in all three dimensions from raw data
• user empowerment – complete flexibility and capability for
  versatile operation
• new interoperability features, readily mixing observables from
  any channel on any constellation (GPS, GLONASS, etc.)
• new insights for much easier implementation.
• formulations for an extensive set of tracking applications
  and supporting operations"

Personal positioning is a challenging topic in the area of navigation mainly because of the cost, size and power consumption constraints imposed on the hardware. Satel- lite based positioning techniques can meet the requirements for many applications, but cover well only outdoor environment. Problems like weak satellite signals make the positioning impossible indoors. Urban canyons are also difficult areas for GNSS based navigation because of large multipath errors and satellite signal outages. Many applications require seamless positioning in all environments. However, there is no overall solution for navigation in GNSS denied environment, which is reliable, ac- curate, cost effective and quickly installed. Recently developed systems for indoor positioning often require pre-installed infrastructure.
Another approach is to use fully autonomous navigation systems based on self-con- tained sensors and street or indoor maps. This thesis is concerned with autonomous personal navigation devices, which do not rely on the reception of external informa- tion, like satellite or terrestrial signals. The three proposed algorithms can be integ- rated into personal navigation systems.
The first algorithm computes positioning for a map aided navigation system designed for land vehicles traveling on road network. The novelty is in application of particle filtering to vehicle navigation using road network database. The second algorithm is aimed at map aided vehicle navigation indoors. The novelty is in the method for correction of position and heading. The third algorithm computes solution for pedestrian navigation system, which is based on body mounted inertial measurement unit and models of human gait.

Center of Mass (CoM) estimation realizes a crucial role in legged locomotion. Most walking pattern generators and real-time gait stabilizers commonly assume that the CoM position and velocity are available for feedback. In this thesis we present one of the first
3D-CoM state estimators for humanoid robot walking. The proposed estimation scheme fuses effectively joint encoder, inertial, and feet pressure measurements with an Extended Kalman Filter (EKF) to accurately estimate the 3D-CoM position, velocity, and external
forces acting on the CoM. Furthermore, it directly considers the presence of uneven terrain and the body’s angular momentum rate and thus effectively couples the frontal with the lateral plane dynamics, without relying on feet Force/Torque (F/T) sensing.
Nevertheless, it is common practice to transform the measurements to a world frame of reference and estimate the CoM with respect to the world frame. Consequently, the robot’s base and support foot pose are mandatory and need to be co-estimated. To this end, we extend a well-established in literature floating mass estimator to account for the
support foot dynamics and fuse kinematic-inertial measurements with the Error State Kalman Filter (ESKF) to appropriately handle the overparametrization of rotations. In such a way, a cascade state estimation scheme consisting of a base and a CoM estimator
is formed and coined State Estimation RObot Walking (SEROW). Additionally, we employ Visual Odometry (VO) and/or LIDAR Odometry (LO) measurements to correct the kinematic drift caused by slippage during walking. Unfortunately, such measurements suffer from outliers in a dynamic environment, since frequently it is assumed that only the
robot is in motion and the world around is static. Thus, we introduce the Robust Gaussian ESKF (RGESKF) to automatically detect and reject outliers without relying on any prior knowledge on measurement distributions or finely tuned thresholds. Therefore, SEROW
is robustified and is suitable for dynamic human environments. In order to reinforce further research endeavors, SEROW is released to the robotic community as an open-source ROS/C++ package.
Up to date control and state estimation schemes readily assume that feet contact status is known a priori. Contact detection is an important and largely unexplored topic in contemporary humanoid robotics research. In this thesis, we elaborate on a broader question: in which gait phase is the robot currently in? To this end, we propose a holistic frame-
work based on unsupervised learning from proprioceptive sensing that accurately and efficiently addresses this problem. More specifically, we robustly detect one of the three gait-phases, namely Left Single Support (LSS), Double Support (DS), and Right Single Support (RSS) utilizing joint encoder, IMU, and F/T measurements. Initially, dimensionality reduction with Principal Components Analysis (PCA) or autoencoders is performed to extract useful features, obtain a compact representation, and reduce the noise. Next, clustering is performed on the low-dimensional latent space with Gaussian Mixture Models (GMMs) and three dense clusters corresponding to the gait-phases are obtained. Interestingly, it is
demonstrated that the gait phase dynamics are low-dimensional which is another indication pointing towards locomotion being a low dimensional skill. Accordingly, given that the proposed framework utilizes measurements from sensors that are commonly available
on humanoids nowadays, we offer the Gait-phase Estimation Module (GEM), an open-source ROS/Python implementation to the robotic community.
SEROW and GEM have been quantitatively and qualitatively assessed in terms of accuracy and efficiency both in simulation and under real-world conditions. Initially, a simulated robot in MATLAB and NASA’s Valkyrie humanoid robot in ROS/Gazebo were employed to establish the proposed schemes with uneven/rough terrain gaits. Subsequently,
the proposed schemes were integrated on a) the small size NAO humanoid robot v4.0 and b) the adult size WALK-MAN v2.0 for experimental validation. With NAO, SEROW was implemented on the robot to provide the necessary feedback for motion planning and real-
time gait stabilization to achieve omni-directional locomotion even on outdoor/uneven terrains. Additionally, SEROW was used in footstep planning and also in Visual SLAM with the same robot. Regarding WALK-MAN v2.0, SEROW was executed onboard with kinematic-inertial and F/T data to provide base and CoM feedback in real-time. Furthermore, VO has also been considered to correct the kinematic drift while walking and facilitate possible footstep planning. GEM was also employed to estimate the gait phase in WALK-MAN’s dynamic gaits.
Summarizing, a robust nonlinear state estimator is proposed for humanoid robot walking. Nevertheless, this scheme can be readily extended to other type of legged robots such
as quadrupeds, since they share the same fundamental principles.

Today very important means of communication is the e-mail that allows people all over the
world to communicate, share data, and perform business. Yet there is nothing worse than an
inbox full of spam; i.e., information crafted to be delivered to a large number of recipients
against their wishes. In this paper, we present a numerous anti-spam methods and solutions that
have been proposed and deployed, but they are not effective because most mail servers rely on
blacklists and rules engine leaving a big part on the user to identify the spam, while others rely
on filters that might carry high false positive rate.

Sensors can be used to measure the position of an object. In the present thesis the effects
which limit the usage of sensors in high dynamic positioning applications on a nanometer
level are discussed. Various sensor principles and their properties are investigated and
compared. Sensors based on the measurement of i.a. magnetic fields, illumination, or
even strain are characterized, as well as their range, bandwidth, resolution, linearity
and disturbance rejection is determined.
It will be shown that the simultaneous use of multiple sensors and the specific
combination of sensors’ data (fusion) enables a higher performance primarily in terms
of resolution and dynamics. Several techniques for the fusion are discussed under
consideration of various aspects, however the ultimate aim of sensor fusion is similar.
The methods of feedforward control, complementary filtering, Kalman filtering and
optimal filtering (robust control) are developed and verified on practical problems in
position sensor systems. To treat various challenges in sensor filtering and sensor fusion
a methodological approach, containing separable steps of
• problem formulation with well-defined prerequisits and simplifications,
• theory discussion with approach to find a solution,
• analytical proof or reasoning by statistical values out of numerical simulations,
• experiment design, and
• verification on a real time platform
are realized.

In recent years, signal processing has come under mounting pressure to accommodate the increasingly high-dimensional raw data generated by modern sensing systems. Despite extraordinary advances in computational power, processing the
signals produced in application areas such as imaging, video, remote surveillance, spectroscopy, and genomic data analysis continues to pose a tremendous challenge. Fortunately, in many cases these high-dimensional signals contain relatively little information compared to their ambient dimensionality. For example, signals can often be well-approximated as a sparse linear combination of elements from a known basis or dictionary.

Traditionally, sparse models have been exploited only after acquisition, typically for tasks such as compression. Recently, however, the applications of sparsity have greatly expanded with the emergence of compressive sensing, a new approach to data acquisition that directly exploits sparsity in order to acquire analog signals more efficiently via a small set of more general, often randomized, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. A common theme in this research is the use of randomness in signal acquisition, inspiring the design of hardware systems that directly implement random measurement protocols.

This thesis builds on the field of compressive sensing and illustrates how sparsity can be exploited to design efficient signal processing algorithms at all stages of the information processing pipeline, with a particular focus on the manner in which randomness can be exploited to design new kinds of acquisition systems for sparse signals. Our key contributions include: (i) exploration and analysis of the appropriate properties for a sparse signal acquisition system; (ii) insight into the useful properties of random measurement schemes; (iii) analysis of an important family of algorithms for recovering sparse signals from random measurements; (iv) exploration of the impact of noise, both structured and unstructured, in the context of random measurements; and (v) algorithms that process random measurements to directly extract higher-level information or solve inference problems without resorting to full-scale signal recovery, reducing both the cost of signal acquisition and the complexity of the post-acquisition processing.

The previously-discussed optimal Kalman filter [1] – [3] is routinely used for tracking observed and unobserved states whose second-order statistics change over time. It is often assumed within Kalman filtering applications that one or more random variable sequences are generated by a random walk or an autoregressive process. That is, common Kalman filter parameterisations do not readily exploit knowledge about the random variables’ probability distributions. More precisely, the filter is optimal only for Gaussian variables whose first and second order moments completely specify all relevant probability distributions. For non-Gaussian data, the filter is only optimal over all linear filters [1].

Rather than assuming that random variable sequences are generated by autoregressive processes they may alternatively be modelled as Markov chains. The phrase ‘Markov chain’ was first coined in 1926 by a Russian mathematician S. N. Bernstein to acknowledge previous discoveries made by Andrei Andreevich Markov [4].  Markov was a professor at St Petersburg University and a member of the St Petersburg Academy of Sciences, which was a hub for scientific advances in many fields including probability theory. Indeed, Markov, along with fellow academy members D. Bernoulli, V. Y. Bunyakovsky and P. L. Chebyshev, all wrote textbooks on probability theory. Markov extended the weak law of large numbers and the central limit theorem to certain sequences of dependent random variables forming special classes of what are now known as Markov chains [4].

The basic theory of Hidden Markov models (HMMs) was first published by Baum et al in the 1960s [5]. HMMs were introduced to the speech recognition field in the 1970s by J. Baker at CMU [6], and F. Jelinek and his colleagues at IBM [7]. One of the most influential papers on HMM filtering and smoothing was the tutorial exposition by L. Rabiner [8], which has been accorded a large number of citations. Rabiner explained how to implement the forward-backward algorithm for estimating Markov state probabilities, together with the Baum-Welch algorithm (also known as the Expectation Maximisation algorithm).  HMM filters and smoothers can be advantageous in applications where sequences of alphabets occur [8] - [10]. For example, in automatic speech recognition, sentence and language models can be constructed by concatenating phoneme and word-level HMMs. Similarly, stroke, character, word and context HMMs can be used in handwriting recognition. HMMs have been useful in modelling in biological sequences such as proteins and DNA sequences.

The Doob–Meyer decomposition theorem [11] states that a stochastic process may be decomposed into the sum of two parts, namely, a prediction and an input process. The standard Kalman filter [1] makes use of both prediction plus input process assumptions and attains minimum-variance optimality. In contrast, the standard hidden Markov model filter/smoother rely exclusively on (Markov model) prediction and is optimum in a Bayesian sense [8] - [10]. It is shown below that minimum-variance and HMM techniques can be combined for improved state recovery.

The minimum-variance, HMM and combined-minimum-variance-HMM predictions are only calculated from states at the previous time step. Improved predictions can be calculated from states at multiple previous time steps. The desired interdependencies between multiple previous states are conveniently captured by constructing high-order-Kronecker-product state vectors. The theory and implementation of such high-order-minimum-variance-HMM filters is also described below.

The afore-mentioned developments are driven by our rapacious appetites for improved estimator performance. In principle, each additional embellishment, spanning HMM filters, minimum-variance-HMM filters to high-order-minimum-variance-HMM filters, has potential to provide further performance gains, subject to the usual proviso that the underlying modelling assumptions are correct. Needless to say, significantly higher calculation overheads must be reconciled against any performance benefits.

Some prerequisites, namely, some results from probability theory including Markov processes, are introduced in Section 11.2. Bayes’ theorem is judiciously applied in Section 11.3 to derive the HMM filters and smoothers for time-homogenous processes. A state-space model having an output covariance equivalent to an HMM is derived in Section 11.4. This enables transition probability matrices to be employed in optimal filter and smoother constructions that minimise the error variance. Section 11.5 describes high-order-minimum-variance-HMM filters, which employ Kronecker product states.

This paper reviews an important result in estimation theory, now known as the Kalman filter, named after Rudolf E. Kalman. The Kalman filter solves the least-squares estimation problem recursively, and in a computationally ecient manner. The problem is carefully stated in the second section and is later solved using matrix derivatives. The resulting solution, the linear Kalman filter, is collected into an algorithm that has a number of applications where one wants to estimate a collection of related, measurable values as data is collected.

— Electrical devices often use RC, LC or RLC circuit to design power amplifiers, filters and mixers etc. Complex iterative algorithms are used for the simulation of these circuits.. This paper illustrates numerical experiments on growth of rounding off error in simulation of simple RC circuit using fourth order Runge-Kutta method (RK) and the Runge-Kutta-Fehlberg with adaptive step size control method (RKF). Our analysis indicates that in simulations with RK method, round off error grows ~ 80% with 10-15 iterations and ~96-98% within 100 iterations with different step sizes and double precision. In the simulations with RKF method round off error grows to 70% with 10-20 iterations and ~80% within 100 iterations. It does not exceed 80% for 1000 of iterations for single and double precision. This indicates that growth of round off error in RKF method is less and it should be used to minimize round off error.

Problemi estimativi seguenti alla risoluzione contrattuale per grave inadempimento.
Il contratto di locazione finanziaria può essere risolto per grave inadempimento qualora l’utilizzatore non provveda al pagamento di almeno sei canoni mensili o due canoni trimestrali, anche non consecutivi, o di importo equivalente. In questo caso, ai sensi dell’art.
1, comma 138 della l. 124/2017 il concedente procede alla risoluzione del contratto con il diritto alla restituzione del bene; tuttavia rimane obbligato a corrispondere all’utilizzatore quanto ricavato dalla vendita o da altra collocazione del bene, effettuata ai valori di mercato, dedotte la somma pari all’ammontare dei canoni scaduti e non pagati alla data della risoluzione, dei canoni a scadere, solo in linea capitale, e del prezzo pattuito per l’esercizio dell’opzione finale di acquisto, nonché le spese anticipate per il recupero del bene, la stima e la sua conservazione per il tempo necessario alla vendita

This chapter presents the minimum-variance filtering results simplified for the case when the model parameters are time-invariant and the noise processes are stationary. The filtering objective remains the same, namely, the task is to estimate a signal in such as way to minimise the filter error covariance.A somewhat naïve approach is to apply the standard filter recursions using the time-invariant problem parameters. Although this approach is valid, it involves recalculating the Riccati difference equation solution and filter gain at each time-step, which is computationally expensive. A lower implementation cost can be realised by recognising that the Riccati difference equation solution asymptotically approaches the solution of an algebraic Riccati equation. In this case, the algebraic Riccati equation solution and hence the filter gain can be calculated before running the filter.
The steady-state discrete-time Kalman filtering literature is vast and some of the more accessible accounts [1] – [14] are canvassed here. The filtering problem and the application of the standard time-varying filter recursions are described in Section 5.2. An important criterion for checking whether the states can be uniquely reconstructed from the measurements is observability. For example, sometimes states may be internal or sensor measurements might not be available, which can result in the system having hidden modes. Section 5.3 describes two common tests for observability, namely, checking that an observability matrix or an observability gramian are of full rank. The subject of Riccati equation monotonicity and convergence has been studied extensively by Chan [4], De Souza [5], [6], Bitmead [7], [8], Wimmer  [9] and Wonham [10], which is discussed in Section 5.4. Chan, et al [4] also showed that if the underlying system is stable and observable then the minimum-variance filter is stable. Section 6 describes a discrete-time version of the Kalman-Yakubovich-Popov Lemma, which states for time-invariant systems that solving a Riccati equation is equivalent to spectral factorisation. In this case, the Wiener and Kalman filters are the same.
Since the optimal filter is model-based, any unknown model parameters need to be estimated (as explained in Chapter 7) prior to implementation. The estimated parameters can be inexact which leads to degraded filter performance. An iterative frequency weighting procedure is described in Section 5.5 for mitigating the performance degradation.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

—In many contemporary engineering problems, model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability, time, or cost. The situation can be treated by assuming that the true model belongs to an uncertainty class of models. In this context, an intrinsically Bayesian robust (IBR) filter is one that is optimal relative to the cost function (in the classical sense) and the prior distribution over the uncertainty class (in the Bayesian sense). IBR filters have previously been found for both Wiener and granulometric morphological filtering. In this paper, we derive the IBR Kalman filter that performs optimally relative to an uncertainty class of state-space models. Introducing the notion of Bayesian innovation process and the Bayesian orthogonality principle, we show how the problem of designing an IBR Kalman filter can be reduced to a recursive system similar to the classical Kalman recursive equations, except with " effective " counterparts, such as the effective Kalman gain matrix. After deriving the recursive IBR Kalman equations for discrete time, we use the limiting method to obtain the IBR Kalman-Bucy equations for continuous time. Finally, we demonstrate the utility of the proposed framework for two real world problems: sensor networks and gene regulatory network inference.

Abstract We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions.

— This article presents a complete formulation of the challenging task of stable humanoid robot omnidirectional walk based on the Cart and Table model for approximating the robot dynamics. For the control task, we propose two novel approaches: preview control augmented with the inverse system for negotiating strong disturbances and uneven terrain and linear model-predictive control approximated by an orthonormal basis for computational efficiency coupled with constraints for stability. For the generation of smooth feet trajectories, we present a new approach based on rigid body interpolation, enhanced by adaptive step correction. Finally, we present a sensor fusion approach for sensor-based state estimation and an effective solution to sensors' noise, delay, and bias issues, as well as to errors induced by the simplified dynamics and actuation imperfections. Our formulation is applied on a real NAO humanoid robot, where it achieves real-time onboard execution and yields smooth and stable gaits.

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.

In this paper, a low power bulk-driven quasi-floating gate MOSFET based Miller compensated Operational Transconductance Amplifier (OTA) is proposed required particularly in design of Gm-C filter. The analysis of amplifier is compared with low power bulk-driven technique. The performance comparison indicates that bulk-driven quasi floating gate configuration offers better performance. In this configuration the combination of bulk-driven input with quasi-floating gate results in improved transconductance and
hence results in high gain and UGB of the OTA. Moreover, simulation of the bulk-driven quasi-floating gate OTA does not suffer from DC convergence problem. A voltage mode multifunction 2nd order filter design based on proposed BDQFG OTA is also presented. The analysis of all the circuits have been carried out in industry specific node UMC 0.18 micron technology with the help of HSpice simulator.

The induction machine, because of its robustness and low-cost, is commonly used in the industry. Nevertheless, as every type of electrical machine, this machine suffers of some limitations. The most important one is the working temperature which is the dimensioning parameter for the definition of the nominal working point and the machine lifetime. Due to a strong demand concerning thermal monitoring methods appeared in the industry sector. In this context, the adding of temperature sensors is not acceptable and the studied methods tend to use sensorless approaches such as observators or parameters estimators like the extended Kalman Filter (EKF). Then the important criteria are reliability, computational cost ad real time implementation.

This chapter reviews the solutions for the discrete-time, linear stationary filtering problems that are attributed to Wiener [1] and Kolmogorov [2]. As in the continuous-time case, a model-based approach is employed. Here, a linear model is specified by the coefficients of the input and output difference equations. It is shown that the same coefficients appear in the system’s (frequency domain) transfer function. In other words, frequency domain model representations can be written down without background knowledge of z-transforms.

In the 1960s and 1970s, continuous-time filters were implemented on analogue computers. This technology has been largely discontinued for two main reasons. First, analogue multipliers and op amp circuits exhibit poor performance whenever (temperature-sensitive) calibrations become out of date. Second, updated software releases are faster to turn around than hardware design iterations. Continuous-time filters are now routinely implemented using digital computers, provided that the signal sampling rates and data processing rates are sufficiently high. Alternatively, continuous-time model parameters may be converted into discrete-time and differential equations can be transformed into difference equations. The ensuing discrete-time filter solutions are then amenable to more economical implementation, namely, employing relatively lower processing rates.

The discrete-time Wiener filtering problem is solved in the frequency domain. Once again, it is shown that the optimum minimum-mean-square-error solution is found by completing the square. The optimum solution is noncausal, which can only be implemented by forward and backward processes. This solution is actually a smoother and the optimum filter is found by taking the causal part.

The developments rely on solving a spectral factorisation problem, which requires pole-zero cancellations. Therefore, some pertinent discrete-time concepts are introduced in Section 2.2 prior to deriving the filtering results. The discussion of the prerequisite concepts is comparatively brief since it mirrors the continuous-time material introduced previously. In Section 2.3 it is shown that the structure of the filter solutions is unchanged – only the spectral factors are calculated differently.

This work mainly focuses on signal processing issues related to continuous-wave, polarization-based direct imaging schemes. Here, we present a mathematical framework to analyze the performance of the Polarization Difference Imaging (PDI) and Polarization Modulation Imaging (PMI). We have considered three visualization parameters, namely, the polarization intensity (PI), Degree of Linear Polarization (DOLP) and polarization orientation (PO) for comparing these schemes. The first two parameters appear frequently in literature, possibly under different names. The last parameter, polarization orientation, has been introduced and elaborated in this thesis. We have also proposed some extensions/alternatives for the existing imaging and processing schemes and analyzed their advantages.

Theoretically and through Monte-Carlo simulations, we have studied the performance of these schemes under white and coloured noise conditions, concluding that, in general, the PMI gives better estimates of all the parameters. Experimental results corroborate our theoretical arguments. PMI is shown to give asymptotically efficient estimates of these parameters, whereas PDI is shown to give biased estimates of the first two and is also shown to be incapable of estimating PO. Moreover, it is shown that PDI is a particular case of PMI. The property of PDI, that it can yield estimates at lower variances has been recognized as its major strength. We have also shown that the three visualization parameters can be fused to form a colour image, giving a holistic view of the scene. We report the advantages of analyzing chunks of data and bootstrapped data under various circumstances.

Experiments were conducted to image objects through calibrated scattering media and natural media like mist, with successful results. Scattering media prepared with polystyrene microspheres of diameters 2.97, 0.06 and 0.13 dispersed in water were used in our experiments. An intensified charge coupled device (CCD) camera was used to capture the images. Results showed that imaging could be performed beyond optical thickness of 40, for particles with 0.13 m diameter. For larger particles, the depth to which we could image was much lesser. An experiment using an incoherent source yielded better results than with coherent sources, which we attribute to the speckle noise induced by coherent sources. We have suggested a harmonic based imaging scheme, which can perhaps be used when we have a mixture of scattering particles. We have also briefly touched upon the possible post processing that can be performed on the obtained results, and as an example, shown segmentation based on a PO imaging result.

This paper investigates the anti-synchronization of identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) via sliding mode control. The stability results derived in this paper for the anti-synchronization of identical hyperchaotic Xu systems are established using Lyapunov stability theory. Since the Lyapunov
exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve anti- synchronization of the identical hyperchaotic Xu systems. Numerical simulations are shown to illustrate and validate the anti-synchronization schemes derived in this paper for the identical hyperchaotic Xu systems.

Optimal filtering is concerned with designing the best linear system for recovering data from noisy measurements. It is a model-based approach requiring knowledge of the signal generating system. The signal models, together with the noise statistics are factored into the design in such a way to satisfy an optimality criterion, namely, minimising the square of the error.

A prerequisite technique, the method of least-squares, has its origin in curve fitting. Amid some controversy, Kepler claimed in 1609 that the planets move around the Sun in elliptical orbits [1]. Carl Freidrich Gauss arrived at a better performing method for fitting curves to astronomical observations and predicting planetary trajectories in 1799 [1]. He formally published a least-squares approximation method in 1809 [2], which was developed independently by Adrien-Marie Legendre in 1806 [1]. This technique was famously used by Giusseppe Piazzi to discover and track the asteroid Ceres using a least-squares analysis which was easier than solving Kepler’s complicated nonlinear equations of planetary motion [1]. Andrey N. Kolmogorov refined Gauss’s theory of least-squares and applied it for the prediction of discrete-time stationary stochastic processes in 1939 [3]. Norbert Wiener, a faculty member at MIT, independently solved analogous continuous-time estimation problems. He worked on defence applications during the Second World War and produced a report entitled Extrapolation, Interpolation and Smoothing of Stationary Time Series in 1943. The report was later published as a book in 1949 [4].

Wiener derived two important results, namely, the optimum (non-causal) minimum-mean-square-error solution and the optimum causal minimum-mean-square-error solution [4] – [6]. The optimum causal solution has since become known at the Wiener filter and in the time-invariant case is equivalent to the Kalman filter that was developed subsequently. Wiener pursued practical outcomes and attributed the term “unrealisable filter” to the optimal non-causal solution because “it is not in fact realisable with a finite network of resistances, capacities, and inductances” [4]. Wiener’s unrealisable filter is actually the optimum linear smoother.

The optimal Wiener filter is calculated in the frequency domain. Consequently, Section 1.2 touches on some frequency-domain concepts. In particular, the notions of spaces, state-space systems, transfer functions, canonical realisations, stability, causal systems, power spectral density and spectral factorisation are introduced. The Wiener filter is then derived by minimising the square of the error. Three cases are discussed in Section 1.3. First, the solution to general estimation problem is stated. Second, the general estimation results are specialised to output estimation. The optimal input estimation or equalisation solution is then described. An example, demonstrating the recovery of a desired signal from noisy measurements, completes the chapter.

Usually, standard inertial navigation unit (INU) with global positioning system (GPS) provides relatively poor accuracy in altitude estimation, while autonomous landing of unmanned aerial vehicles (UAVs) requires accurate position estimation. In this paper, a UAV navigation system with aid from an external camera for landing is investigated. This paper presents: (i) a sensor fusion algorithm for passive monocular vision and INU based on the extended Kalman filter (EKF) considering measurement delay to improve the accuracy of position estimates, and (ii) a robust object-detection vision algorithm using optical flow. Pilot controlled landing experiments on a NASA UAV platform and the filter simulations validate the feasibility and performance of the proposed approach.