913 resultados para THERMAL RATE COEFFICIENT
Resumo:
Bayer hydrotalcites prepared using the seawater neutralisation (SWN) process of Bayer liquors are characterised using X-ray diffraction and thermal analysis techniques. The Bayer hydrotalcites are synthesised at four different temperatures (0, 25, 55, 75 °C) to determine the effect on the thermal stability of the hydrotalcite structure, and to identify other precipitates that form at these temperatures. The interlayer distance increased with increasing synthesis temperature, up to 55 °C, and then decreased by 0.14 Å for Bayer hydrotalcites prepared at 75 °C. The three mineralogical phases identified in this investigation are; 1) Bayer hydrotalcite, 2), calcium carbonate species, and 3) hydromagnesite. The DTG curve can be separated into four decomposition steps; 1) the removal of adsorbed water and free interlayer water in hydrotalcite (30 – 230 °C), 2) the dehydroxylation of hydrotalcite and the decarbonation of hydrotalcite (250 – 400 °C), 3) the decarbonation of hydromagnesite (400 – 550 °C), and 4) the decarbonation of aragonite (550 – 650 °C).
Thermal analysis of synthetic reevesite and cobalt substituted reevesite (Ni,Co)6Fe2(OH)16(CO3)•4H2O
Resumo:
The mineral reevesite and the cobalt substituted reevesite have been synthesised. The d(003) spacings of the minerals ranged from 7.54 to 7.95 Å. The maximum d(003) value occurred at around Ni:Co 0.4:0.6. This maximum in interlayer distance is proposed to be due to a greater number of carbonate anions and water molecules intercalated into the structure. The stability of the reevesite and cobalt doped reevesite was determined by thermogravimetric analysis. The maximum temperature of the reevesite occurs for the unsubstituted reevesite and is around 220°C. The effect of cobalt substitution results in a decrease in thermal stability of the reevesites. Four thermal decomposition steps are observed and are attributed to dehydration, dehydroxylation and decarbonation, decomposition of the formed carbonate and oxygen loss at ~807 °C. A mechanism for the thermal decomposition of the reevesite and the cobalt substituted reevesite is proposed.
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In this thesis an investigation into theoretical models for formation and interaction of nanoparticles is presented. The work presented includes a literature review of current models followed by a series of five chapters of original research. This thesis has been submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by publication and therefore each of the five chapters consist of a peer-reviewed journal article. The thesis is then concluded with a discussion of what has been achieved during the PhD candidature, the potential applications for this research and ways in which the research could be extended in the future. In this thesis we explore stochastic models pertaining to the interaction and evolution mechanisms of nanoparticles. In particular, we explore in depth the stochastic evaporation of molecules due to thermal activation and its ultimate effect on nanoparticles sizes and concentrations. Secondly, we analyse the thermal vibrations of nanoparticles suspended in a fluid and subject to standing oscillating drag forces (as would occur in a standing sound wave) and finally on lattice surfaces in the presence of high heat gradients. We have described in this thesis a number of new models for the description of multicompartment networks joined by a multiple, stochastically evaporating, links. The primary motivation for this work is in the description of thermal fragmentation in which multiple molecules holding parts of a carbonaceous nanoparticle may evaporate. Ultimately, these models predict the rate at which the network or aggregate fragments into smaller networks/aggregates and with what aggregate size distribution. The models are highly analytic and describe the fragmentation of a link holding multiple bonds using Markov processes that best describe different physical situations and these processes have been analysed using a number of mathematical methods. The fragmentation of the network/aggregate is then predicted using combinatorial arguments. Whilst there is some scepticism in the scientific community pertaining to the proposed mechanism of thermal fragmentation,we have presented compelling evidence in this thesis supporting the currently proposed mechanism and shown that our models can accurately match experimental results. This was achieved using a realistic simulation of the fragmentation of the fractal carbonaceous aggregate structure using our models. Furthermore, in this thesis a method of manipulation using acoustic standing waves is investigated. In our investigation we analysed the effect of frequency and particle size on the ability for the particle to be manipulated by means of a standing acoustic wave. In our results, we report the existence of a critical frequency for a particular particle size. This frequency is inversely proportional to the Stokes time of the particle in the fluid. We also find that for large frequencies the subtle Brownian motion of even larger particles plays a significant role in the efficacy of the manipulation. This is due to the decreasing size of the boundary layer between acoustic nodes. Our model utilises a multiple time scale approach to calculating the long term effects of the standing acoustic field on the particles that are interacting with the sound. These effects are then combined with the effects of Brownian motion in order to obtain a complete mathematical description of the particle dynamics in such acoustic fields. Finally, in this thesis, we develop a numerical routine for the description of "thermal tweezers". Currently, the technique of thermal tweezers is predominantly theoretical however there has been a handful of successful experiments which demonstrate the effect it practise. Thermal tweezers is the name given to the way in which particles can be easily manipulated on a lattice surface by careful selection of a heat distribution over the surface. Typically, the theoretical simulations of the effect can be rather time consuming with supercomputer facilities processing data over days or even weeks. Our alternative numerical method for the simulation of particle distributions pertaining to the thermal tweezers effect use the Fokker-Planck equation to derive a quick numerical method for the calculation of the effective diffusion constant as a result of the lattice and the temperature. We then use this diffusion constant and solve the diffusion equation numerically using the finite volume method. This saves the algorithm from calculating many individual particle trajectories since it is describes the flow of the probability distribution of particles in a continuous manner. The alternative method that is outlined in this thesis can produce a larger quantity of accurate results on a household PC in a matter of hours which is much better than was previously achieveable.
Resumo:
The literature identifies several models that describe inter-phase mass transfer, key to the emission process. While the emission process is complex and these models may be more or less successful at predicting mass transfer rates, they identify three key variables for a system involving a liquid and an air phase in contact with it: • A concentration (or partial pressure) gradient driving force; • The fluid dynamic characteristics within the liquid and air phases, and • The chemical properties of the individual components within the system. In three applied research projects conducted prior to this study, samples collected with two well-known sampling devices resulted in very different odour emission rates. It was not possible to adequately explain the differences observed. It appeared likely, however, that the sample collection device might have artefact effects on the emission of odorants, i.e. the sampling device appeared to have altered the mass transfer process. This raised the obvious question: Where two different emission rates are reported for a single source (differing only in the selection of sampling device), and a credible explanation for the difference in emission rate cannot be provided, which emission rate is correct? This research project aimed to identify the factors that determine odour emission rates, the impact that the characteristics of a sampling device may exert on the key mass transfer variables, and ultimately, the impact of the sampling device on the emission rate itself. To meet these objectives, a series of targeted reviews, and laboratory and field investigations, were conducted. Two widely-used, representative devices were chosen to investigate the influence of various parameters on the emission process. These investigations provided insight into the odour emission process generally, and the influence of the sampling device specifically.
Resumo:
An experimental investigation has been made of a round, non-buoyant plume of nitric oxide, NO, in a turbulent grid flow of ozone, 03, using the Turbulent Smog Chamber at the University of Sydney. The measurements have been made at a resolution not previously reported in the literature. The reaction is conducted at non-equilibrium so there is significant interaction between turbulent mixing and chemical reaction. The plume has been characterized by a set of constant initial reactant concentration measurements consisting of radial profiles at various axial locations. Whole plume behaviour can thus be characterized and parameters are selected for a second set of fixed physical location measurements where the effects of varying the initial reactant concentrations are investigated. Careful experiment design and specially developed chemilurninescent analysers, which measure fluctuating concentrations of reactive scalars, ensure that spatial and temporal resolutions are adequate to measure the quantities of interest. Conserved scalar theory is used to define a conserved scalar from the measured reactive scalars and to define frozen, equilibrium and reaction dominated cases for the reactive scalars. Reactive scalar means and the mean reaction rate are bounded by frozen and equilibrium limits but this is not always the case for the reactant variances and covariances. The plume reactant statistics are closer to the equilibrium limit than those for the ambient reactant. The covariance term in the mean reaction rate is found to be negative and significant for all measurements made. The Toor closure was found to overestimate the mean reaction rate by 15 to 65%. Gradient model turbulent diffusivities had significant scatter and were not observed to be affected by reaction. The ratio of turbulent diffusivities for the conserved scalar mean and that for the r.m.s. was found to be approximately 1. Estimates of the ratio of the dissipation timescales of around 2 were found downstream. Estimates of the correlation coefficient between the conserved scalar and its dissipation (parallel to the mean flow) were found to be between 0.25 and the significant value of 0.5. Scalar dissipations for non-reactive and reactive scalars were found to be significantly different. Conditional statistics are found to be a useful way of investigating the reactive behaviour of the plume, effectively decoupling the interaction of chemical reaction and turbulent mixing. It is found that conditional reactive scalar means lack significant transverse dependence as has previously been found theoretically by Klimenko (1995). It is also found that conditional variance around the conditional reactive scalar means is relatively small, simplifying the closure for the conditional reaction rate. These properties are important for the Conditional Moment Closure (CMC) model for turbulent reacting flows recently proposed by Klimenko (1990) and Bilger (1993). Preliminary CMC model calculations are carried out for this flow using a simple model for the conditional scalar dissipation. Model predictions and measured conditional reactive scalar means compare favorably. The reaction dominated limit is found to indicate the maximum reactedness of a reactive scalar and is a limiting case of the CMC model. Conventional (unconditional) reactive scalar means obtained from the preliminary CMC predictions using the conserved scalar p.d.f. compare favorably with those found from experiment except where measuring position is relatively far upstream of the stoichiometric distance. Recommendations include applying a full CMC model to the flow and investigations both of the less significant terms in the conditional mean species equation and the small variation of the conditional mean with radius. Forms for the p.d.f.s, in addition to those found from experiments, could be useful for extending the CMC model to reactive flows in the atmosphere.
Resumo:
The hydrotalcite based upon manganese known as charmarite Mn4Al2(OH)12CO3•3H2O has been synthesised with different Mn/Al ratios from 4:1 to 2:1. Impurities of manganese oxide, rhodochrosite and bayerite at low concentrations were also produced during the synthesis. The thermal stability of charmarite was investigated using thermogravimetry. The manganese hydrotalcite decomposed in stages with mass loss steps at 211, 305 and 793°C. The product of the thermal decomposition was amorphous material mixed with manganese oxide. A comparison is made with the thermal decomposition of the Mg/Al hydrotalcite. It is concluded that the synthetic charmarite is slightly less stable than hydrotalcite.
Resumo:
Dynamic and controlled rate thermal analysis (CRTA) has been used to characterise alunites of formula [M(Al)3(SO4)2(OH)6 ] where M+ is the cations K+, Na+ or NH4+. Thermal decomposition occurs in a series of steps. (a) dehydration, (b) well defined dehydroxylation and (c) desulphation. CRTA offers a better resolution and a more detailed interpretation of water formation processes via approaching equilibrium conditions of decomposition through the elimination of the slow transfer of heat to the sample as a controlling parameter on the process of decomposition. Constant-rate decomposition processes of water formation reveal the subtle nature of dehydration and dehydroxylation.
Resumo:
Smart materials, such as thin-film piezoelectric polymers, are interesting for potential applications on Gossamer spacecraft. This investigation aims to predict the performance and long-term stability of the piezoelectric properties of poly(vinylidene fluoride) (PVDF) and its copolymers under conditions simulating the low-Earthorbit environment. To examine the effects of temperature on the piezoelectric properties of PVDF, poly(vinylidenefluoride-co-trifluoroethylene), and poly(vinylidenefluoride-cohexafluoropropylene), the d33 piezoelectric coefficients were measured up to 160 8C, and the electric displacement/electric field (D–E) hysteresis loops were measured from �80 to þ110 8C. The room-temperature d33 coefficient of PVDF homopolymer films, annealed at 50, 80, and 125 8C, dropped rapidly within a few days of thermal exposure and then remained unchanged. In contrast, the TrFE copolymer exhibited greater thermal stability than the homopolymer, with d33 remaining almost unchanged up to 125 8C. The HFP copolymer exhibited poor retention of d33 at temperatures above 80 8C. In situ D–E loop measurements from �80 to þ110 8C showed that the remanent polarization of the TrFE copolymer was more stable than that of the PVDF homopolymer. D–E hysteresis loop and d33 results were also compared with the deflection of the PVDF homopolymer and TrFE copolymer bimorphs tested over a wide temperature range.
Resumo:
The radiation chemistry and the grafting of a fluoropolymer, poly(tetrafluoroethylene-coperfluoropropyl vinyl ether) (PFA), was investigated with the aim of developing a highly stable grafted support for use in solid phase organic chemistry (SPOC). A radiation-induced grafting method was used whereby the PFA was exposed to ionizing radiation to form free radicals capable of initiating graft copolymerization of styrene. To fully investigate this process, both the radiation chemistry of PFA and the grafting of styrene to PFA were examined. Radiation alone was found to have a detrimental effect on PFA when irradiated at 303 K. This was evident from the loss in the mechanical properties due to chain scission reactions. This meant that when radiation was used for the grafting reactions, the total radiation dose needed to be kept as low as possible. The radicals produced when PFA was exposed to radiation were examined using electron spin resonance spectroscopy. Both main-chain (–CF2–C.F–CF2-) and end-chain (–CF2–C.F2) radicals were identified. The stability of the majority of the main-chain radicals when the polymer was heated above the glass transition temperature suggested that they were present mainly in the crystalline regions of the polymer, while the end-chain radicals were predominately located in the amorphous regions. The radical yield at 77 K was lower than the radical yield at 303 K suggesting that cage recombination at low temperatures inhibited free radicals from stabilizing. High-speed MAS 19F NMR was used to identify the non-volatile products after irradiation of PFA over a wide temperature range. The major products observed over the irradiation temperature 303 to 633 K included new saturated chain ends, short fluoromethyl side chains in both the amorphous and crystalline regions, and long branch points. The proportion of the radiolytic products shifted from mainly chain scission products at low irradiation temperatures to extensive branching at higher irradiation temperatures. Calculations of G values revealed that net crosslinking only occurred when PFA was irradiated in the melt. Minor products after irradiation at elevated temperatures included internal and terminal double bonds and CF3 groups adjacent to double bonds. The volatile products after irradiation at 303 K included tetrafluoromethane (CF4) and oxygen-containing species from loss of the perfluoropropyl ether side chains of PFA as identified by mass spectrometry and FTIR spectroscopy. The chemical changes induced by radiation exposure were accompanied by changes in the thermal properties of the polymer. Changes in the crystallinity and thermal stability of PFA after irradiation were examined using DSC and TGA techniques. The equilibrium melting temperature of untreated PFA was 599 K as determined using a method of extrapolation of the melting temperatures of imperfectly formed crystals. After low temperature irradiation, radiation- induced crystallization was prevalent due to scission of strained tie molecules, loss of perfluoropropyl ether side chains, and lowering of the molecular weight which promoted chain alignment and hence higher crystallinity. After irradiation at high temperatures, the presence of short and long branches hindered crystallization, lowering the overall crystallinity. The thermal stability of the PFA decreased with increasing radiation dose and temperature due to the introduction of defect groups. Styrene was graft copolymerized to PFA using -radiation as the initiation source with the aim of preparing a graft copolymer suitable as a support for SPOC. Various grafting conditions were studied, such as the total dose, dose rate, solvent effects and addition of nitroxides to create “living” graft chains. The effect of dose rate was examined when grafting styrene vapour to PFA using the simultaneous grafting method. The initial rate of grafting was found to be independent of the dose rate which implied that the reaction was diffusion controlled. When the styrene was dissolved in various solvents for the grafting reaction, the graft yield was strongly dependent of the type and concentration of the solvent used. The greatest graft yield was observed when the solvent swelled the grafted layers and the substrate. Microprobe Raman spectroscopy was used to map the penetration of the graft into the substrate. The grafted layer was found to contain both poly(styrene) (PS) and PFA and became thicker with increasing radiation dose and graft yield which showed that grafting began at the surface and progressively penetrated the substrate as the grafted layer was swollen. The molecular weight of the grafted PS was estimated by measuring the molecular weight of the non-covalently bonded homopolymer formed in the grafted layers using SEC. The molecular weight of the occluded homopolymer was an order of magnitude greater than the free homopolymer formed in the surrounding solution suggesting that the high viscosity in the grafted regions led to long PS grafts. When a nitroxide mediated free radical polymerization was used, grafting occurred within the substrate and not on the surface due to diffusion of styrene into the substrate at the high temperatures needed for the reaction to proceed. Loading tests were used to measure the capacity of the PS graft to be functionialized with aminomethyl groups then further derivatized. These loading tests showed that samples grafted in a solution of styrene and methanol had superior loading capacity over samples graft using other solvents due to the shallow penetration and hence better accessibility of the graft when methanol was used as a solvent.
Resumo:
The study described in this paper developed a model of animal movement, which explicitly recognised each individual as the central unit of measure. The model was developed by learning from a real dataset that measured and calculated, for individual cows in a herd, their linear and angular positions and directional and angular speeds. Two learning algorithms were implemented: a Hidden Markov model (HMM) and a long-term prediction algorithm. It is shown that a HMM can be used to describe the animal's movement and state transition behaviour within several “stay” areas where cows remained for long periods. Model parameters were estimated for hidden behaviour states such as relocating, foraging and bedding. For cows’ movement between the “stay” areas a long-term prediction algorithm was implemented. By combining these two algorithms it was possible to develop a successful model, which achieved similar results to the animal behaviour data collected. This modelling methodology could easily be applied to interactions of other animal species.
Resumo:
This paper introduces an energy-efficient Rate Adaptive MAC (RA-MAC) protocol for long-lived Wireless Sensor Networks (WSN). Previous research shows that the dynamic and lossy nature of wireless communication is one of the major challenges to reliable data delivery in a WSN. RA-MAC achieves high link reliability in such situations by dynamically trading off radio bit rate for signal processing gain. This extra gain reduces the packet loss rate which results in lower energy expenditure by reducing the number of retransmissions. RA-MAC selects the optimal data rate based on channel conditions with the aim of minimizing energy consumption. We have implemented RA-MAC in TinyOS on an off-the-shelf sensor platform (TinyNode), and evaluated its performance by comparing RA-MAC with state-ofthe- art WSN MAC protocol (SCP-MAC) by experiments.
Resumo:
Insight into the unique structure of layered double hydroxides has been obtained using a combination of X-ray diffraction and thermal analysis. Indium containing hydrotalcites of formula Mg4In2(CO3)(OH)12•4H2O (2:1 In-LDH) through to Mg8In2(CO3)(OH)18•4H2O (4:1 In-LDH) with variation in the Mg:In ratio have been successfully synthesised. The d(003) spacing varied from 7.83 Å for the 2:1 LDH to 8.15 Å for the 3:1 indium containing layered double hydroxide. Distinct mass loss steps attributed to dehydration, dehydroxylation and decarbonation are observed for the indium containing hydrotalcite. Dehydration occurs over the temperature range ambient to 205 °C. Dehydroxylation takes place in a series of steps over the 238 to 277 °C temperature range. Decarbonation occurs between 763 and 795 °C. The dehydroxylation and decarbonation steps depend upon the Mg:In ratio. The formation of indium containing hydrotalcites and their thermal activation provides a method for the synthesis of indium oxide based catalysts.
Resumo:
A major challenge of the 21st century will be to generate transportation fuels using feedstocks such as lignocellulosic waste materials as a substitute for existing fossil and nuclear fuels. The advantages of lignocellulosics as a feedstock material are that they are abundant, sustainable and carbon-neutral. To improve the economics of producing liquid transportation fuels from lignocellulosic biomass, the development of value-added products from lignin, a major component of lignocellulosics, is necessary. Lignins produced from black liquor through the fractionation of sugarcane bagasse with soda and organic solvents have been characterised by physical, chemical and thermal means. The soda lignin fractions have different physico-chemical and thermal properties from one another. Some of these properties have been compared to bagasse lignin extracted with aqueous ethanol.
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High-rate flooding attacks (aka Distributed Denial of Service or DDoS attacks) continue to constitute a pernicious threat within the Internet domain. In this work we demonstrate how using packet source IP addresses coupled with a change-point analysis of the rate of arrival of new IP addresses may be sufficient to detect the onset of a high-rate flooding attack. Importantly, minimizing the number of features to be examined, directly addresses the issue of scalability of the detection process to higher network speeds. Using a proof of concept implementation we have shown how pre-onset IP addresses can be efficiently represented using a bit vector and used to modify a “white list” filter in a firewall as part of the mitigation strategy.
Resumo:
Uninhabited aerial vehicles (UAVs) are a cutting-edge technology that is at the forefront of aviation/aerospace research and development worldwide. Many consider their current military and defence applications as just a token of their enormous potential. Unlocking and fully exploiting this potential will see UAVs in a multitude of civilian applications and routinely operating alongside piloted aircraft. The key to realising the full potential of UAVs lies in addressing a host of regulatory, public relation, and technological challenges never encountered be- fore. Aircraft collision avoidance is considered to be one of the most important issues to be addressed, given its safety critical nature. The collision avoidance problem can be roughly organised into three areas: 1) Sense; 2) Detect; and 3) Avoid. Sensing is concerned with obtaining accurate and reliable information about other aircraft in the air; detection involves identifying potential collision threats based on available information; avoidance deals with the formulation and execution of appropriate manoeuvres to maintain safe separation. This thesis tackles the detection aspect of collision avoidance, via the development of a target detection algorithm that is capable of real-time operation onboard a UAV platform. One of the key challenges of the detection problem is the need to provide early warning. This translates to detecting potential threats whilst they are still far away, when their presence is likely to be obscured and hidden by noise. Another important consideration is the choice of sensors to capture target information, which has implications for the design and practical implementation of the detection algorithm. The main contributions of the thesis are: 1) the proposal of a dim target detection algorithm combining image morphology and hidden Markov model (HMM) filtering approaches; 2) the novel use of relative entropy rate (RER) concepts for HMM filter design; 3) the characterisation of algorithm detection performance based on simulated data as well as real in-flight target image data; and 4) the demonstration of the proposed algorithm's capacity for real-time target detection. We also consider the extension of HMM filtering techniques and the application of RER concepts for target heading angle estimation. In this thesis we propose a computer-vision based detection solution, due to the commercial-off-the-shelf (COTS) availability of camera hardware and the hardware's relatively low cost, power, and size requirements. The proposed target detection algorithm adopts a two-stage processing paradigm that begins with an image enhancement pre-processing stage followed by a track-before-detect (TBD) temporal processing stage that has been shown to be effective in dim target detection. We compare the performance of two candidate morphological filters for the image pre-processing stage, and propose a multiple hidden Markov model (MHMM) filter for the TBD temporal processing stage. The role of the morphological pre-processing stage is to exploit the spatial features of potential collision threats, while the MHMM filter serves to exploit the temporal characteristics or dynamics. The problem of optimising our proposed MHMM filter has been examined in detail. Our investigation has produced a novel design process for the MHMM filter that exploits information theory and entropy related concepts. The filter design process is posed as a mini-max optimisation problem based on a joint RER cost criterion. We provide proof that this joint RER cost criterion provides a bound on the conditional mean estimate (CME) performance of our MHMM filter, and this in turn establishes a strong theoretical basis connecting our filter design process to filter performance. Through this connection we can intelligently compare and optimise candidate filter models at the design stage, rather than having to resort to time consuming Monte Carlo simulations to gauge the relative performance of candidate designs. Moreover, the underlying entropy concepts are not constrained to any particular model type. This suggests that the RER concepts established here may be generalised to provide a useful design criterion for multiple model filtering approaches outside the class of HMM filters. In this thesis we also evaluate the performance of our proposed target detection algorithm under realistic operation conditions, and give consideration to the practical deployment of the detection algorithm onboard a UAV platform. Two fixed-wing UAVs were engaged to recreate various collision-course scenarios to capture highly realistic vision (from an onboard camera perspective) of the moments leading up to a collision. Based on this collected data, our proposed detection approach was able to detect targets out to distances ranging from about 400m to 900m. These distances, (with some assumptions about closing speeds and aircraft trajectories) translate to an advanced warning ahead of impact that approaches the 12.5 second response time recommended for human pilots. Furthermore, readily available graphic processing unit (GPU) based hardware is exploited for its parallel computing capabilities to demonstrate the practical feasibility of the proposed target detection algorithm. A prototype hardware-in- the-loop system has been found to be capable of achieving data processing rates sufficient for real-time operation. There is also scope for further improvement in performance through code optimisations. Overall, our proposed image-based target detection algorithm offers UAVs a cost-effective real-time target detection capability that is a step forward in ad- dressing the collision avoidance issue that is currently one of the most significant obstacles preventing widespread civilian applications of uninhabited aircraft. We also highlight that the algorithm development process has led to the discovery of a powerful multiple HMM filtering approach and a novel RER-based multiple filter design process. The utility of our multiple HMM filtering approach and RER concepts, however, extend beyond the target detection problem. This is demonstrated by our application of HMM filters and RER concepts to a heading angle estimation problem.