A piece of popular music is usually defined as a combination of vocal melody and instrumental accompaniment. People often start with the melody part when they are trying to compose or reproduce a piece of popular music. However, creating appropriate instrumental accompaniment part for a melody line can be a difficult task for non-musicians. Automation of accompaniment generation for vocal melodies thus can be very useful for those who are interested in singing for fun. Therefore, a computer software system which is capable of generating harmonic accompaniment for a given vocal melody input has been presented in this thesis. This automatic accompaniment system uses a Hidden Markov Model to assign chord to a given part of melody based on the knowledge learnt from a bank of vocal tracks of popular music. Comparing with other similar systems, our system features a high resolution key estimation algorithm which is helpful to adjust the generated accompaniment to the input vocal. Moreover, we designed a structure analysis subsystem to extract the repetition and structure boundaries from the melody. These boundaries are passed to the chord assignment and style player subsystems in order to generate more dynamic and organized accompaniment. Finally, prototype applications are discussed and the entire system is evaluated.

Thesis (MSc (Mathematical Sciences))-- University of Stellenbosch, 2010. / ENGLISH ABSTRACT: We investigate the suitability of applying some of the probabilistic and automata theoretic ideas, that have been extremely successful in the areas of speech and natural language processing, to the area of musical style imitation. By using music written in a certain style as training data, parameters are calculated for (visible and hidden) Markov models (of mixed, higher or first order), in order to capture the musical style of the training data in terms of mathematical models. These models are then used to imitate two instrument music in the trained style. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die toepasbaarheid van probabilitiese en outomaatteoretiese konsepte, wat uiters suksesvol toegepas word in die gebied van spraak en natuurlike taal-verwerking, op die gebied van musiekstyl nabootsing. Deur gebruik te maak van musiek wat geskryf is in ’n gegewe styl as aanleer data, word parameters vir (sigbare en onsigbare) Markov modelle (van gemengde, hoër- of eerste- orde) bereken, ten einde die musiekstyl van die data waarvan geleer is, in terme van wiskundige modelle te beskryf. Hierdie modelle word gebruik om musiek vir twee instrumente te genereer, wat die musiek waaruit geleer is, naboots.

Les Interfaces Cerveau-Machine (ICM) sont des systèmes qui permettent à des patients souffrant d'un handicap moteur sévère d'utiliser leur activité cérébrale pour contrôler des effecteurs, par exemple des prothèses des membres supérieurs dans le cas d'ICM motrices. Les intentions de mouvement de l'utilisateur sont estimées en appliquant un décodeur sur des caractéristiques extraites de son activité cérébrale. Des challenges spécifiques au déploiement clinique d'ICMs motrices ont été considérés, à savoir le contrôle mono-membre ou séquentiel multi-membre asynchrone et précis. Un décodeur, le Markov Switching Linear Model (MSLM), a été développé pour limiter les activations erronées de l'ICM, empêcher des mouvements parallèles des effecteurs et décoder avec précision des mouvements complexes. Le MSLM associe des modèles linéaires à différents états possibles, e.g. le contrôle d'un membre spécifique ou une phase de mouvement particulière. Le MSLM réalise une détection d'état dynamique, et les probabilités des états sont utilisées pour pondérer les modèles linéaires.La performance du décodeur MSLM a été évaluée pour la reconstruction asynchrone de trajectoires de poignet et de doigts à partir de signaux electrocorticographiques. Il a permis de limiter les activations erronées du système et d'améliorer la précision du décodage du signal cérébral. / Brain-Computer Interfaces (BCI) are systems that allow severely motor-impaired patients to use their brain activity to control external devices, for example upper-limb prostheses in the case of motor BCIs. The user's intentions are estimated by applying a decoder on neural features extracted from the user's brain activity. Signal processing challenges specific to the clinical deployment of motor BCI systems are addressed in the present doctoral thesis, namely asynchronous mono-limb or sequential multi-limb decoding and accurate decoding during active control states. A switching decoder, namely a Markov Switching Linear Model (MSLM), has been developed to limit spurious system activations, to prevent parallel limb movements and to accurately decode complex movements.The MSLM associates linear models with different possible control states, e.g. activation of a specific limb, specific movement phases. Dynamic state detection is performed by the MSLM, and the probability of each state is used to weight the linear models. The performance of the MSLM decoder was assessed for asynchronous wrist and multi-finger trajectory reconstruction from electrocorticographic signals. It was found to outperform previously reported decoders for the limitation of spurious activations during no-control periods and permitted to improve decoding accuracy during active periods.

[pt] A ocorrência de erros em surto é observada principalmente em canais sem fio. Para a análise e melhor entendimento deste tipo de erro, a fim de se melhorar os projetos de sistemas de comunicações digitais, uma modelagem mais precisa, de canais com esta característica, torna-se necessária. Uma diversidade de métodos de estimação de parâmetros tem sido estudada, principalmente aquelas baseadas nos Modelos Escondidos de Markov (HMM do ingês). Em geral cada método é focado em um sistema de comunicações específico, sobre uma camada específica. Neste trabalho é proposto um novo método baseado em um HMM com uma estrutura particular, que permite a dedução de expressões analíticas para todas as estatísticas de interesse. A estrutura do modelo proposto permite a geração de eventos que ocorrem numa sequência binária de dados sujeita a surtos de erro, de acordo com a definição de surtos de erro do CCITT. O modelo proposto possui um número fixo de apenas sete parâmetros, mas o seu número de estados cresce com um de seus parâmetros, que aumenta a precisão, mas não a complexidade. Este trabalho adotou técnicas de otimização, associadas aos métodos de Máxima Verossimilhança e Particle Swarm Optimization (PSO) a fim de realizar a estimação dos parâmetros do modelo proposto. Os resultados demonstram que o modelo proposto permite a caracterização precisa de canais com memória de diversas origens. / [en] The occurrence of error busts is mainly observed in wireless channels. For analysis and a better understanding of such errors, in order to improve the design of communication systems, an accurate modeling of channels with this characteristic is necessary. A lot of parameter estimation methods have been studied, mainly the ones based on Hidden Markov Models (HMM). In general each method is focused in a specific communication system, on a specific layer. In this work it is proposed a new method based on a HMM with particular structure that allows the deduction of analytical expressions for all statistics of interest. The structure of the proposed model permits the generation of events that occur in a binary data sequence subject to bursts of error concerning CCITT error burst definition. The proposed model has a fixed number of only seven parameters but its number of states increase with one of those parameters that increase the accuracy but not the complexity. This work adopted techniques of optimization associated to Maximum Likelihood (ML) and Particle Swarm Optimization (PSO) to perform the parameter estimation to the proposed model. The results show that the proposed model achieves accurate characterization of channels with memory from many different sources.

Made available in DSpace on 2014-06-11T19:29:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-08-05Bitstream added on 2014-06-13T19:38:57Z : No. of bitstreams: 1 kami_gjc_me_sjrp.pdf: 1342570 bytes, checksum: 240c6d6b92fda1861dfbed94c9213a10 (MD5) / As técnicas para identificação biométrica têm evoluído cada vez mais devido à necessidade que os seres humanos têm de identificar as pessoas em tempo real e de forma precisa para permitir o acesso a determinados recursos, como por exemplo, as aplicações e serviços WEB. O reconhecimento facial é uma técnica biométrica que apresenta várias vantagens em relação às demais, tais como: uso de equipamentos simples e baratos para a obtenção das amostras e a possibilidade de se realizar o reconhecimento em sigilo e à distância. O reconhecimento de faces a partir de vídeo é uma tendência recente na área de Biometria. Esta dissertação tem por objetivo principal comparar diferentes técnicas de reconhecimento facial a partir de vídeo para determinar as que apresentam um melhor compromisso entre tempo de processamento e precisão. Outro objetivo é a incorporação dessas melhores técnicas no sistema de autenticação biométrica em ambientes de E-Learning, proposto em um trabalho anterior. Foi comparado o classificador vizinho mais próximo usando as medidas de distância Euclidiana e Mahalanobis com os seguintes classificadores: Redes Neurais MLP e SOM, K Vizinhos mais Próximos, Classificador Bayesiano, Máquinas de Vetores de Suporte (SVM) e Floresta de Caminhos Ótimos (OPF). Também foi avaliada a técnica de Modelos Ocultos de Markov (HMM). Nos experimentos realizados com a base Recogna Video Database, criada especialmente para uso neste trabalho, e Honda/UCSD Video Database, os classificadores apresentaram os melhores resultados em termos de precisão, com destaque para o classificador SVM da biblioteca SVM Torch. A técnica HMM, que incorpora informações temporais, apresentou resultados melhores do que as funções de distância, em termos de precisão, mas inferiores aos classificadores / The biometric identification techniques have evolved increasingly due to the need that humans have to identify people in real time to allow access to certain resources, such as applications and Web services. Facial recognition is a biometric technique that has several advantages over others. Some of these advantages are the use of simple and cheap equipment to obtain the samples and the ability to perform the recognition in covert mode. The face recognition from video is a recent approach in the area of Biometrics. The work in this dissertation aims at comparing different techniques for face recognition from video in order to find the best rates on processing time and accuracy. Another goal is the incorporation of these techniques in the biometric authentication system for E-Learning environments, proposed in an earlier work. We have compared the nearest neighbor classifier using the Euclidean and Mahalanobis distance measures with some other classifiers, such as neural networks (MLP and SOM), k-nearest neighbor, Bayesian classifier, Support Vector Machines (SVM), and Optimum Path Forest (OPF). We have also evaluated the Hidden Markov Model (HMM) approach, as a way of using the temporal information. In the experiments with Recogna Video Database, created especially for this study, and Honda/UCSD Video Database, the classifiers obtained the best accuracy, especially the SVM classifier from the SVM Torch library. HMM, which takes into account temporal information, presented better performance than the distance metrics, but worse than the classifiers

Submitted by (ana.araujo@ufrpe.br) on 2016-08-10T13:59:35Z No. of bitstreams: 1 Rita de Cassia de Lima Idalino.pdf: 2600123 bytes, checksum: 41f878b68e3437742821d874a6955502 (MD5) / Made available in DSpace on 2016-08-10T13:59:35Z (GMT). No. of bitstreams: 1 Rita de Cassia de Lima Idalino.pdf: 2600123 bytes, checksum: 41f878b68e3437742821d874a6955502 (MD5) Previous issue date: 2010-12-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Given the large amount of data that is generated in the field of molecular genetics, is of paramount importance that techniques which allow the organization and interpretation of such data be developed and widely disseminated. Initially, we carried out a composition analysis of three gene sequences of the species: ox (Bos taurus), goat (Capra hircus), and sheep (Ovis aries), then we applied alignment techniques for identification of similarities between them. Subsequently, we used the Markov Chain theory with hidden states, i.e. Hidden Markov Models (HMMs, hereafter), in the application of discrimination problem of homogeneous regions in DNA sequences. We used the Viterbi algorithm as an auxiliary tool to obtain homogeneous regions, and then the Baum-Eelch algorithm in order to maximize the probability of a sequence of observations. We analyzed portions of HSP70.1 and NRAMP-1 genes for three different species. / Diante da grande massa de dados que é gerada na área da genética molecular, é de suma importância que técnicas que possibilitem a organização e interpretação desses dados sejam desenvolvidas e amplamente divulgadas. Inicialmente, neste trabalho, foi realizada uma análise da composição de três sequências genéticas, das espécies Bovina (Bos taurus), Caprina (Capra hircus) e Ovina (Ovis aries), em seguida aplicamos técnicas de alinhamentos para identificação de similaridades entre estas. Posteriormente, utilizamos a teoria das cadeias de Markov com estados ocultos, HMM’s (Hidden Markov Models), na aplicação do problema de discriminação de regiões homogêneas em sequências de DNA. Utilizamos o algoritmo de Viterbi como uma ferramenta auxiliar para obtenção de regiões homogêneas e em seguida o algoritmo Baum-Welch para maximizar as probabilidades de uma sequência de observações. Foram analisados trechos dos genes HSP70.1 e NRAMP-1 para três espécies diferentes.

Orientador: Fabio Violaro / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-06T10:44:21Z (GMT). No. of bitstreams: 1 Yared_GlaucoFerreiraGazel_D.pdf: 5774867 bytes, checksum: 49a79d9495ce25c8a69ca34858a956ee (MD5) Previous issue date: 2006 / Resumo: Atualmente os sistemas de reconhecimento de fala baseados em HMMs são utilizados em diversas aplicações em tempo real, desde telefones celulares até automóveis. Nesse contexto, um aspecto importante que deve ser considerado é a complexidade dos HMMs, a qual está diretamente relacionada com o custo computacional. Assim, no intuito de permitir a aplicação prática do sistema, é interessante otimizar a complexidade dos HMMs, impondo-se restrições em relação ao desempenho no reconhecimento. Além disso, a otimização da topologia é importante para uma estimação confiável dos parâmetros dos HMMs. Os trabalhos anteriores nesta área utilizam medidas de verossimilhança para a obtenção de sistemas que apresentem um melhor compromisso entre resolução acústica e robustez. Este trabalho apresenta o novo Algoritmo para Eliminação de Gaussianas (GEA), o qual é baseado em uma análise discriminativa e em uma análise interna, para a determinação da complexidade mais apropriada para os HMMs. O novo método é comparado com o Critério de Informação Bayesiano (BIC), com um método baseado em medidas de entropia, com um método discriminativo para o aumento da resolução acústica dos modelos e com os sistemas contendo um número fixo de Gaussianas por estado / Abstract: Nowadays, HMM-based speech recognition systems are used in many real time processing applications, from cell phones to auto mobile automation. In this context, one important aspect to be considered is the HMM complexity, which directly determines the system computational load. So, in order to make the system feasible for practical purposes, it is interesting to optimize the HMM size constrained to a minimum acceptable recognition performance. Furthermore, topology optimization is also important for reliable parameter estimation. Previous works in this area have used likelihood measures in order to obtain models with a better compromise between acoustic resolution and robustness. This work presents the new Gaussian Elimination Algorithm (GEA), which is based on a discriminative analysis and on an internal analysis, for determining the more suitable HMM complexity. The new approach is compared to the classical Bayesian Information Criterion (BIC), to an entropy based method, to a discriminative-based method for increasing the acoustic resolution of the HMMs and also to systems containing a fixed number of Gaussians per state / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Le travail de recherche de cette thèse de doctorat s'inscrit dans le cadre du suivi médical des patients atteints de démences liées à l'âge à l'aide des caméras videos portées par les patients. L'idée est de fournir aux médecins un nouvel outil pour le diagnostic précoce de démences liées à l'âge telles que la maladie d'Alzheimer. Plus précisément, les Activités Instrumentales du Quotidien (IADL: Instrumental Activities of Daily Living en anglais) doivent être indexées automatiquement dans les vidéos enregistrées par un dispositif d'enregistrement portable.Ces vidéos présentent des caractéristiques spécifiques comme de forts mouvements ou de forts changements de luminosité. De plus, la tâche de reconnaissance visée est d'un très haut niveau sémantique. Dans ce contexte difficile, la première étape d'analyse est la définition d'un équivalent à la notion de « plan » dans les contenus vidéos édités. Nous avons ainsi développé une méthode pour le partitionnement d'une vidéo tournée en continu en termes de « points de vue » à partir du mouvement apparent.Pour la reconnaissance des IADL, nous avons développé une solution selon le formalisme des Modèles de Markov Cachés (MMC). Un MMC hiérarchique à deux niveaux a été introduit, modélisant les activités sémantiques ou des états intermédiaires. Un ensemble complexe de descripteurs (dynamiques, statiques, de bas niveau et de niveau intermédiaire) a été exploité et les espaces de description joints optimaux ont été identifiés expérimentalement.Dans le cadre de descripteurs de niveau intermédiaire pour la reconnaissance d'activités nous nous sommes particulièrement intéressés aux objets sémantiques que la personne manipule dans le champ de la caméra. Nous avons proposé un nouveau concept pour la description d'objets ou d'images faisant usage des descripteurs locaux (SURF) et de la structure topologique sous-jacente de graphes locaux. Une approche imbriquée pour la construction des graphes où la même scène peut être décrite par plusieurs niveaux de graphes avec un nombre de nœuds croissant a été introduite. Nous construisons ces graphes par une triangulation de Delaunay sur des points SURF, préservant ainsi les bonnes propriétés des descripteurs locaux c'est-à-dire leur invariance vis-à-vis de transformations affines dans le plan image telles qu'une rotation, une translation ou un changement d'échelle.Nous utilisons ces graphes descripteurs dans le cadre de l'approche Sacs-de-Mots-Visuels. Le problème de définition d'une distance, ou dissimilarité, entre les graphes pour la classification non supervisée et la reconnaissance est nécessairement soulevé. Nous proposons une mesure de dissimilarité par le Noyau Dépendant du Contexte (Context-Dependent Kernel: CDK) proposé par H. Sahbi et montrons sa relation avec la norme classique L2 lors de la comparaison de graphes triviaux (les points SURF).Pour la reconnaissance d'activités par MMC, les expériences sont conduites sur le premier corpus au monde de vidéos avec caméra portée destiné à l'observation des d'IADL et sur des bases de données publiques comme SIVAL et Caltech-101 pour la reconnaissance d'objets. / The research of this PhD thesis is fulfilled in the context of wearable video monitoring of patients with aged dementia. The idea is to provide a new tool to medical practitioners for the early diagnosis of elderly dementia such as the Alzheimer disease. More precisely, Instrumental Activities of Daily Living (IADL) have to be indexed in videos recorded with a wearable recording device.Such videos present specific characteristics i.e. strong motion or strong lighting changes. Furthermore, the tackled recognition task is of a very strong semantics. In this difficult context, the first step of analysis is to define an equivalent to the notion of “shots” in edited videos. We therefore developed a method for partitioning continuous video streams into viewpoints according to the observed motion in the image plane.For the recognition of IADLs we developed a solution based on the formalism of Hidden Markov Models (HMM). A hierarchical HMM with two levels modeling semantic activities or intermediate states has been introduced. A complex set of features (dynamic, static, low-level, mid-level) was proposed and the most effective description spaces were identified experimentally.In the mid-level features for activities recognition we focused on the semantic objects the person manipulates in the camera view. We proposed a new concept for object/image description using local features (SURF) and the underlying semi-local connected graphs. We introduced a nested approach for graphs construction when the same scene can be described by levels of graphs with increasing number of nodes. We build these graphs with Delaunay triangulation on SURF points thus preserving good properties of local features i.e. the invariance with regard to affine transformation of image plane: rotation, translation and zoom.We use the graph features in the Bag-of-Visual-Words framework. The problem of distance or dissimilarity definition between graphs for clustering or recognition is obviously arisen. We propose a dissimilarity measure based on the Context Dependent Kernel of H. Sahbi and show its relation with the classical entry-wise norm when comparing trivial graphs (SURF points).The experiments are conducted on the first corpus in the world of wearable videos of IADL for HMM based activities recognition, and on publicly available academic datasets such as SIVAL and Caltech-101 for object recognition.

We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heuristic global optimization techniques. We benchmark the model against a GLMM model in the context of bond portfolio risk management. The proposed model yields stronger dependencies and higher risks than the GLMM model. As a result, the risk optimal portfolios are more conservative than the decisions resulting from the benchmark model.

La restauration statistique non-supervisée de signaux admet d'innombrables applications dans les domaines les plus divers comme économie, santé, traitement du signal, ... Un des problèmes de base, qui est au coeur de cette thèse, est d'estimer une séquence cachée (Xn)1:N à partir d'une séquence observée (Yn)1:N. Ces séquences sont considérées comme réalisations, respectivement, des processus (Xn)1:N et (Yn)1:N. Plusieurs techniques ont été développées pour résoudre ce problème. Le modèle parmi le plus répandu pour le traiter est le modèle dit "modèle de Markov caché" (MMC). Plusieurs extensions de ces modèles ont été proposées depuis 2000. Dans les modèles de Markov couples (MMCouples), le couple (X, Y) est markovien, ce qui implique que p(x|y) est également markovienne (alors que p(x) ne l'est plus nécessairement), ce qui permet les mêmes traitements que dans les MMC. Plus récemment (2002) les MMCouples ont été étendus aux "modèles de Markov triplet" (MMT), dans lesquels on introduit un processus auxiliaire U et suppose que le triplet T = (X, U, Y) est markovien. Là encore il est possible, dans un cadre plus général que celui des MMCouples, d'effectuer des traitements avec une complexité raisonnable. L'objectif de cette thèse est de proposer des nouvelles modélisations faisant partie des MMT et d'étudier leur pertinence et leur intérêt. Nous proposons deux types de nouveautés: (i) Lorsque la chaîne cachée est discrète et lorsque le couple (X, Y) n'est pas stationnaire, avec un nombre fini de "sauts" aléatoires dans les paramètres, l'utilisation récente des MMT dans lesquels les sauts sont modélisés par un processus discret U a donné des résultats très convaincants (Lanchantin, 2006). Notre première idée est d'utiliser cette démarche avec un processus U continu, qui modéliserait des non-stationnarités "continues" de(X, Y). Nous proposons des chaînes et des champs triplets et présentons quelques expériences. Les résultats obtenus dans la modélisation de la non-stationnarité continue semblent moins intéressants que dans le cas discret. Cependant, les nouveaux modèles peuvent présenter d'autres intérêts; en particulier, ils semblent plus efficaces que les modèles "chaînes de Markov cachées" classiques lorsque le bruit est corrélé; (ii) Soit un MMT T = (X, U, Y) tel que X et Y sont continu et U est discret fini. Nous sommes en présence du problème de filtrage, ou du lissage, avec des sauts aléatoires. Dans les modélisations classiques le couple caché (X, U) est markovien mais le couple (U, Y) ne l'est pas, ce qui est à l'origine de l'impossibilité des calculs exacts avec une complexité linéaire en temps. Il est alors nécessaire de faire appel à diverses méthodes approximatives, dont celles utilisant le filtrage particulaire sont parmi les plus utilisées. Dans des modèles MMT récents le couple caché (X, U) n'est pas nécessairement markovien, mais le couple (U, Y) l'est, ce qui permet des traitements exacts avec une complexité raisonnable (Pieczynski 2009). Notre deuxième idée est d'étendre ces derniers modèles aux triplets T = (X, U, Y) dans lesquels les couples (U, Y) sont "partiellement" de Markov. Un tel couple (U, Y) n'est pas de Markov mais U est de Markov conditionnellement àY. Nous obtenons un modèle T = (X, U, Y) plus général, qui n'est plus de Markov, dans lequel le filtrage et le lissage exacts sont possibles avec une complexité linéaire en temps. Quelques premières simulations montrent l'intérêt des nouvelles modélisations en lissage en présence des sauts. / Statistical unsupervised restoration of signal can be applied in many fields such as economy, health, signal processing, meteorology, finance, biology, reliability, transportation, environment, ... the main problem treated in this thesis is to estimate a hidden sequence (Xn)1:N based on an observed sequence (Yn)1:N. In Probabilistic treatment of the problem in these sequences are considered as accomplishments of respectively, process (Xn)1:N and (Yn)1:N. Several techniques based on statistical methods have been developed to solve this problem. The most common model known for this kind of problems is the “hidden Markov model”. In this model we assume that the hidden process X is Markovian and laws p(y|x) of Y are conditional on X are sufficiently simple so that the law p(x|y) is also Markovian, this property is necessary for treatment. Many Extensions of these models have been proposed since 2000. In Markov models couples (MMCouples), more general than the MMC, the pair (X,Y) is Markovian), implying that p(x|y) is also Markovian (when p(x) is not necessarily markovian), which allows the same treatment as in MMC. More recently (2002), were extended to MMCouples are extended to Markov models Triplet (MMT), in which we introduce an auxiliary process U and suppose that the triple T=(X,U,Y) is Markovian. It’s again possible, in a general case of MMCouples, to perform treatments with a reasonable complexity. The objective of this thesis is to propose new modeling of MMT and to investigate their relevance and interest. We offer two types of innovations: (i) When the hidden system is discrete and when the couple (X,Y) is not stationary with a finite number of random “jumps” in parameters, the recent use of MMT where the jumps are modelized by a discrete process U has been very convincing (Lanchantin, 2006). Our first idea is to use this approach with a continuous process U, which models non-steady "continuous" of (X,Y). We propose chains and triplet fields and present some experiments. The results obtained in the modeling of non-stationarity still seem less interesting that in the discrete case. However, new models may have other interests, in particular, they seem more efficient than “classic hidden Markov” when the noise is correlated; (ii) Considering an MMT T=(X,U,Y) such that X and Y are continuous and U is discrete finite. We are dealing with a problem of filtering, or smoothing, with random jumps. In classic modelling the hidden pair (X,U) is Markovian, but the pair (U,Y) is not, what is the cause of the impossibility of Exact calculations with time linear complexity. It is then necessary to use various approximate methods, including methods using particle filtering which are the most common. In recent models MMT the hidden pair (X,U) is not necessarily Markovian, but the pair (U,Y) is Markovian, which allows accurate treatment with a reasonable complexity (Pieczynski 2009). Our second idea is to extend these models to triplets T=(X,U,Y) where the pairs (U,Y) are "partially" Markovian. Such a pair (U,Y) is not Markovian but U is conditionally Markovian on Y. We have in result a model with general model T=(X,U,Y) , which is no more Markovian, wherein the filtering and smoothing are accurate possible with time linear complexity. Some preliminary Simulations show the importance of new smoothing models with of jumps.