For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive gaussian white noise, the extended Kalman filter (EKF) covariance propagation equations linearized about the true unknown trajectory provide the Cramér-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.
{"title":"The Cramer-Rao estimation error lower bound computation for deterministic nonlinear systems","authors":"James H. Taylor","doi":"10.1109/CDC.1978.268121","DOIUrl":"https://doi.org/10.1109/CDC.1978.268121","url":null,"abstract":"For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive gaussian white noise, the extended Kalman filter (EKF) covariance propagation equations linearized about the true unknown trajectory provide the Cramér-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115659583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Among the deterministic policies for the optimal control of stochastic systems the best one is of closed-loop type, because it presents the "dual effect" of control. The theoretical closed-loop solution structure is deduced from Bellman's principle but is very difficult to implement in the non-linear case. This communication presents a closed-loop solution by approximation of the minimum cost function by introduction of the gaussian sum method.
{"title":"Optimal control of non-linear stochastic systems by approximation of the optimal cost functional","authors":"G. Campion","doi":"10.1109/CDC.1978.268044","DOIUrl":"https://doi.org/10.1109/CDC.1978.268044","url":null,"abstract":"Among the deterministic policies for the optimal control of stochastic systems the best one is of closed-loop type, because it presents the \"dual effect\" of control. The theoretical closed-loop solution structure is deduced from Bellman's principle but is very difficult to implement in the non-linear case. This communication presents a closed-loop solution by approximation of the minimum cost function by introduction of the gaussian sum method.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114129782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Time estimation has been proposed as a measure of pilot workload and it appears that the production method provides a useful measure. The verbal estimation method has also been investigated and it appears that it does not provide as sensitive a measure of workload as does the production method. Verbal estimates are given with less precision and a series of verbal estimates tends to reflect a relative judgement of the duration of different intervals rather than an absolute judgement of the length of each interval. Overestimation may either reflect boredom during the interval, or the fact that a great deal of activity was performed during the interval that was remembered. Underestimation may either reflect a feeling that time passed quickly because interesting activities were engaged in, or that so little activity was performed or remembered, that very little time passed.
{"title":"Pilot workload during final approach in congested airspace","authors":"S. Hart","doi":"10.1109/CDC.1978.268137","DOIUrl":"https://doi.org/10.1109/CDC.1978.268137","url":null,"abstract":"Time estimation has been proposed as a measure of pilot workload and it appears that the production method provides a useful measure. The verbal estimation method has also been investigated and it appears that it does not provide as sensitive a measure of workload as does the production method. Verbal estimates are given with less precision and a series of verbal estimates tends to reflect a relative judgement of the duration of different intervals rather than an absolute judgement of the length of each interval. Overestimation may either reflect boredom during the interval, or the fact that a great deal of activity was performed during the interval that was remembered. Underestimation may either reflect a feeling that time passed quickly because interesting activities were engaged in, or that so little activity was performed or remembered, that very little time passed.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116072985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper a feedforward control technique is developed which enables a plant to perfectly track a model in the presence of a disturbance. It is assumed that both the model and the disturbance have time-varying inputs which are not known in advance. The technique used here develops dynamic compensators which have as inputs only a finite number of derivatives of the model and disturbance inputs. A procedure for using this technique in conjunction with optimal control is also given. Examples of how these teckniques can be used are presented.
{"title":"Feedforward control to track the output of a forced model","authors":"M. O'Brien, J. Broussard","doi":"10.1109/CDC.1978.268115","DOIUrl":"https://doi.org/10.1109/CDC.1978.268115","url":null,"abstract":"In this paper a feedforward control technique is developed which enables a plant to perfectly track a model in the presence of a disturbance. It is assumed that both the model and the disturbance have time-varying inputs which are not known in advance. The technique used here develops dynamic compensators which have as inputs only a finite number of derivatives of the model and disturbance inputs. A procedure for using this technique in conjunction with optimal control is also given. Examples of how these teckniques can be used are presented.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116083940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper a partially observable system governed by a linear stochastic differential equation is considered. The expected loss is to be minimized in the class of all feedback controls depending linearly on the observation process subject to the condition that the terminal point of the system process lies in some fixed target set with a prescribed probability. The existence of optimal controls is shown via the construction of an equivalent deterministic control problem.
{"title":"Stochastic control under chance constraints","authors":"N. Christopeit","doi":"10.1109/CDC.1978.267977","DOIUrl":"https://doi.org/10.1109/CDC.1978.267977","url":null,"abstract":"In this paper a partially observable system governed by a linear stochastic differential equation is considered. The expected loss is to be minimized in the class of all feedback controls depending linearly on the observation process subject to the condition that the terminal point of the system process lies in some fixed target set with a prescribed probability. The existence of optimal controls is shown via the construction of an equivalent deterministic control problem.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121743310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, a new class of time-domain state space models has been developed (Ref. 1) to describe layered media systems. When layers are uniform, the resulting state equations are referred to as uniform causal functional equations (UCFE). An example of a UCFE is: x (t + ¿) = Ax (t) + b [m(t) + w(t)] (1) where, for a K-layer system, x (t) is a 2K x 1 state vector comprised of K upgoing states and K downgoing states, m(t) is the source signature, w(t) is a random process which reflects uncertainty about our knowledge of m(t), and A and b are matrices (of appropriate dimensions) which are functions of reflection coefficients r0, r1,..., rK which characterize the system. Additionally, ¿ is the one-way travel time for each layer. A surface measurement (i.e., seismogram) y(t), where y(t) = h' x(t) + n(t) (2) is also assumed available. This measurement is corrupted by measurement noise, n(t) and is in terms of vector h which is also a function of some of the reflection coefficients.
最近，一类新的时域状态空间模型被开发出来(参考文献1)来描述分层介质系统。当各层均匀时，产生的状态方程称为均匀因果泛函方程(UCFE)。UCFE的一个例子是:x (t +¿)= Ax (t) + b [m(t) + w(t)](1)，其中，对于K层系统，x (t)是由K个上升状态和K个下降状态组成的2K x 1状态向量，m(t)是源签名，w(t)是反映我们对m(t)知识的不确定性的随机过程，a和b是矩阵(具有适当的维数)，它们是反射系数r0, r1，…， rK表示系统的特征。此外，¿是每层的单程旅行时间。地面测量(即地震图)y(t)，其中y(t) = h' x(t) + n(t)(2)也假定可用。这个测量被测量噪声n(t)所破坏，并且用向量h表示，它也是一些反射系数的函数。
{"title":"Identification of reflection coefficients from noisy data by means of extended minimum variance estimators: A critical examination","authors":"J. Mendel","doi":"10.1109/CDC.1978.267957","DOIUrl":"https://doi.org/10.1109/CDC.1978.267957","url":null,"abstract":"Recently, a new class of time-domain state space models has been developed (Ref. 1) to describe layered media systems. When layers are uniform, the resulting state equations are referred to as uniform causal functional equations (UCFE). An example of a UCFE is: x (t + ¿) = Ax (t) + b [m(t) + w(t)] (1) where, for a K-layer system, x (t) is a 2K x 1 state vector comprised of K upgoing states and K downgoing states, m(t) is the source signature, w(t) is a random process which reflects uncertainty about our knowledge of m(t), and A and b are matrices (of appropriate dimensions) which are functions of reflection coefficients r0, r1,..., rK which characterize the system. Additionally, ¿ is the one-way travel time for each layer. A surface measurement (i.e., seismogram) y(t), where y(t) = h' x(t) + n(t) (2) is also assumed available. This measurement is corrupted by measurement noise, n(t) and is in terms of vector h which is also a function of some of the reflection coefficients.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121415421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a new approach to the frequency-domain analysis of multiloop linear feed-back systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.
{"title":"Robustness of multiloop linear feedback systems","authors":"J. Doyle","doi":"10.1109/CDC.1978.267885","DOIUrl":"https://doi.org/10.1109/CDC.1978.267885","url":null,"abstract":"This paper presents a new approach to the frequency-domain analysis of multiloop linear feed-back systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123809423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, maximum likelihood estimates of the mean and the covariance of a normal random variable, based on a set of independently, but nonidentically distributed observations, are discussed. An efficient algorithm for computing MLEs is introduced. The asymptotic properties such as strong consistency and asymptotic normality are examined.
{"title":"Maximum likelihood theory for a class of independently, but nonidentically distributed observations","authors":"Fang-kuo Sun, T. Lee","doi":"10.1109/CDC.1978.268023","DOIUrl":"https://doi.org/10.1109/CDC.1978.268023","url":null,"abstract":"In this paper, maximum likelihood estimates of the mean and the covariance of a normal random variable, based on a set of independently, but nonidentically distributed observations, are discussed. An efficient algorithm for computing MLEs is introduced. The asymptotic properties such as strong consistency and asymptotic normality are examined.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125046360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Until now the human vocal tract area function and transfer function were studied from a time-series analysis of the speech signal alone, making some simple assumptions about the glottal source. In this paper we will present a study of the tract from measurements of the speech signal at the lips and the external throat-wall vibration signal near the glottis ("input/output measurements").
{"title":"Models for the human throat-wall and a study of the vocal tract from input/output measurements","authors":"N. Vemula, A. Engebretson, D. Elliott","doi":"10.1109/CDC.1978.268070","DOIUrl":"https://doi.org/10.1109/CDC.1978.268070","url":null,"abstract":"Until now the human vocal tract area function and transfer function were studied from a time-series analysis of the speech signal alone, making some simple assumptions about the glottal source. In this paper we will present a study of the tract from measurements of the speech signal at the lips and the external throat-wall vibration signal near the glottis (\"input/output measurements\").","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125061631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Adaptive Line Enhancer (ALE) was first described by Widrow et al, as a practical on-line technique for separating the coherent components from the incoherent components of an input signal. Subsequent work has shown this same adaptive filtering structure to be applicable to maximum entropy spectral estimation, predictive deconvolution, and narrowband interference rejection, as well as other applications which have historically used matrix inversion and Levinson's algorithm techniques. While an often cited advantage of adaptive filtering is its tolerance of slowly time-varying input statistics, the existing analyses of the ALE have concentrated on the stationary case. This paper extends these results, applying the theory to the case of inputs containing sinusoids whose frequencies slowly vary in time. This is approached by developing a time-varying eigenvalue-eigenvector description of the expected filter impulse response vector which holds for any slowly nonstationary input. These results are then used to predict the expected impulse response vector for the ALE input of stationary white noise plus a sinusoid with linearly swept frequency. The response of the ALE for this particular input signal provides useful benchmarks for dealing with more complex forms of frequency modulation.
{"title":"Response of the adaptive line enhancer to chirped sinusoids","authors":"J. Treichler","doi":"10.1109/CDC.1978.268141","DOIUrl":"https://doi.org/10.1109/CDC.1978.268141","url":null,"abstract":"The Adaptive Line Enhancer (ALE) was first described by Widrow et al, as a practical on-line technique for separating the coherent components from the incoherent components of an input signal. Subsequent work has shown this same adaptive filtering structure to be applicable to maximum entropy spectral estimation, predictive deconvolution, and narrowband interference rejection, as well as other applications which have historically used matrix inversion and Levinson's algorithm techniques. While an often cited advantage of adaptive filtering is its tolerance of slowly time-varying input statistics, the existing analyses of the ALE have concentrated on the stationary case. This paper extends these results, applying the theory to the case of inputs containing sinusoids whose frequencies slowly vary in time. This is approached by developing a time-varying eigenvalue-eigenvector description of the expected filter impulse response vector which holds for any slowly nonstationary input. These results are then used to predict the expected impulse response vector for the ALE input of stationary white noise plus a sinusoid with linearly swept frequency. The response of the ALE for this particular input signal provides useful benchmarks for dealing with more complex forms of frequency modulation.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130206873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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