Observation Equation

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Hironori Suzuki - One of the best experts on this subject based on the ideXlab platform.

  • application of probe vehicle data for real time traffic state estimation and short term travel time prediction on a freeway
    Transportation Research Record, 2003
    Co-Authors: Chumchoke Nanthawichit, Takashi Nakatsuji, Hironori Suzuki
    Abstract:

    Traffic information from probe vehicles has great potential for improving the estimation accuracy of traffic situations, especially where no traffic detector is installed. A method for dealing with probe data along with conventional detector data to estimate traffic states is proposed. The probe data were integrated into the Observation Equation of the Kalman filter, in which state Equations are represented by a macroscopic traffic-flow model. Estimated states were updated with information from both stationary detectors and probe vehicles. The method was tested under several traffic conditions by using hypothetical data, giving considerably improved estimation results compared to those estimated without probe data. Finally, the application of the proposed method was extended to the estimation and short-term prediction of travel time. Travel times were obtained indirectly through the conversion of speeds estimated or predicted by the proposed method. Experimental results show that the performance of travel-time estimation or prediction is comparable to that of some existing methods.

  • application of probe vehicle data for real time traffic state estimation and short term travel time prediction on a freeway
    Transportation Research Board 82nd Annual MeetingTransportation Research Board, 2003
    Co-Authors: Chumchoke Nanthawichit, Takashi Nakatsuji, Hironori Suzuki
    Abstract:

    Traffic information from probe vehicles has great potential for improving the estimation accuracy of traffic situations, especially where no traffic detector is installed. A method for dealing with probe data along with conventional detector data to estimate traffic states is proposed in this paper. The probe data were integrated into the Observation Equation of the Kalman filter, in which state Equations are represented by a macroscopic traffic flow model. Estimated states were updated with information from both stationary detectors and probe vehicles. The method was tested under several traffic conditions based on hypothetical data, giving considerably improved estimation results compared to those estimated without probe data. Finally, the application of the proposed method was extended to the estimation and short-term prediction of travel time. Travel times were obtained indirectly through the conversion of speeds estimated/predicted by the proposed method. Experimental results show that the performance of travel time estimation/prediction is comparable to those of some existing methods

Seiichi Nakamori - One of the best experts on this subject based on the ideXlab platform.

  • RLS Filter Using Covariance Information and RLS Wiener Type Filter based on Innovation Theory for Linear Discrete-Time Stochastic Descriptor Systems
    2018
    Co-Authors: Seiichi Nakamori
    Abstract:

    It is known that the stochastic descriptor systems are transformed into the conventional state Equation, the Observation Equation and the other Equation, by using the singular value decomposition. Based on the preliminary problem formulation for the linear discrete-time stochastic descriptor systems in section 2, this paper, in Theorem 1, based on the innovation theory, proposes the recursive least-squares (RLS) filter using the covariance information of the state vector in the state Equation and the covariance information of the Observation noise in the Observation Equation. The state Equation and the Observation Equation are transformed from the descriptor systems. Secondly, in Theorem 2, based on the innovation theory, this paper proposes the RLS Wiener type filter for the descriptor systems. It might be advantageous that these filtering algorithms in this paper are derived based on the innovation theory in a unified manner. A numerical simulation example is demonstrated to show the estimation characteristics of the proposed RLS Wiener type filtering algorithm for the descriptor systems.

  • New RLS Wiener Smoother for Colored Observation Noise in Linear Discrete-time Stochastic Systems
    International Journal of Information Technology and Computer Science, 2013
    Co-Authors: Seiichi Nakamori
    Abstract:

    In the estimation problems, rather than the white Observation noise, there are cases where the Observation noise is modeled by the colored noise process. In the Observation Equation, the observed value ) (k y is given as a sum of the signal ) ( ) ( k Hx k z  and the colored Observation noise ) (k vc . In this paper, the Observation Equation is converted to the new Observation Equation for the white Observation noise. In accordance with the Observation Equation for the white Observation noise, this paper proposes new RLS Wiener estimation algorithms for the fixed-point smoothing and filtering estimates in linear discrete-time wide-sense stationary stochastic systems. The RLS Wiener estimators require the following information: (a) the system matrix for the state vector ) (k x ; (b) the Observation matrix H ; (c) the variance of the state vector ) (k x ; (d) the system matrix for the colored Observation noise ) (k vc ; (e) the variance of the colored Observation noise.

  • Polynomial fixed-point smoothing of uncertainly observed signals based on covariances
    International Journal of Systems Science, 2008
    Co-Authors: Seiichi Nakamori, Aurora Hermoso-carazo, Raquel Caballero-Águila, J.d. Jiménez-lópez, Josefa Linares-pérez
    Abstract:

    In this article, the least-squares νth-order polynomial fixed-point smoothing problem of uncertainly observed signals is considered, when only some information about the moments of the processes involved is available. For this purpose, a suitable augmented Observation Equation is defined such that the optimal polynomial estimator of the original signal is obtained from the optimal linear estimator of the augmented signal based on the augmented Observations and, hence, a recursive algorithm for this linear estimator is deduced. The proposed estimator does not require the knowledge of the state-space model of the signal, but only the moments (up to the 2νth one) of the signal and Observation noise, as well as the probability that the signal exists in the Observations.

  • Chandrasekhar-type recursive Wiener filter using covariance information in linear discrete-time wide-sense stationary stochastic systems
    IFAC Proceedings Volumes, 2004
    Co-Authors: Seiichi Nakamori, Aurora Hermoso-carazo, J.d. Jiménez-lópez, J. Linares-pérez
    Abstract:

    Abstract This paper designs the Chandrasekhar-type recursive Wiener filter for the white Observation noise in linear discrete-time wide-sense stationary stochastic systems. The system matrix in the state-space model of the signal, the crossvariance function of the state variable of the signal with the observed value, the Observation matrix for the signal, the variance of the white Observation noise and the observed value are assumed to be known. In particular, this paper extends the Chandrasekhar-type recursive Wiener filter for a scalar Observation Equation to the case of a vector Observation Equation. The characteristic of the Chandrasekhar-type filter is to calculate the filter gain directly by solving the recursive difference Equations.

  • Short communication Linear recursive discrete-time estimators using covariance information under uncertain Observations
    2003
    Co-Authors: Seiichi Nakamori, Raquel Caballero, Aurora Hermoso-carazo, Josefa Linares-p
    Abstract:

    This paper, using the covariance information, proposes recursive least-squares (RLS) 4ltering and 4xed-point smoothing algorithms with uncertain Observations in linear discrete-time stochastic systems. The Observation Equation is given by y(k )= � (k)Hx(k )+ v(k), where {� (k)} is a binary switching sequence with conditional probability distribution verifying Eq. (3). This Observation Equation is suitable for modeling the transmission of data in multichannels as in remote sensing

Chumchoke Nanthawichit - One of the best experts on this subject based on the ideXlab platform.

  • application of probe vehicle data for real time traffic state estimation and short term travel time prediction on a freeway
    Transportation Research Record, 2003
    Co-Authors: Chumchoke Nanthawichit, Takashi Nakatsuji, Hironori Suzuki
    Abstract:

    Traffic information from probe vehicles has great potential for improving the estimation accuracy of traffic situations, especially where no traffic detector is installed. A method for dealing with probe data along with conventional detector data to estimate traffic states is proposed. The probe data were integrated into the Observation Equation of the Kalman filter, in which state Equations are represented by a macroscopic traffic-flow model. Estimated states were updated with information from both stationary detectors and probe vehicles. The method was tested under several traffic conditions by using hypothetical data, giving considerably improved estimation results compared to those estimated without probe data. Finally, the application of the proposed method was extended to the estimation and short-term prediction of travel time. Travel times were obtained indirectly through the conversion of speeds estimated or predicted by the proposed method. Experimental results show that the performance of travel-time estimation or prediction is comparable to that of some existing methods.

  • application of probe vehicle data for real time traffic state estimation and short term travel time prediction on a freeway
    Transportation Research Board 82nd Annual MeetingTransportation Research Board, 2003
    Co-Authors: Chumchoke Nanthawichit, Takashi Nakatsuji, Hironori Suzuki
    Abstract:

    Traffic information from probe vehicles has great potential for improving the estimation accuracy of traffic situations, especially where no traffic detector is installed. A method for dealing with probe data along with conventional detector data to estimate traffic states is proposed in this paper. The probe data were integrated into the Observation Equation of the Kalman filter, in which state Equations are represented by a macroscopic traffic flow model. Estimated states were updated with information from both stationary detectors and probe vehicles. The method was tested under several traffic conditions based on hypothetical data, giving considerably improved estimation results compared to those estimated without probe data. Finally, the application of the proposed method was extended to the estimation and short-term prediction of travel time. Travel times were obtained indirectly through the conversion of speeds estimated/predicted by the proposed method. Experimental results show that the performance of travel time estimation/prediction is comparable to those of some existing methods

Josefa Linares-pérez - One of the best experts on this subject based on the ideXlab platform.

  • Polynomial fixed-point smoothing of uncertainly observed signals based on covariances
    International Journal of Systems Science, 2008
    Co-Authors: Seiichi Nakamori, Aurora Hermoso-carazo, Raquel Caballero-Águila, J.d. Jiménez-lópez, Josefa Linares-pérez
    Abstract:

    In this article, the least-squares νth-order polynomial fixed-point smoothing problem of uncertainly observed signals is considered, when only some information about the moments of the processes involved is available. For this purpose, a suitable augmented Observation Equation is defined such that the optimal polynomial estimator of the original signal is obtained from the optimal linear estimator of the augmented signal based on the augmented Observations and, hence, a recursive algorithm for this linear estimator is deduced. The proposed estimator does not require the knowledge of the state-space model of the signal, but only the moments (up to the 2νth one) of the signal and Observation noise, as well as the probability that the signal exists in the Observations.

  • Linear recursive discrete-time estimators using covariance information under uncertain Observations
    Signal Processing, 2003
    Co-Authors: Seiichi Nakamori, Aurora Hermoso-carazo, Raquel Caballero-Águila, Josefa Linares-pérez
    Abstract:

    This paper, using the covariance information, proposes recursive least-squares (RLS) filtering and fixed-point smoothing algorithms with uncertain Observations in linear discrete-time stochastic systems. The Observation Equation is given by y(k) = γ(k)Hx(k) + v(k), where {γ(k)} is a binary switching sequence with conditional probability distribution verifying Eq. (3). This Observation Equation is suitable for modeling the transmission of data in multichannels as in remote sensing situations. The estimators require the information of the system matrix Φ concerning the state variable which generates the signal, the Observation vector H, the crossvariance function Kxz(k,k) of the state variable with the signal, the variance R(k) of the white Observation noise, the observed values, the probability p(k): P{γ(k)= 1} that the signal exists in the uncertain Observation Equation and the (2,2) element [P(k|j)]2,2 of the conditional probability matrix of γ(k), given γ(j).

Takashi Nakatsuji - One of the best experts on this subject based on the ideXlab platform.

  • application of probe vehicle data for real time traffic state estimation and short term travel time prediction on a freeway
    Transportation Research Record, 2003
    Co-Authors: Chumchoke Nanthawichit, Takashi Nakatsuji, Hironori Suzuki
    Abstract:

    Traffic information from probe vehicles has great potential for improving the estimation accuracy of traffic situations, especially where no traffic detector is installed. A method for dealing with probe data along with conventional detector data to estimate traffic states is proposed. The probe data were integrated into the Observation Equation of the Kalman filter, in which state Equations are represented by a macroscopic traffic-flow model. Estimated states were updated with information from both stationary detectors and probe vehicles. The method was tested under several traffic conditions by using hypothetical data, giving considerably improved estimation results compared to those estimated without probe data. Finally, the application of the proposed method was extended to the estimation and short-term prediction of travel time. Travel times were obtained indirectly through the conversion of speeds estimated or predicted by the proposed method. Experimental results show that the performance of travel-time estimation or prediction is comparable to that of some existing methods.

  • application of probe vehicle data for real time traffic state estimation and short term travel time prediction on a freeway
    Transportation Research Board 82nd Annual MeetingTransportation Research Board, 2003
    Co-Authors: Chumchoke Nanthawichit, Takashi Nakatsuji, Hironori Suzuki
    Abstract:

    Traffic information from probe vehicles has great potential for improving the estimation accuracy of traffic situations, especially where no traffic detector is installed. A method for dealing with probe data along with conventional detector data to estimate traffic states is proposed in this paper. The probe data were integrated into the Observation Equation of the Kalman filter, in which state Equations are represented by a macroscopic traffic flow model. Estimated states were updated with information from both stationary detectors and probe vehicles. The method was tested under several traffic conditions based on hypothetical data, giving considerably improved estimation results compared to those estimated without probe data. Finally, the application of the proposed method was extended to the estimation and short-term prediction of travel time. Travel times were obtained indirectly through the conversion of speeds estimated/predicted by the proposed method. Experimental results show that the performance of travel time estimation/prediction is comparable to those of some existing methods