Pyung Soo Kim

A receding horizon Kalman FIR filter for discrete time-invariant systems

A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.

A receding horizon Kalman FIR filter for linear continuous-time systems

A receding horizon Kalman finite-impulse response (FIR) filter is suggested for continuous-time systems, combining the Kalman filter with the receding horizon strategy. In the suggested filter, the horizon initial state is assumed to be unknown. It can always be obtained irrespective of unknown information on the horizon initial state. The filter may be the first stochastic FIR form for continuous-time systems that may have many good inherent properties. The suggested filter can be represented in an iterative form and also in a standard FIR form. The suggested filter turns out to be a remarkable deadbeat observer. The validity of the suggested filter is illustrated by numerical examples.

Receding-horizon unbiased FIR filters for continuous-time state-space models without a priori initial state information

A receding horizon unbiased finite-impulse response filter (RHUFF) is proposed for continuous-time state space models. Linearity, unbiasedness, finite-impulse response (FIR) structure, and independence of the initial state information will be required in advance, in addition to a performance index of minimum variance. The proposed RHUFF is obtained by directly minimizing the performance index with the unbiasedness constraint. The proposed RHUFF is represented first in a standard FIR form and then in an iterative form. It is shown that the RHUFF is equivalent to the existing receding horizon (RH) Kalman FIR filter. The former is more systematic and logical, while the latter is heuristic due to the handling of infinite covariance of the initial state information.

Quasi-deadbeat minimax filters for deterministic state~space models

In this note, a quasi-deadbeat property is introduced and a quasi-deadbeat minimax filter (DMF) is proposed as a new class of filters for deterministic discrete-time state?space models. Constraints such as linearity, quasi-deadbeat property, and independence of the initial-state information will be required in advance, in addition to a new performance index of the worst-case gain between the disturbance and the current estimation error. The proposed DMF is obtained by directly minimizing the new performance index with above constraints. Finite impulse response (FIR) and infinite impulse response (IIR) structures are suggested with emphasis on the FIR structure. The proposed DMF is represented first, in a standard batch form and then in an iterative form. It is shown that the DMF with FIR and IIR structures for deterministic systems are similar in form to the existing receding horizon unbiased FIR filter (RHUFF) and the Kalman filter, respectively, for stochastic systems.

Brief Estimation and detection of unknown inputs using optimal FIR filter

The optimal finite impulse response (FIR) filter is applied to systems with both unknown inputs and noise, in order to obtain noise-suppressed estimates of the unknown inputs. The unknown inputs are modeled as random-walk processes and estimated together with the state. Using the optimal FIR filtering algorithm, the estimate for each unknown input is shown to be independent of the window initial state and also of other unknown inputs. A detection scheme for an unknown input is developed utilizing a test variable independently of other unknown inputs. Finally, numerical examples are given to show the performance of the proposed estimation and detection method.

Best linear unbiased estimation filters with FIR structures for state space signal models

In this paper, a new best linear unbiased estimation (BLUE) finite impulse response (FIR) filter called the BLUE FIR filter is proposed for discrete-time state space signal models with system noises and inputs. The proposed BLUE FIR filter is a linear function of only the finite measurements and inputs on the most recent horizon, does not require a priori information about the horizon initial state, and has both unbiasedness and efficiency properties. The proposed BLUE FIR filter has time-invariance and dead-beat properties. The proposed BLUE FIR filter is represented in batch form and then iterative form for computational advantage. It is shown to be equivalent to the existing receding horizon (RH) FIR filter with completely unknown horizon initial state, whose efficiency was difficult to obtain and was thus unknown.

Forgetting least squares estimation FIR filters without noise covariance information

This paper concerns with a new estimation filter with a finite impulse response (FIR) structure under a least squares (LS) criterion using a forgetting factor. This filter will be called the forgetting least squares estimation (FLSE) FIR filter. The proposed FLSE FIR filter does not require information of the noise covariances as well as the initial state. It will be shown that, in particular case, the proposed FLSE FIR filter can be reduced to the simple least squares estimation FIR filter called the LSE FIR filter. The proposed FLSE FIR filter has also some inherent properties such as time-invariance, unbiasedness and deadbeat. The proposed FLSE FIR filter will be represented in a batch form and then a recursive form, which will be remarkable in the view of computational advantage. From discussions about the choice of a forgetting factor and a horizon length, it will be shown that they can be considered as useful parameters to make the estimation performance of the proposed FLSE FIR filter as good as possible. Via simulations, it will be shown that the proposed FLSE FIR filter consistently outperforms the LSE FIR filter, and can outperform the existing best linear unbiased estimation (BLUE) FIR filter with incorrect noise covariances.

Receding horizon FIR filter with estimated horizon initial state and its application to aircraft engine systems

Proposes a version of the discrete-time receding horizon FIR filter (RHFF) using the estimated horizon initial state. The estimated horizon initial state is obtained from the best linear unbiased estimator (BLUE) scheme. The proposed RHFF for the current state can be represented in either an iterative form or a batch form. The proposed RHFF is always time-invariant and has unbiasedness and remarkable deadbeat properties. The proposed RHFF is shown to be equivalent to the existing RHFF with unknown horizon initial state. For the validity of the proposed RHFF, the problem of a third-order dynamic model of an F-404 aircraft engine system is considered via simulation studies.

Manoeuvre detection and target tracking using state-space optimal FIR filters

Three hypothesized phases of manoeuvres are proposed to describe various behaviors of flying targets. The three phases consist of the zero phase, the bias phase and the transition phase, which represent intervals of nonmaneuver, a constant-bias manoeuvre and a random-walk manoeuvre, respectively. Using the corresponding target models for the three phases, a filter bank based on optimal FIR filters is developed to reduce the computation amount for real-time processing. A detection scheme employing two test variables is also developed in order to detect the phase of the manoeuvre and to select a filter from the filter bank. The proposed scheme is tested via computer simulations.

Estimation and detection of unknown inputs using optimal FIR filter

Abstract The optimal FIR filter is applied to systems with both unknown inputs and noise, in order to obtain noise-suppressed estimates of the unknown inputs. The unknown inputs are modeled as random-walk processes and estimated together with the state. Using the optimal FIR filtering algorithm, the estimate for each unknown input is shown to be independent of the window initial state and also of other unknown inputs. A detection scheme for an unknown input is developed utilizing a test variable independently of other unknown inputs. Finally, numerical examples are given to show the performance of the proposed estimation and detection method.