Fast bias-constrained optimal FIR filtering for time-invariant state space models

This paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias-constrained optimal finite impulse response filtering algorithm for linear discrete time-invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite-horizon and full-horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade-off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full-horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate

Investigation in Low Drive Level Sensitivity of Quartz Resonator Affecting its Motional Parameters

Usually, starting of oscillation in a quartz crystal oscillator requires a resonator's input power in the range of – 20 dBm, but under storage a phenomenon known as Drive Level Dependency (DLD) or Drive Level Sensitivity (DLS) may appear that prevents the starting of oscillation. Several studies performed in the past have shown that at low drive level some quartz resonators may exhibit a large increase of their series resistance preventing the starting of oscillation. This work reviews the studies and results obtained for nearly fifty years on very low drive level sensitivity of quartz. The various mechanisms and models based on the hypothesis of moving particles and surface defects in the resonator inducing resistance increase and its relation with noise mechanism are reviewed as well. Also, the paper describes several experimental set-ups, and measurement procedures used to obtain very low drive level motional parameters. This work is a contribution to understand the problem of starting quartz after a long storage period. Some preliminary results of the series resistance measured at very low drive level are also presented

Combined extended FIR/Kalman filtering for indoor robot localization via triangulation

A combined unbiased finite impulse response (UFIR) and Kalman filtering algorithm is proposed for mobile robot localization via triangulation utilizing noisy measurements. We consider a mobile robot travelling on an indoor floorspace with three nodes in a view. Under the not well-known initial robot state and noise statistics, the extended Kalman filter (EKF) may produce unacceptable estimates. The iterative extended UFIR (EFIR) filter ignores the noise statistics, but requires N initial points of linear measurements which are unavailable. The combined EFIR/Kalman algorithm utilizes N first EKF estimates with approximately set initial conditions and noise statistics as linear measurements for EFIR filter. It is shown that the combined algorithm is more accurate than EKF in robot localization under the real operation conditions. Simulations are provided for piecewise and circular robot trajectories

Effect of embedded unbiasedness on discrete-time optimal FIR filtering estimates

Unbiased estimation is an efficient alternative to optimal estimation when the noise statistics are not fully known and/or the model undergoes temporary uncertainties. In this paper, we investigate the effect of embedded unbiasedness (EU) on optimal finite impulse response (OFIR) filtering estimates of linear discrete time-invariant state-space models. A new OFIR-EU filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint. We show that the OFIR-UE filter is equivalent to the minimum variance unbiased FIR (UFIR) filter. Unlike the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. Contrary to the UFIR filter which MSE is minimized by the optimal horizon of N opt points, the MSEs in the OFIR-EU and OFIR filters diminish with N and these filters are thus full-horizon. Based upon several examples, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters

Three-dimensional optimal kalman algorithm for GPS-based positioning estimation of the stationary object

This project presents the design and development of a multidimensional Kalman filter with the purpose to estimate the tri-dimensional position of a stationary object based on GPS measurements. Because this is not the only filtering algorithm available, a comparison with other four types of filters (one-dimensional optimal Kalman algorithm, quasi-optimal stationary Kalman algorithm, simple moving average algorithm and optimally unbiased moving average algorithm) is also developed.Consejo Nacional de Ciencia y TecnologíaUniversidad de Guanajuat

Improving state estimates over finite data using optimal FIR filtering with embedded unbiasedness

In this paper, the optimal finite impulse response (OFIR) with embedded unbiasedness (EU) filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint for discrete time-invariant state-space models. Un like the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. With a two-state harmonic model, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters

GPS Based Design of the Local Clock Control System based on the Optimally Unbiased Moving Average Filter

In this paper we made the simulation steering of the local clock t'ime errors with simple moving average (MA), optimally unbiased moving average (OMA), the two and three-state Kalman filters. The references signal (precise time) was suministred by GPS. In this task we have two important activities, estimating and the error control, so the,principal parameter in this study is the root mean square error (RMSE) of steering. When steering the GPS-based time error in the local clock with four filters, we found out that, of the filter with the same time constant, the optimally unbiased MA filter desmostred the steering error between the two and three state Kalman filter.Universidad de Guanajuat