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

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

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

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

New results in nonlinear state estimation using extended unbiased fir filtering

This paper discusses two algorithms of extended unbiased FIR (EFIR) filtering of nonlinear discrete-time state-space models used in tracking and state estimation. The basic algorithm employs the extended nonlinear state and observation equations. The modified algorithm utilizes the nonlinear-to-linear conversion of the observation equation which is provided using a batch EFIR filter having small memory. Unlike the extended Kalman filter (EKF), both EFIR algorithms ignore the noise statistics and demonstrate better robustness against temporary model uncertainties. These algorithms require an optimal horizon in order to minimize the mean square error. Applications are given for robot indoor self-localization utilizing radio frequency identification tags

Ultimate iterative UFIR filtering algorithm

Measurements are often provided in the presence of noise and uncertainties that require optimal filters to estimate processes with highest accuracy. The ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm presented in this paper is more robust in real world than the Kalman filter. It completely ignores the noise statistics and initial values while demonstrating better accuracy under the mismodeling and temporary uncertainties and lower sensitivity to errors in the noise statistics

General Unbiased FIR Filter With Applications to GPS-Based Steering of Oscillator Frequency

The general unbiased finite-impulse response (UFIR) filter proposed in this brief has important structural advantages against its basic predecessor. It can be applied to systems with or without the control input. We derive this filter in a batch form and then design its fast iterative Kalman-like algorithm using recursions. The iterative UFIR algorithm proposed is applied to the three-state polynomial model which is basic in clock synchronization. We test it by the global positioning system-based frequency steering of an oven-controlled crystal oscillator. Better robustness and higher accuracy of the UFIR filter against the Kalman filter are shown experimentally

Demonstration of a Transportable 1 Hz-Linewidth Laser

We present the setup and test of a transportable clock laser at 698 nm for a strontium lattice clock. A master-slave diode laser system is stabilized to a rigidly mounted optical reference cavity. The setup was transported by truck over 400 km from Braunschweig to D\"usseldorf, where the cavity-stabilized laser was compared to a stationary clock laser for the interrogation of ytterbium (578 nm). Only minor realignments were necessary after the transport. The lasers were compared by a Ti:Sapphire frequency comb used as a transfer oscillator. The thus generated virtual beat showed a combined linewidth below 1 Hz (at 1156 nm). The transport back to Braunschweig did not degrade the laser performance, as was shown by interrogating the strontium clock transition.Comment: 3 pages, 4 figure

Real-time optimal state estimation of multi-DOF industrial systems using FIR filtering

Date of publication August 17, 2016Industrial processes are often organized using mechanical systems with multiple degrees-of-freedom (DOF). For real-time operation of such systems in noise environments, fast, optimal, and robust estimators are required. In this paper, information gathering aboutmulti-DOF system states is provided using the optimal finite impulse response (OFIR) filter. To use this filter in real time, a fast iterative algorithm is developed with a pseudocode available for immediate use. Although the iterative algorithm utilizes Kalman recursions, it is more robust against uncertainties andmodel errors owing to the transversal structure.We use this algorithm to estimate state in the 1-DOF torsion system and the 3-DOF helicopter system.Shunyi Zhao, Yuriy S. Shmaliy, Choon Ki Ahn, and Peng Sh