Evaluation of linear Kalman filter processing geodetic kinematic measurements

Bogatin, Sonja; Foppe, Karl; Wasmeier, Peter; Wunderlich, Thomas; Schäfer, Thomas; Kogoj, Dušan

doi:10.1016/j.measurement.2007.03.003

Cited by 13 publications

(11 citation statements)

References 3 publications

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“…The state-transition matrix for position-velocity-acceleration components of the aircraft can be derived with the assumption that the kinematic acceleration is Gaussian white noise process [6,11,14]:

{boldnormal Φ}_{j_p v a} = [\begin{matrix} 1 & Δ t & \frac{{(Δ t)}^{2}}{2} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & Δ t & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & Δ t & \frac{{(Δ t)}^{2}}{2} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & Δ t & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & Δ t & \frac{{(Δ t)}^{2}}{2} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & Δ t \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}]

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Medium to Long Range Kinematic GPS Positioning with Position-Velocity-Acceleration Model Using Multiple Reference Stations

Hong

Park

Han

et al. 2015

Sensors

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In order to obtain precise kinematic global positioning systems (GPS) in medium to large scale networks, the atmospheric effects from tropospheric and ionospheric delays need to be properly modeled and estimated. It is also preferable to use multiple reference stations to improve the reliability of the solutions. In this study, GPS kinematic positioning algorithms are developed for the medium to large-scale network based on the position-velocity-acceleration model. Hence, the algorithm can perform even in cases where the near-constant velocity assumption does not hold. In addition, the estimated kinematic accelerations can be used for the airborne gravimetry. The proposed algorithms are implemented using Kalman filter and are applied to the in situ airborne GPS data. The performance of the proposed algorithms is validated by analyzing and comparing the results with those from reference values. The results show that reliable and comparable solutions in both position and kinematic acceleration levels can be obtained using the proposed algorithms.

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{boldnormal Φ}_{j_p v a} = [\begin{matrix} 1 & Δ t & \frac{{(Δ t)}^{2}}{2} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & Δ t & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & Δ t & \frac{{(Δ t)}^{2}}{2} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & Δ t & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & Δ t & \frac{{(Δ t)}^{2}}{2} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & Δ t \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}]

…”

Section: Methodsmentioning

confidence: 99%

“…An efficient PVA model for Kalman filter is proposed and demonstrated using the measurements from the electronic tacheometer, i.e. , geodetic kinematic measurements [11]. However, it should be noted that the experiments are conducted in an indoor environment, and the measurement used in the experiments are not from the GPS.…”

Section: Introductionmentioning

confidence: 99%

Medium to Long Range Kinematic GPS Positioning with Position-Velocity-Acceleration Model Using Multiple Reference Stations

Hong

Park

Han

et al. 2015

Sensors

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“…Therefore, we introduce a factor, c, that scales the predicted process state parameters. After testing different values, we set it to 0.2, which is verified by the indicators of inner confidence (Bogatin et al 2008) and which corresponds to the estimate of the RP accuracy by Hirn et al (2009).…”

Section: Kalman Filter Set-upmentioning

confidence: 99%

Thermal monitoring of volcanic effusive activity: the uncertainties and outlier detection

Zakšek

Pick

Shirzaei

et al. 2015

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Thermal observations of volcanic activity when the volcano is partially covered by clouds or observed under a wide-scan angle are often removed from further analyses. In the event of a volcanic crisis, such a reduced set of data is not adequate. Even when the observation conditions are favourable, the full observation set is still required to provide decision-makers with quality information about the data. Automatic quality estimation and outlier detection was not estimated in the past. We propose to analytically define the uncertainty for individual observations based on the measurement circumstances. To additionally reduce the temporal noise of the radiant power (RP) time series we apply a Kalman Filter (KF). The KF is able to recursively analyse an unevenly sampled time series. Based on some proposed rules, it can also detect outliers. We apply the proposed methodology to the 2008-09 Etna eruption monitored by MODIS (Moderate Resolution Imaging Spectroradiometer). The analysis of the results shows that the topography has a greater influence on RP than previously considered.

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“…Investigators have presented several Kalman filter related applications in the fields of navigation, such as GPS receiver position and velocity determination [8], inertial navigation alignment [9], attitude determination [10,11], and integrated navigation system design [12,13]. Shmaliy et al [8] proposed a thinning algorithm for real-time unbiased finite impulse response (FIR) estimation of the local clock time interval error (TIE) model, and compared to that of three state Kalman filter, in terms of the Allan deviation and precision time protocol deviation.…”

Section: Introductionmentioning

confidence: 99%

“…Zhu et al [11] investigated the linear fusion algorithm for attitude determination using low-cost MEMS-based sensors. Bogatin et al [12] assessed the efficiency of the linear Kalman filter as a method for the estimation of kinematic process observed with electronic tacheometer. In their contribution, the efficiency of the three-dimensional linear Kalman filter model, in combination with the law on transfer of variances and covariances, is controlled using a known reference trajectory and statistical tests.…”

Section: Introductionmentioning

confidence: 99%

Critical remarks on the linearised and extended Kalman filters with geodetic navigation examples

Jwo

Cho

2010

Measurement

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Evaluation of linear Kalman filter processing geodetic kinematic measurements

Cited by 13 publications

References 3 publications

Medium to Long Range Kinematic GPS Positioning with Position-Velocity-Acceleration Model Using Multiple Reference Stations

Medium to Long Range Kinematic GPS Positioning with Position-Velocity-Acceleration Model Using Multiple Reference Stations

Thermal monitoring of volcanic effusive activity: the uncertainties and outlier detection

Critical remarks on the linearised and extended Kalman filters with geodetic navigation examples

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