Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

Mixture reduction algorithms for target tracking

Abstract: The paper is concerned with the development of practical filters for tracking a target when the origin of sensor measurements is uncertain. The full Bayesian solution to this problem gives rise to mixture distributions. From knowledge of the mixture distribution, in principle, an optimal estimate of the state vector for any criteria may be obtained. Also, if the problem is linear and Gaussian, the distribution becomes a Gaussian mixture in which each component probability density function is given by a Kalman filter. The author only considers this case. The methods presented are based on the premise that the number of mixture components should be minimized without modifying the 'structure' of the distribution beyond a specified limit. The techniques operate by merging similar components in such a way that the approximation preserves the mean and covariance of the original mixture. Also to allow the tracking filter to be implemented as a bank of Kalman filters, it is required that the approximated distribution is itself a Gaussian mixture.

The Kalman Filter for the Equalization of a Digital Communications Channel

Abstract: Consideration is given to the use of the discrete Kalman filter as an equalizer for digital binary transmission in the presence of noise and intersymbol interference. When the channel is modeled as an n -tap transversal filter, the Kalman filter assumes a similar form with "feed forward and feedback." It is shown how the Kalman filter can be used to estimate both the tap weights and the binary signal. Computer results on a fixed 6-tap channel show that use of the 6-tap Kalman filter yields a considerably smaller error probability than when a conventional transversal equalizer with 15 taps is used. Limited computer studies on the same channel, assumed to be initially unknown, suggest that the Kalman filter is capable of converging rapidly in the adaptive mode. Though these results are very encouraging, much work remains in the study and optimization of performance in the adaptive mode.

Applications of Kalman filters based on non-linear functions to numerical weather predictions

Abstract: . This paper investigates the use of non-linear functions in classical Kalman filter algorithms on the improvement of regional weather forecasts. The main aim is the implementation of non linear polynomial mappings in a usual linear Kalman filter in order to simulate better non linear problems in numerical weather prediction. In addition, the optimal order of the polynomials applied for such a filter is identified. This work is based on observations and corresponding numerical weather predictions of two meteorological parameters characterized by essential differences in their evolution in time, namely, air temperature and wind speed. It is shown that in both cases, a polynomial of low order is adequate for eliminating any systematic error, while higher order functions lead to instabilities in the filtered results having, at the same time, trivial contribution to the sensitivity of the filter. It is further demonstrated that the filter is independent of the time period and the geographic location of application.

The Accurate Continuous-Discrete Extended Kalman Filter for Radar Tracking

Abstract: This paper elaborates the Accurate Continuous-Discrete Extended Kalman Filter grounded in an ODE solver with global error control and its comparison to the Continuous-Discrete Cubature and Unscented Kalman Filters. All these state estimators are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. Our numerical results show that all the methods can be used for practical target tracking, but the Accurate Continuous-Discrete Extended Kalman Filter is more flexible and robust. It treats successfully (and without any manual tuning) the air traffic control scenario for various initial data and for a range of sampling times.