https://folk.ntnu.no/bjarnean/pubs/journals/journal-51.pdf

Constrained nonlinear state estimation based on the UKF approach

This paper develops a square root unscented Kalman filter (SRUKF) for performing video-rate visual simultaneous localization and mapping (SLAM) using a single camera. The conventional UKF has been proposed previously for SLAM, improving the handling of nonlinearities compared with the more widely used extended Kalman filter (EKF). However, no account was taken of the comparative complexity of the algorithms: In SLAM, the UKF scales as O(N 3) in the state length, compared to the EKF's O(N 2), making it unsuitable for video-rate applications with other than unrealistically few scene points. Here, it is shown that the SRUKF provides the same results as the UKF to within machine accuracy and that it can be reposed with complexity O(N 2) for state estimation in visual SLAM. This paper presents results from video-rate experiments on live imagery. Trials using synthesized data show that the consistency of the SRUKF is routinely better than that of the EKF, but that its overall cost settles at an order of magnitude greater than the EKF for large scenes.

/pdf/an-o-n-square-root-unscented-kalman-filter-for-visual-55v8ac7l4j.pdf

An O(N²) Square Root Unscented Kalman Filter for Visual Simultaneous Localization and Mapping

To solve the radar target tracking problem with range rate measurements, in which the errors between range and range rate measurements are correlated, a sequential unscented Kalman filter (SUKF) is proposed in this paper. A pseudo measurement is constructed by block-partitioned Cholesky factorization first, this can keep the range, bearing and elevation (or two direction cosine) measurements unchanged, while the errors between the original range and range rate measurement are decorrelated; then based on the UKF, the bearing, elevation (or two direction cosine) and the pseudo measurement are sequentially processed to enhance the filtering precision and the computational efficiency simultaneously. Validity and consistency of the new proposed algorithm is verified by Monte-Carlo simulation.

Sequential unscented Kalman filter for radar target tracking with range rate measurements

The aim of the radar systems is to collect information about their surroundings. In many scenarios besides static targets there are numerous moving objects with very different characteristics, such as extent, movement behavior or micro-Doppler spread. It would be most desirable to have algorithms that extract all information on static and moving object automatically, without a system operator. In this paper, we present measurements conducted with a commercially available high-resolution multi-channel linear frequency-modulated continuous-wave radar and algorithms that do not only produce radar images but a description of the scenario on a higher level. After conventional spectrum estimation and thresholding, we present a clustering stage that combines individual detections and generates representations of each target individually. This stage is followed by a Kalman filter based multi-target tracking block. The tracker allows us to follow each target and collect its properties over time. With this method of jointly estimating tracks and characteristics of each individual target in a scenario, inputs for classifiers can be generated. Which, in turn, will be able to generate information that could be used for driver assistance or alarm trigger systems.

Radar Signal Processing for Jointly Estimating Tracks and Micro-Doppler Signatures

The work presented in this paper makes two contributions for exploiting Doppler (range rate) measurements in tracking systems. First, a new linear filter, the converted Doppler measurement Kalman filter (CDMKF), is presented to extract nonlinear pseudostates from converted Doppler measurements (i.e., the product of the range measurements and Doppler measurements). The pseudostates are constructed from the converted Doppler and its derivatives. The linearly evolving equations of the pseudostates are derived for common target motion models. The second contribution of this paper is using the CDMKF along with the converted position measurement Kalman filter (CPMKF), in which only the position measurements are used, to establish a new filtering structure, statically fused converted measurement Kalman filters (SF-CMKF). The resulting states of CPMKF and CDMKF are combined by a static minimum mean squared error (MMSE) estimator, where the nonlinearity and correlation between the pseudostates and the Cartesian states are handled simultaneously, to yield the final state estimates. The dynamic nonlinear estimation problem is converted into dynamic linear estimation followed by static nonlinear fusion. The estimation accuracy can be enhanced by incorporating the Doppler measurements via the linear CDMKF, while the filtering stability can be improved by dealing with nonlinearity outside the filtering recursions. Monte Carlo simulations and comparison with the posterior Cramer-Rao bound demonstrate the effectiveness of the CDMKF and SF-CMKF.

Statically Fused Converted Position and Doppler Measurement Kalman Filters

Radar range rate measurements are not always used in target tracking filters because they are highly nonlinear in Cartesian space. A linear approxi- mation of range rate composed of its partial derivatives with respect to the track state vector is sometimes used in the measurement equation of an Extended Kalman filter. Unfortunately, this naive linearization can de- grade the filter's position estimates. The origins of this phenomenon are investigated and found to lie in the functional relationship induced by the linearization between the position elements of the track state vec- tor and the range rate innovation. An alternative lin- earization of range rate that is not a function of the position elements is derived. It is shown that the new linearization improves position estimate for some tra- jectories. An ordinary Kalman filter's gains are com- pared to those of the usual and alternative extended Kalman filters analytically and via simulation. The results show that the alternative linearization leads to a filter having the same position gains as an ordinary Kalman filter, and an additional gain on the track's radial velocity. This new extended Kalman filter can improve a tracking system's velocity estimates without risk to its position estimates.

/pdf/the-over-extended-kalman-filter-don-t-use-it-6g0xxzpbi7.pdf

D.F. Bizup

Papers

The over-extended Kalman filter - don't use it!