# J.K. Uhlmann's research while affiliated with University of Missouri and other places

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## Publications (20)

In this paper we consider the use of Covariance Union (CU) with multi-hypothesis techniques (MHT) and Gaussian Mixture Models (GMMs) to generalize the conventional mean and covariance representation of information. More specifically, we address the representation of multimodal information using multiple mean and covariance estimates. A significant...

In this paper we consider the use of Covariance Union (CU) with multi-hypothesis techniques (MHT) and Gaussian mixture models (GMMs) to generalize the conventional mean and covariance representation of information. More specifically, we address the representation of multi-modal information using multiple mean and covariance estimates. A significant...

In this paper we consider the problem of estimating the state of a dynamic system from a sequence of observations that are imprecisely timestamped. We argue that this problem can be addressed using the covariance union (CU) technique, and we demonstrate its application in a particular example.

The state of the art in unscented techniques for nonlinear estimation is surveyed. The process noise covariance matrix used on each filter is not the same as the process noise used to drive the motion of the true projectile in the simulation. All the Jacobian matrices for the extended Kalman filter (EKF) are calculated numerically using a central d...

This paper analyses the properties of the full covariance simultaneous map building problem (SLAM). We prove that, for the special case of a stationary vehicle (with no process noise) which uses a range-bearing sensor and has non-zero angular uncertainty, the fullcovariance SLAM algorithm always yields an inconsistent map. We also show, through sim...

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficul...

Many landmark-based navigation systems suffer from the problem of assignment ambiguity: the navigation system receives a measurement from a landmark, but the identity of the landmark is not uniquely known. This uncertainty is frequently addressed by attempting to identify the landmark which caused the measurements. Two common approaches are the nea...

Simultaneous localisation and map building (SLAM) is one of the most important and challenging areas of mobile robotics. Unfortunately, the optimal Kalman filter solution incurs computational costs that scale quadratically with the number of beacons, which is prohibitive for many real time and large scale applications. Consequently, there is a sign...

A novel image interpolation method for resolution enhancement of still images is proposed. The approach consists of a nonlinear mapping from pixel index space to color space based on the low-resolution image so that nonintegral pixel indices in a super-sampling can be mapped to colors, i.e., interpolated. This nonlinear mapping is based on an exten...

The Unscented Transform (UT) approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher moments, as the given estimate. The given nonlinear...

Measurement and track fusion in decentralised sensor network architectures is investigated. The investigation employs FLAMES<sup>TM</sup>, an advanced military scenario generator. This was specifically customised for distributed data fusion experiments and involves a model of the delays in a realistic communication system. Here the delays were used...

This paper describes a new approach for generalizing the Kalman
filter to nonlinear systems. A set of samples are used to parametrize
the mean and covariance of a (not necessarily Gaussian) probability
distribution. The method yields a filter that is more accurate than an
extended Kalman filter (EKF) and easier to implement than an EKF or a
Gauss s...

This paper examines the problem of automatically constructing a
map of an unknown environment from a vehicle whose location is also
unknown. The application of the Kalman filter to this problem is briefly
described and the practical limitation of the filter in this context is
discussed. A suboptimal algorithm, the relative filter, is introduced
tha...

In this paper we describe a new recursive linear estimator for
filtering systems with nonlinear process and observation models. This
method uses a new parameterisation of the mean and covariance which can
be transformed directly by the system equations to give predictions of
the transformed mean and covariance. We show that this technique is more
a...

This article describes a method of implementation linearised
approximations to nonlinear systems that does not require the direct
derivation of Jacobian matrices. The approach is simpler to implement
than current techniques used with extended Kalman filters and other
linearised estimation and control algorithms

## Citations

... In this study, a deterministic sampling method using sigma points based on the unscented transform [9][10][11][12], generally used in the field of uncertainty quantification, was applied to the nuclear data adjustment method using covariance matrices (i.e. MOCABA). ...

... Definition 1 (conservative). An estimate pair (x, Px) regarding the real state x, is conservative [33]- [36] when ...

... With the Unscented Kalman Filter (UKF) see [6] and [7], a small number of points selected about the perimeter of the error basket (a region about the mean defined by one-sigma covariance) are propagated Δt using the plant dynamics. These propagated points are used to construct the propagated mean and covariance. ...

... represent a state-space model with unknown states (i.e., model parameters and FIMs herein). An Unscented Kalman Filtering (UKF) [27] method is used to estimate the unknown states. The estimation process is iterative at each estimation window. ...

... l Add a small disturbance to the noise-free sub-dynamics to make the noise covariance positive definite (See Example 2 about the velocity ). This strategy has been commonly used in the traditional state estimation methods, see e.g., [16] and [55]. Note that the first strategy helps decrease the state space dimensionality, which is preferable than the other two strategies in reducing computation burden. ...

... Given a dataset with GM distribution, GM parameters may be learned from data using expectation-maximization (EM) algorithm, and Bayesian information criterion (BIC) and Akaike information criterion (AIC) may be used for choosing the number of modes [16]. Given the GM parameters, several algorithms have been proposed to reduce the number of modes, ranging from adhoc measure-based clustering [17,18] and covariance union [19] to clustering using KL divergence-based measures [20]. This paper addresses the more difficult problem of GM mode selection in the dynamic (spatial/temporal) as opposed to static (spatial-only) context. ...

... In our case d 2 = x i − x j 2 and R 2 is a user defined positive constant. This function is similar to the extensor function for interpolation [14]. Equations in (1) constitute a linear system of equations and the constraint in (2) ensures that the system of equations has a unique solution. ...

... In particular, this lag is different for GNSS and UWB measurements because sampling rates are different and clocks are independent. Consequently, an unknown time-offset exists between the GNSS observables' timestamps and the UWB measurements' timestamps which models the relative misalignment between the GNSS and UWB time-scales as well the shift of these scales with respect to the integration filter time-scale [15], [16]. If neglected, this time-offset can inject an inconsistency bias inside the hybridisation filter which may jeopardise state-estimation accuracy [17], [18]. ...

... ω =ω ρ(1) 11. end if 12. Calculate (u, U) using ω and (3)-(6) can handle inconsistent sensor data fusion [26]; 3) the CU algorithm proposed by Julier (JCU) [20], and 4) CI [15]. ...

... The authors in [26] proposed a covariance intersection filter [27] to handle the inter-estimate correlation issue. Similar work can also be found in [28,29], which exploits the advantage of estimation. However, as mentioned above, the computational complexity becomes an issue when the number of vehicles increases. ...