Urban Forssell

Particle filters for positioning, navigation, and tracking

A framework for positioning, navigation, and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low dimensional. This is of utmost importance for high-performance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter-based algorithms. Here, the use of nonlinear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircrafts elevation profile to a digital elevation map and a cars horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable with satellite navigation (as GPS) but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

A projection method for closed-loop identification

A new method for closed-loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed. Just as the direct method, this new method is applicable to systems with arbitrary feedback mechanisms. This is in contrast to other methods, such as the indirect method and the two-stage method, that assume linear feedback. The finite sample behavior of the proposed method is illustrated in a simulation study.

Identification of unstable systems using output error and Box-Jenkins model structures

It is well known that the output error and Box-Jenkins model structures cannot be used for prediction error identification of unstable systems. The reason for this is that the predictors in this case generically will be unstable. Typically, this problem is handled by projecting the parameter vector onto the region of stability, which gives erroneous results when the underlying system is unstable. The main contribution of this work is that we derive modified, but asymptotically equivalent, versions of these model structures that can also be applied in the case of unstable systems.

Virtual Sensors of Tire Pressure and Road Friction

The idea of a virtual sensor is to extract information of parameters that cannot be measured directly, or at least would require very costly sensors, by only using available information. Virtual se ...

Sensor Fusion for Accurate Computation of Yaw Rate and Absolute Velocity

In the presented sensor fusion approach, centralized filtering of related sensor signals is used to improve and correct low price sensor measurements. From this, we compute high-quality state information as drift-free yaw rate and exact velocity (accounting for unknown tire radius and slipping wheels on 4WD vehicles). The basic tool here is a Kalman filter supported by change detection for sensor diagnosis. Results and experience of real-time implementations are presented.

An alternative motivation for the indirect approach to closed-loop identification

Direct prediction error identification of systems operating in closed loop may lead to biased results due to the correlation between the input and the output noise. The authors study this error, what factors affect it, and how it may be avoided. In particular, the role of the noise model is discussed and the authors show how the noise model should be parameterized to avoid the bias. Apart from giving important insights into the properties of the direct method, this provides a nonstandard motivation for the indirect method.

Identification for control: some results on optimal experiment design

The problem of designing identification experiments to make them maximally informative with respect to the intended use of the model is studied. Focus is on model based control and we show how to choose the feedback regulator and the spectrum of the reference signal in case of closed-loop experiments. A main result is that when only the misfit in the dynamics model is penalized and when both the input and the output power are constrained then the optimal controller is given by the solution to a standard LQ problem. When only the input power is constrained, it is shown that open-loop experiments are optimal. Some examples are also given to exemplify the theoretical results.

Maximum likelihood estimation of models with unstable dynamics and nonminimum phase noise zeros

Abstract Maximum likelihood estimation of single-input single-output linear time-invariant dynamic models requires that the model innovation (the nonmeasurable white noise source that is assumed to be the source of the randomness of the system) can be computed from the observed data. For many model structures, the prediction error and the model innovation coincide and the prediction error can be used in maximum likelihood estimation. However, when the model dynamics and the noise model have unstable poles which are not shared or when the noise dynamics have unstable zeros this is not the case. One such example is an unstable output error model. In this contribution we show that in this situation the model innovation can be computed by noncausal filtering. Different implementations of the model innovation filter are also studied.

Variance results for closed-loop identification methods

We study the statistical properties of a number of closed-loop identification methods and parameterizations. The focus is on asymptotic variance expressions for these methods and by studying the asymptotic variance for the parameter vector estimates we show that indirect methods fail to give better accuracy than the direct method.

Time-domain identification of dynamic errors-in-variables systems using periodic excitation signals

The use of periodic excitation signals in identification experiments is advocated. With periodic excitation it is possible to separate the driving signals and the disturbances, which for instance implies that the noise properties can be independently estimated. In the paper a non-parametric noise model, estimated directly from the measured data, is used in a compensation strategy applicable to both least squares and total least squares estimation. The resulting least squares and total least squares methods are applicable in the errors-in-variables situation and give consistent estimates regardless of the noise. The feasibility of the idea is illustrated in a simulation study.