Michel Kieffer

Robust Autonomous Robot Localization Using Interval Analysis

This paper deals with the determination of the position and orientation of a mobile robot from distance measurements provided by a belt of onboard ultrasonic sensors. The environment is assumed to be two-dimensional, and a map of its landmarks is available to the robot. In this context, classical localization methods have three main limitations. First, each data point provided by a sensor must be associated with a given landmark. This data-association step turns out to be extremely complex and time-consuming, and its results can usually not be guaranteed. The second limitation is that these methods are based on linearization, which makes them inherently local. The third limitation is their lack of robustness to outliers due, e.g., to sensor malfunctions or outdated maps. By contrast, the method proposed here, based on interval analysis, bypasses the data-association step, handles the problem as nonlinear and in a global way and is (extraordinarily) robust to outliers.

Guaranteed nonlinear estimation using constraint propagation on sets

Bounded-error estimation is the estimation of the parameter or state vector of a model from experimental data, under the assumption that some suitably defined errors should belong to some prior feasible sets. When the model outputs are linear in the vector to be estimated, a number of methods are available to contain all estimates that are consistent with the data within simple sets such as ellipsoids, orthotopes or parallelotopes, thereby providing guaranteed set estimates. In the non-linear case, the situation is much less developed and there are very few methods that produce such guaranteed estimates. In this paper, the problem of characterizing the set of all state vectors that are consistent with all data in the case of non-linear discrete-time systems is cast into the more general framework of constraint satisfaction problems. The state vector at time k should be estimated either on-line from past measurement only or off-line from a series of measurements that may include measurements posterior to k . Even in the causal case, prior information on the future value of the state and output vectors, due for instance to physical constraints, is readily taken into account. Algorithms taken from the literature of interval constraint propagation are extended by replacing intervals by more general subsets of real vector spaces. This makes it possible to propose a new algorithm that contracts the feasible domain for each uncertain variable optimally (i.e. no smaller domain could be obtained) and efficiently.

Guaranteed Nonlinear State Estimator for Cooperative Systems

This paper is about state estimation for continuous-time nonlinear models, in a context where all uncertain variables can be bounded. More precisely, cooperative models are considered, i.e., models that satisfy some constraints on the signs of the entries of the Jacobian of their dynamic equation. In this context, interval observers and a guaranteed recursive state estimation algorithm are combined to enclose the state at any given instant of time in a subpaving. The approach is illustrated on the state estimation of a waste-water treatment process.

Guaranteed recursive nonlinear state estimation using interval analysis

The problem considered is state estimation in the presence of unknown state and measurement noise, each noise component being assumed to belong to some known interval. In such a bounded-error context, most available results are for linear models, and the purpose of the present paper is to deal with the nonlinear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first time that such a guaranteed estimator is made available. The precision of the set estimate can be improved, at the cost of more computation. The theoretical properties of the estimator are studied, and computer implementation has received special attention. A simple illustrative example is treated.

Oversampled filter banks as error correcting codes: theory and impulse noise correction

Oversampled filter banks (OFBs) provide an overcomplete representation of their input signal. This paper describes how OFBs can be considered as error-correcting codes acting on real or complex sequences, very much like classical binary convolutional codes act on binary sequences. The structured redundancy introduced by OFBs in subband signals can be used to increase robustness to noise. In this paper, we define the notions of code subspace, syndrome, and parity-check polynomial matrix for OFBs. Furthermore, we derive generic expressions for projection-based decoding, suitable for the case when a simple second-order model completely characterizes the noise incurred by subband signals. We also develop a nonlinear hypotheses-test based decoding algorithm for the case when the noise in subbands is constituted by a Gaussian background noise and impulsive errors (a model that adequately describes the action of both quantization noise and transmission errors). Simulation results show that the algorithm effectively removes the effect of impulsive errors occurring with a probability of 10/sup -3/.

Joint Source-Channel Coding Using Real BCH Codes for Robust Image Transmission

In this paper, a new still image coding scheme is presented. In contrast with standard tandem coding schemes, where the redundancy is introduced after source coding, it is introduced before source coding using real BCH codes. A joint channel model is first presented. The model corresponds to a memoryless mixture of Gaussian and Bernoulli-Gaussian noise. It may represent the source coder, the channel coder, the physical channel, and their corresponding decoder. Decoding algorithms are derived from this channel model and compared to a state-of-art real BCH decoding scheme. A further comparison with two reference tandem coding schemes and the proposed joint coding scheme for the robust transmission of still images has been presented. When the tandem scheme is not accurately tuned, the joint coding scheme outperforms the tandem scheme in all situations. Compared to a tandem scheme well tuned for a given channel situation, the joint coding scheme shows an increased robustness as the channel conditions worsen. The soft performance degradation observed when the channel worsens gives an additional advantage to the joint source-channel coding scheme for fading channels, since a reconstruction with moderate quality may be still possible, even if the channel is in a deep fade

Real-time Bounded-error State Estimation for Vehicle Tracking

Estimating the configuration of a vehicle is crucial for its navigation. Most approaches are based on (extended) Kalman filtering or particle filtering. An attractive alternative is considered here, which relies on interval analysis. Contrary to classical extended Kalman filtering it allows global localization, and contrary to particle filtering it provides guaranteed results in the sense that a set is computed that contains all of the configurations that are consistent with the data and hypotheses. This paper presents a real-time implementation of the process including a description of the platform and its modeling, the integration of the errors on the model and the localization method itself.

Robust MAC-lite and soft header recovery for packetized multimedia transmission

This paper presents an enhanced permeable layer mechanism useful for highly robust packetized multimedia transmission. Packet header recovery at various protocol layers using MAP estimation is the cornerstone of the proposed solution. The inherently available intra-layer and inter-layer header correlation proves to be very effective in selecting a reduced set of possible header configurations for further processing. The best candidate is then obtained through soft decoding of CRC protected data and CRC redundancy information itself. Simulation results for WiFi transmission using DBPSK modulated signals over AWGN channels show a substantial (4 to 12 dB) link budget improvement over classical hard decision procedures. We also introduce a sub-optimal and hardware realizable version of the proposed algorithm.

GUARANTEED NONLINEAR STATE ESTIMATION FOR CONTINUOUS-TIME DYNAMICAL MODELS FROM DISCRETE-TIME MEASUREMENTS

Abstract This paper is about bounded-error state estimation for models described by a continuous-time state equation from discrete-time measurements. A guaranteed solution to this problem is proposed, based on Mullers theorems and interval analysis. This technique allows, at any time instant, the characterization of the set of all state vectors that are consistent with the error bounds, measurements and model structure. Joint state and parameter estimation is also possible. The resulting methodology is illustrated on the estimation of the state of a compartmental model.

Guaranteed robust nonlinear estimation with application to robot localization

When reliable prior bounds on the acceptable errors between the data and corresponding model outputs are available, bounded-error estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, even when the model is nonlinear and the number of data points small. However, when the data may contain outliers, i.e., data points for which these bounds should be violated, this set may turn out to be empty, or at least unrealistically small. The outlier minimal number estimator (OMNE) has been designed to deal with such a situation, by minimizing the number of data points considered as outliers. OMNE has been shown in previous papers to be remarkably robust, even to a majority of outliers. Up to now, it was implemented by random scanning, so its results could not be guaranteed. In this paper, a new algorithm based on set inversion via interval analysis provides a guaranteed OMNE, which is applied to the initial localization of an actual robot in a partially known two-dimensional (2-D) environment. The difficult problems of associating range data to landmarks of the environment and of detecting potential outliers are solved as byproducts of the procedure.