Tohid Ardeshiri

Robust Inference for State-Space Models with Skewed Measurement Noise

Filtering and smoothing algorithms for linear discrete- time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew- t-distributed measurement noise. The proposed filter and smoother are compared with conventional low- complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

Convex Optimization Approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints

The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new ...

Maximum entropy properties of discrete-time first-order stable spline kernel

The first order stable spline (SS-1) kernel (also known as the tuned-correlated (TC) kernel) is used extensively in regularized system identification, where the impulse response is modeled as a zero-mean Gaussian process whose covariance function is given by well designed and tuned kernels. In this paper, we discuss the maximum entropy properties of this kernel. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling assumption, we also derive the special structure of the SS-1 kernel (e.g. its tridiagonal inverse and factorization have closed form expression), also giving to it a maximum entropy covariance completion interpretation.

Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.

Greedy Reduction Algorithms for Mixtures of Exponential Family

In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.

A NLOS-robust TOA positioning filter based on a skew-t measurement noise model

A skew-t variational Bayes filter (STVBF) is applied to indoor positioning with time-of-arrival (TOA) based distance measurements and pedestrian dead reckoning (PDR). The proposed filter accommodates large positive outliers caused by occasional non-line-of-sight (NLOS) conditions by using a skew-t model of measurement errors. Real-data tests using the fusion of inertial sensors based PDR and ultra-wideband based TOA ranging show that the STVBF clearly outperforms the extended Kalman filter (EKF) in positioning accuracy with the computational complexity about three times that of the EKF.

Efficient bridging-based destination inference in object tracking

This paper proposes a probabilistic intent inference approach that is significantly more computationally efficient than other existing bridging-distributions-based predictors. It sequentially determines the probabilities of all possible destinations of a tracked object, whose motion is modelled by a Markov chain with the distribution of its terminal state equal to that of a nominal endpoint. This encapsulates the long term dependencies in the object trajectory as dictated by intent. Simulations using real data show that the notable reductions in computations achieved by the introduced bridging-based predictor does not impact the quality of the overall inference results.

Modelling received signal strength from on-vehicle BLE beacons using skewed distributions: A preliminary study

This paper describes a study on modelling the Received Signal Strength Indicator (RSSI) measured by the smartphone of a vehicle user. The present transmissions are emitted by dedicated radio frequency sources, such as Bluetooth Low Energy (BLE) beacons, mounted to the vehicle to determine the driver/passenger(s) proximity or relative position(s). Based on empirical data, a model of the measurements noise, which utilises skewed distributions, is proposed to capture inconsistencies in reception and the impact of occlusions on the RSSI profile in an automotive setting, for example occlusions in car parks. Experimental data is used to demonstrate the suitability of the introduced model.

Convergence results for tractable inference in α-stable stochastic processes

The α-stable distribution is highly intractable for inference because of the lack of a closed form density function in the general case. However, it is well-established that the α-stable distribution admits a Poisson series representation (PSR) in which the terms of the series are a function of the arrival times of a unit rate Poisson process. In our previous work, we have shown how to carry out inference for regression models using this series representation, which leads to a very convenient conditionally Gaussian framework, amenable to tractable Gaussian inference procedures. The PSR has to be truncated to a finite number of terms for practical purposes. The residual error terms have been approximated in our previous work by a Gaussian distribution, and we have recently shown that this approximation can be justified through a Central Limit Theorem (CLT). In this paper we present a new and exact characterisation of the first and second moments of the residual series over finite time intervals for the unit rate Poisson process, correcting a previous version that was only true in the infinite time limit. This enables us to test through simulation the rapid convergence of the residual terms to a Gaussian distribution of the Poisson series residual. We test this convergence using both Q-Q plots and the classical Kolmogorov-Smirnov test of Gaussianity.

State Estimation for a Class of Piecewise Affine State-Space Models

We propose a filter for piecewise affine state-space models. In each filtering recursion, the true filtering posterior distribution is a mixture of truncated normal distributions. The proposed filter approximates the mixture with a single normal distribution via moment matching. The proposed algorithm is compared with the extended Kalman filter (EKF) in a numerical simulation, where the proposed method obtains, on average, better root mean square error than the EKF.