Falls are a major health problem with one in three people over the age of 65 falling each year, oftentimes causing hip fractures, disability, reduced mobility, hospitalization and death. A major limitation in fall detection algorithm development is an absence of real-world falls data. Fall detection algorithms are typically trained on simulated fall data that contain a well-balanced number of examples of falls and activities of daily living. However, real-world falls occur infrequently, making them difficult to capture and causing severe data imbalance. People with multiple sclerosis (MS) fall frequently, and their risk of falling increases with disease progression. Because of their high fall incidence, people with MS provide an ideal model for studying falls. This paper describes the development of a context-aware fall detection system based on inertial sensors and time of flight sensors that is robust to imbalance, which is trained and evaluated on real-world falls in people with MS. The algorithm uses an auto-encoder that detects fall candidates using reconstruction error of accelerometer signals followed by a hyper-ensemble of balanced random forests trained using both acceleration and movement features. On a clinical dataset obtained from 25 people with MS monitored over eight weeks during free-living conditions, 54 falls were observed and our system achieved a sensitivity of 92.14%, and false-positive rate of 0.65 false alarms per day.

indoor tracking system that uses received signal strength (RSS) from radio frequency (RF) transceivers to estimate the location of a person. While many RSS-based tracking systems use a body-worn device or tag, this approach requires no such tag. The approach is based on the key principle that RF signals between wall-mounted transceivers reflect and absorb differently depending on a person's movement within their home. A hierarchical neural network hidden Markov model (NN-HMM) classifier estimates both movement patterns and stand vs. walk conditions to perform tracking accurately. The algorithm and features used are specifically robust to changes in RSS mean shifts in the environment over time allowing for greater than 90% region level classification accuracy over an extended testing period. In addition to tracking, the system also estimates the number of people in different regions. It is currently being developed to support independent living and long-term monitoring of seniors.

Methods for indoor tracking typically require a person to carry some type of a body worn tag. A novel tag-free solution is presented that utilizes low cost wall-mounted ultrasonic transducers. The active ultrasonic transducers capture analog echoes, which are then digitized and analyzed in order to calculate the 1-D range of the moving person. The tracking algorithm utilizes a number of signal processing techniques including band-pass filtering, Hilbert transformation, and background subtraction to remove interference from other objects in the room. The range data from multiple sensors are treated as observations in a Bayesian framework using the sigma-point Kalman smoother (SPKS) to determine a person's 2-D position and velocity. The SPKS also performs “self-calibration” or simultaneous localization and mapping (SLAM) to determine the location of the wall-mounted transducers. The indoor tracking accuracy of the tag-free system is better than 0.5 meters.

A new formulation for nonlinear smoothing is derived using forward-backward sigma-point Kalman filtering (SPKF). The forward filter uses the standard SPKF. The backward filter requires the use of the inverse dynamics of the forward filter. While smoothers based on the extended Kalman filter (EKF) simply invert the linearized dynamics, with the SPKF the forward nonlinear dynamics are never analytically linearized. Thus the backward nonlinear dynamics are not well defined. In previous work, a sigma-point Kalman smoother (SPKS) was derived by learning a nonlinear model of the backward dynamics from empirical data. In this paper, we make use of the relationship between the SPKF and weighted statistical linear regression (WSLR). The resulting pseudo-linearized dynamics obtained by WSLR is more accurate in the statistical sense than using a first order truncated Taylor series expansion as with the EKF. A new backward information filter can then be derived, which is combined with the forward SPKF to form the smoothed estimates.

In this paper, we address a method for terrain aided navigation of unmanned vehicles in unknown environments. The task is to simultaneously estimate the state of the vehicle (position and attitude) and a map of the surrounding environment given limited sensing capabilities. Possible available sensors include an on-board inertial measurement unit (IMU) and other simple "terrain sensors" such as altitude, temperature, or vision based features. Explicit positioning sensors such as GPS or a prior land map are not available. This problem is widely known as simultaneous localization and mapping (SLAM). A dual Kalman filter framework is proposed that works by alternating between using one Kalman filter to localize the vehicle given the current estimated map, and a second Kalman filter to update the estimate of the map given the position of the vehicle. Simulation results are generated for a two dimensional environment comparing the extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) based implementations. It is shown that the SPKF based approach converges faster and also to a lower mean square error (MSE) than that of the EKF counterpart.

For sequential probabilistic inference in nonlinear non-Gaussian systems, approximate solutions must be used. We present a novel recursive Bayesian estimation algorithm that combines an importance sampling based measurement update step with a bank of sigma-point Kalman filters for the time-update and proposal distribution generation. The posterior state density is represented by a Gaussian mixture model that is recovered from the weighted particle set of the measurement update step by means of a weighted EM algorithm. This step replaces the resampling stage needed by most particle filters and mitigates the "sample depletion" problem. We show that this new approach has an improved estimation performance and reduced computational complexity compared to other related algorithms.

Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented fil(cid:173) ters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms stan(cid:173) dard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.

Noise reduction for speech signals has applications ranging from speech enhancement for cellular communications, to front ends for speech recognition systems. A neural network based time-domain method called dual extended Kalman filtering (dual EKF) is presented for removing nonstationary and colored noise from speech. This paper describes the algorithm and provides a set of experimental results.

The Filtered-x LMS algorithm is currently the most popular method for adapting a filter when there exists a transfer function in the error path. Such instances arise, for example, in active control of sound and vibration. For multiple-input-multiple-output systems the Multiple Error LMS Algorithm is a generalization of Filtered-x LMS. The derivation of both algorithms rely on several assumptions, including linearity of the adaptive filter and error channel. Furthermore, in the Multiple Error LMS Algorithm the desirable order N computational complexity of LMS is lost, resulting in a prohibitive cost in certain DSP implementations. In this paper, we describe a new algorithm termed adjoint LMS which provides a simple alternative to the previously mentioned algorithms. In adjoint LMS, the error (rather than the input) is filtered through an adjoint filter of the error channel. Performance regarding convergence and misadjustment are equivalent. However, linearity is not assumed in the derivation of the algorithm. Furthermore, equations for single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) are identical and both remain order N.

Deriving gradient algorithms for time-dependent neural network structures typically requires numerous chain rule expansions, diligent bookkeeping, and careful manipulation of terms. In this paper, we show how to derive such algorithms via a set of simple block diagram manipulation rules. The approach provides a common framework to derive popular algorithms including backpropagation and backpropagation-through-time without a single chain rule expansion. Additional examples are provided for a variety of complicated architectures to illustrate both the generality and the simplicity of the approach.

Finite impulse response (FIR) Wiener-like filters are applied to time trajectories of the cubic-root compressed short-term power spectrum of noisy speech recorded over cellular telephone communications. Informal listenings indicate that the technique brings a noticeable improvement to the quality of processed noisy speech while not causing any significant degradation to clean speech. Alternative filter structures are being investigated as well as other potential applications in cellular channel compensation and narrowband to wideband speech mapping.

A new technique is presented which improves the subjective quality of band-limited speech. The approach is based on a linear model of speech production, in which we independently estimate the spectral envelope and excitation function for a broad-bandwidth speech signal to reconstruct missing frequency components in narrow-bandwidth speech.

We show that signal flow graph theory provides a simple way to relate two popular algorithms used for adapting dynamic neural networks, real-time backpropagation and backpropagation-through-time. Starting with the flow graph for real-time backpropagation, we use a simple transposition to produce a second graph. The new graph is shown to be interreciprocal with the original and to correspond to the backpropagation-through-time algorithm. Interreciprocity provides a theoretical argument to verify that both flow graphs implement the same overall weight update.

The traditional feedforward neural network is a static structure which simply maps input to output. To better reflect the dynamics in a biological system, a network structure which models each synapse by a finite-impulse response (FIR) linear filter is proposed. An efficient-gradient descent algorithm which is shown to be a temporal generalization of the familiar backpropagation algorithm is derived. By modeling each synapse as a linear filter, the neural network as a whole may be thought of as an adaptive system with its own internal dynamics. Equivalently, one may think of the network as a complex nonlinear filter. Applications should thus include areas of pattern recognition where there is an inherent temporal quality to the data, such as in speech recognition. The networks should also find a natural use in areas of nonlinear control, and other adaptive signal processing and filtering applications such as noise cancellation or equalization

The relationship between minimizing a mean squared error and finding the optimal Bayesian classifier is reviewed. This provides a theoretical interpretation for the process by which neural networks are used in classification. A number of confidence measures are proposed to evaluate the performance of the neural network classifier within a statistical framework.