A Survey of Code Optimization Methods for Kalman Filter Extensions <s> Pedestrian Dead Reckoning <s> The Huge Microphone Array project began in February 1994 to design, construct, debug, and test a real-time 512-microphone array system and to develop algorithms for it. Analysis of known algorithms indicated that signal-processing performance of over 6 Gflops would be required, while the need for portability-fitting it into a small van-also set an upper limit to the power required. These trade-offs and many others have led to a unique design in both hardware and software. This two-part article presents the full design and its justifications. The authors also discuss performance for a few important algorithms relative to the use of processing capability, response latency, and difficulty of programming. <s> BIB001 </s> A Survey of Code Optimization Methods for Kalman Filter Extensions <s> Pedestrian Dead Reckoning <s> A system for three-dimensional passive acoustic speaker localization and tracking using a microphone array is presented and evaluated. Initial speaker position estimates are provided by a time-delay-based localization algorithm. These raw estimates are spatially smoothed by a multiple model adaptive estimator consisting of three extended Kalman filters running in parallel. The performance of the proposed system is evaluated for real data in a common office environment. The reference trajectory of the moving speaker is delivered by visually tracking a color marker on the speaker's forehead by a stereo-camera system. The proposed acoustic source tracker shows robustness and accuracy in a variety of different scenarios. <s> BIB002 </s> A Survey of Code Optimization Methods for Kalman Filter Extensions <s> Pedestrian Dead Reckoning <s> Traditionally, time difference of arrival (TDOA) based acoustic source tracking consists of two stages, more precisely, estimation of TDOAs followed by a tracking algorithm. In general, these two stages are performed separately and presume that (1) TDOAs can be estimated reliably; and (2) the errors in detection behave in a well-defined fashion. The presence of noise and reverberation, however, leads to multimodal TDOA distributions and causes larger errors in the estimates, which ultimately lowers the tracking performance. To counteract this effect, we propose an approach that enhances TDOA estimation by (1) accounting for the multimodal aspect through a Gaussian mixture model and (2) integrating knowledge that has been obtained in the tracking stage. In doing so, this approach tightly couples the two stages. Experimental results on the AV16.3 corpus show that the proposed approach significantly improves the tracking performance compared to various other tracking algorithms. <s> BIB003 </s> A Survey of Code Optimization Methods for Kalman Filter Extensions <s> Pedestrian Dead Reckoning <s> We present a real-time particle filter for 2D and 3D hybrid indoor positioning. It uses wireless local area network (WLAN) based position measurements, step and turn detection from a hand-held inertial sensor unit, floor plan restrictions, altitude change measurements from barometer and possibly other measurements such as occasional GNSS fixes. We also present a particle smoother, which uses future measurements to improve the position estimate for non-real-time applications. A light-weight fallback filter is run in the background for initialization, divergence monitoring and possibly re-initialization. In real-data tests the particle filter is more accurate and consistent than the methods that do not use floor plans. An example is shown on how smoothing helps to improve the filter estimate. Moreover, a floor change case is presented, in which the filter is capable of detecting the floor change and improving the 2D accuracy using the floor change information. <s> BIB004
In Pedestrian Dead Reckoning (PDR), pedestrian's steps and heading changes are measured with accelerometers and gyroscopes. The change of position is based on these. In BIB004 , a state consists of two-dimensional position r, heading θ, step length l, and possibly a floor index. The state transition is computed with a particle filter. Here we show how the state model without floor index and with normal noise can be optimized for use with KFEs. We use in this example algorithms presented in Sections 4.1 and 4.2. The nonlinear state transition model is where ε θ ∼ N(∆ t , σ 2 θ ) is the noisy heading change, with ∆ t measured from gyroscopes, l is the footstep length and r is the position of the pedestrian. The augmented state is z = r 1 r 2 θ l ε r,1 ε r,2 ε θ ε l T . The state transition model can be written in the form of (28): In this formulation the reduced statez is two-dimensional and the nonlinear part of the state transition function is also two-dimensional. If this problem is to be solved with a KFE that uses sigma-points, we can optimize the implementation further. This can be done becausez 2 in (63) is conditionally linear, givenz 1 . The parts of function (37) are Using this the dimension of the nonlinear part of the state is reduced to 1 and the sigma-points are generated for only one dimension. Figure 1 shows mean estimates of the first position variable (r 1 ) after one propagation step in a test. The estimates are computed using S 2 KF with varying number of sigma-points. Implementation of the sigma-point generator and S 2 KF can be found in  . S 2 KF is applied to original state (60) and to above presented reduced states with 2 and 1 nonlinear variables. The propagation of the state with the full state model cannot be computed with fewer than 9 sigmapoints. The state computed using the model that uses conditional linearity in addition to the linearity has the smoothest convergence to an estimate and the estimate with full state estimate has the largest variation. This shows that the use of optimizations can also improve the estimation accuracy.  where r 0 is the location of the sound source, r i is the location of ith microphone and v is the speed of sound. When there are m microphones in the array there are at most TDoA measurements available BIB003 . In practice, measurements contain noise. Here we consider model with noises where ε i is the noise corresponding to ith microphone and ε i,j is error corresponding to the correlation of the measured signals from the microphone pair and the speed of sound is multiplied out from the equation. When ε i,j = 0 for all microphone pairs the measurement noises are not independent for all possible pairs and the measurements can be modeled with m − 1 measurements of form This kind of assumption is done for example in BIB002 . In practice, this assumption does not hold and the selection of microphone pairs is a tradeoff, where pairs close to each other have smaller correlation error ε i,j , but worse geometry than pairs far away from each other BIB001 . Here we consider the situation where all possible microphone pairs are used and errors ε i and ε i,j are modeled as Gaussians. The augmented state model is where x contains 3 position and velocity variables. Using (24)- (26) the nonlinear part of the estimation can be done only for the state variables and sigma-points would be required only for 6 dimensional state instead of using sigma-points also for noise terms. The measurement model can be written in compact form using (28): . . . Using these the dimension of the nonlinear function is reduced from . The computation of the inverse of the innovation covariance for Kalman gain (7) can be optimized using the inversion formula (59). The noise terms are assumed independent and, thus, the noise covariance matrix R is diagonal. We split noises into two parts, whose covariance matrices are D 1 and D 2 . D 1 corresponds to microphone specific terms ε y i and D 2 to microphone pair specific terms ε y i,j . Becausez contains only state variables and they do not contribute to the linear part (AP zg(z) T H T = 0), the innovation covariance can be written as and its inverse is 