Antonio Cantoni

Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter

The probability hypothesis density (PHD) recursion propagates the posterior intensity of the random finite set (RFS) of targets in time. The cardinalized PHD (CPHD) recursion is a generalization of the PHD recursion, which jointly propagates the posterior intensity and the posterior cardinality distribution. In general, the CPHD recursion is computationally intractable. This paper proposes a closed-form solution to the CPHD recursion under linear Gaussian assumptions on the target dynamics and birth process. Based on this solution, an effective multitarget tracking algorithm is developed. Extensions of the proposed closed-form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques. The proposed CPHD implementations not only sidestep the need to perform data association found in traditional methods, but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard PHD filter. Our implementations only have a cubic complexity, but simulations suggest favorable performance compared to the standard Joint Probabilistic Data Association (JPDA) filter which has a nonpolynomial complexity.

The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations

It is shown analytically that the multitarget multiBernoulli (MeMBer) recursion, proposed by Mahler, has a significant bias in the number of targets. To reduce the cardinality bias, a novel multiBernoulli approximation to the multi-target Bayes recursion is derived. Under the same assumptions as the MeMBer recursion, the proposed recursion is unbiased. In addition, a sequential Monte Carlo (SMC) implementation (for generic models) and a Gaussian mixture (GM) implementation (for linear Gaussian models) are proposed. The latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform.

The Cardinalized Probability Hypothesis Density Filter for Linear Gaussian Multi-Target Models

The probability hypothesis density (PHD) recursion propagates the posterior intensity of the random finite set of targets in time. The cardinalized PHD (CPHD) recursion is a generalization of the PHD recursion, which jointly propagates the posterior intensity and the posterior cardinality distribution. The incorporation of cardinality information naturally improves the accuracy and stability of state estimates. In general, the CPHD recursions are computationally intractable. This paper proposes a closed-form solution to the CPHD recursions under linear Gaussian assumptions on the target dynamics and birth process. Based on this solution, an effective multi-target tracking algorithm is developed. Extensions to non-linear models are also given using linearization and unscented transform techniques. The proposed CPHD implementations not only sidestep the need to perform data association found in traditional methods, but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard PHD filter.

Cascading content-addressable memories

The various methods of connecting multiple content-addressable memory (CAM) devices to form a memory system of larger dimensions are surveyed. They include daisy-chaining CAMs to increase the number of elements and possibly using carry-lookahead logic to increase the cascade. To increase the data size, one can replicate the labels in distinct CAMs, use the data storage available in a primary CAM to index a secondary CAM/RAM (read-only memory), or reduce redundancy in labels. To increase the label size, one can use an element cascade with or without a shift register, a master-slave cascade, or a trie cascade. One of the methods examined for increasing the label size is a new trie cascade approach.<<ETX>>

A new approach to the optimization of envelope-constrained filters with uncertain input

In envelope-constrained filtering, the filter is optimized subject to the constraint that the filter response to a given signal lies within a specified envelope or mask. In a number of signal processing applications, the envelope-constrained filtering problem is more directly relevant than least squares approximation-based approaches. The present authors develop an efficient method for solving an extended version of the envelope-constrained filtering problem in which the input pulse is not known exactly but is known to lie within a specified mask. This envelope-constrained problem with uncertain input (ECUI) has been examined elsewhere, but the algorithm proposed there for its solution has, in general, inferior convergence characteristics. >

Iterative method for the design of DFT filter Bank

Multirate adaptive filters have numerous advantages such as low computational load, fast convergence, and parallelism in the adaptation. Drawbacks when using multirate processing are mainly related to aliasing and reconstruction effects. These effects can be minimized by introducing appropriate problem formulation and employing sophisticated optimization techniques. In this paper, we propose a formulation for the design of a filter bank which controls the distortion level for each frequency component directly and minimizes the inband aliasing and the residual aliasing between different subbands. The advantage of this problem formulation is that the distortion level can be weighted for each frequency depending on the particular practical application. A new iterative algorithm is proposed to optimize simultaneously over both the analysis and the synthesis filter banks. This algorithm is shown to have a unique solution for each iteration. For a fixed distortion level, the proposed algorithm yields a significant reduction in both the inband aliasing and the residual aliasing levels compared to existing methods applied to the numerical examples.

Envelope constrained filter with linear interpolator

The envelope constrained (EC) filtering problem is the minimization of the noise gain of the filter while satisfying the constraint that its noiseless response to a specified input lies within a prescribed envelope. Using a hybrid filter consisting of an A/D converter, an FIR filter, and a linear interpolator, the problem is posed as a functional inequality constrained optimization problem. A technique for solving this problem is proposed by approximating it with a conventional unconstrained optimization problem that is then solved by a descent direction-based algorithm.

Variable Digital Filter With Least-Square Criterion and Peak Gain Constraints

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this brief, we present a formulation that allows the tradeoff between the total squared error and the maximum deviation from the desired response in the passband and stopband. With this formulation, the maximum deviation can be reduced below the least-square solution with only a slight change in the performance of the total squared error. Similarly, the total squared error can be reduced below the minmax solution with a minor change in the maximum deviation from the minmax solution

The dual parameterization approach to optimal least square FIR filter design subject to maximum error constraints

This paper is concerned with the design of linear-phase finite impulse response (FIR) digital filters for which the weighted least square error is minimized, subject to maximum error constraints. The design problem is formulated as a semi-infinite quadratic optimization problem. Using a newly developed dual parameterization method in conjunction with the Caratheodorys dimensional theorem, an equivalent dual finite dimensional optimization problem is obtained. The connection between the primal and the dual problems is established. A computational procedure is devised for solving the dual finite dimensional optimization problem. The optimal solution to the primal problem can then be readily obtained from the dual optimal solution. For illustration, examples are solved using the proposed computational procedure.

FIR Variable Digital Filter With Signed Power-of-Two Coefficients

Variable digital filters (VDFs) are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this paper, we investigate the design of VDFs with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two terms with a restriction on the total number of power-of-two for the filter coefficients. An efficient design procedure is proposed that includes an improved method for handling the quantization of the VDF coefficients for both the min-max and the least-square criteria leading to an optimum quantized solution. For the least-square criterion, a reduced search region around the optimum quantized solution is further constructed and the branch and bound method in conjunction with an efficient branch cutting scheme is presented to search for an optimum solution in this reduced region.