Probabilistic GOSPA: A Metric for Performance Evaluation of Multi-Object Filters with Uncertainties

This paper presents a probabilistic generalization of the generalized optimal subpattern assignment (GOSPA) metric, termed P-GOSPA metric. GOSPA is a popular metric for evaluating the distance between finite sets, typically in multi-object estimation applications. P-GOSPA extends GOSPA to the space of multi-Bernoulli set densities, incorporating the inherent uncertainty in probabilistic multi-object representations. In addition, P-GOSPA retains the interpretability of GOSPA, such as decomposability into localization, missed and false detection errors, in a sound manner. Examples and simulations are presented to demonstrate the efficacy of P-GOSPA.

Optimal Preprocessing for Joint Detection and Classification of Wireless Communication Signals in Congested Spectrum Using Computer Vision Methods

The joint detection and classification of RF signals has been a critical problem in the field of wideband RF spectrum sensing. Recent advancements in deep learning models have revolutionized this field, remarkably through the application of state-of-the-art computer vision algorithms such as YOLO (You Only Look Once) and DETR (Detection Transformer) to the spectrogram images. This paper focuses on optimizing the preprocessing stage to enhance the performance of these computer vision models. Specifically, we investigated the generation of training spectrograms via the classical Short-Time Fourier Transform (STFT) approach, examining four classical STFT parameters: FFT size, window type, window length, and overlapping ratio. Our study aims to maximize the mean average precision (mAP) scores of YOLOv10 models in detecting and classifying various digital modulation signals within a congested spectrum environment. Firstly, our results reveal that additional zero padding in FFT does not enhance detection and classification accuracy and introduces unnecessary computational cost. Secondly, our results indicated that there exists an optimal window size that balances the trade-offs between and the time and frequency resolution, with performance losses of approximately 10% and 30% if the window size is four or eight times off from the optimal. Thirdly, regarding the choice of window functions, the Hamming window yields optimal performance, with non-optimal windows resulting in up to a 10% accuracy loss. Finally, we found a 10% accuracy score performance gap between using 10% and 90% overlap. These findings highlight the potential for significant performance improvements through optimized spectrogram parameters when applying computer vision models to the problem of wideband RF spectrum sensing.

Joint Detection and Classification of Communication and Radar Signals in Congested RF Environments Using YOLOv8

In this paper, we present a comprehensive study on the application of YOLOv8, a state-of-the-art computer vision (CV) model, to the challenging problem of joint detection and classification of signals in a highly dynamic and congested RF environment. Using our synthetic RF datasets, we explored three different scenarios with congested communication and radar signals. In the first study, we applied YOLOv8 to detect and classify multiple digital modulation signals coexisting within a highly congested and dynamic spectral environment with significant overlap in both frequency and time domains. The trained model was able to achieve an impressive mean average precision (mAP) of 0.888 at an IoU threshold of 50%, signifying its robustness against spectral congestion. The second part of our research focuses on the detection and classification of multiple polyphase pulse radar signals, including Frank code and P1 through P4 codes. We were able to successfully train YOLOv8 to deliver a nearly perfect mAP50 score of 0.995 in a densely populated signal environment, further showcasing its capability in radar signal processing. In the last scenario, we demonstrated that the model can also be applied to the multi-target detection problem for continuous-wave radar. The synthetic datasets used in these experiments reflect a realistic mix of communication and radar signals with varying degrees of interference and congestion - a setup that has been overlooked by many past research efforts, which have primarily focused on ML-based classification of digital communication signal modulation schemes. Our study demonstrated the potential of advanced CV models in addressing spectrum sensing challenges in congested and dynamic RF environments involving both communication and radar signals. We hope our findings will spur further collaborative efforts to tackle the complexities of congested RF spectrum environments.

Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks

Stochastic simulation approaches perform probabilistic inference in Bayesian networks by estimating the probability of an event based on the frequency that the event occurs in a set of simulation trials. This paper describes the evidence weighting mechanism, for augmenting the logic sampling stochastic simulation algorithm [Henrion, 1986]. Evidence weighting modifies the logic sampling algorithm by weighting each simulation trial by the likelihood of a network's evidence given the sampled state node values for that trial. We also describe an enhancement to the basic algorithm which uses the evidential integration technique [Chin and Cooper, 1987]. A comparison of the basic evidence weighting mechanism with the Markov blanket algorithm [Pearl, 1987], the logic sampling algorithm, and the evidence integration algorithm is presented. The comparison is aided by analyzing the performance of the algorithms in a simple example network.

Refinement and Coarsening of Bayesian Networks

In almost all situation assessment problems, it is useful to dynamically contract and expand the states under consideration as assessment proceeds. Contraction is most often used to combine similar events or low probability events together in order to reduce computation. Expansion is most often used to make distinctions of interest which have significant probability in order to improve the quality of the assessment. Although other uncertainty calculi, notably Dempster-Shafer [Shafer, 1976], have addressed these operations, there has not yet been any approach of refining and coarsening state spaces for the Bayesian Network technology. This paper presents two operations for refining and coarsening the state space in Bayesian Networks. We also discuss their practical implications for knowledge acquisition.

Symbolic Probabilistic Inference with Evidence Potential

Recent research on the Symbolic Probabilistic Inference (SPI) algorithm[2] has focused attention on the importance of resolving general queries in Bayesian networks. SPI applies the concept of dependency-directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. In response to this research we have extended the evidence potential algorithm [3] with the same features. We call the extension symbolic evidence potential inference (SEPI). SEPI like SPI can handle generic queries and is incremental with respect to queries and observations. While in SPI, operations are done on a search tree constructed from the nodes of the original network, in SEPI, a clique-tree structure obtained from the evidence potential algorithm [3] is the basic framework for recursive query processing. In this paper, we describe the systematic query and caching procedure of SEPI. SEPI begins with finding a clique tree from a Bayesian network-the standard procedure of the evidence potential algorithm. With the clique tree, various probability distributions are computed and stored in each clique. This is the ?pre-processing? step of SEPI. Once this step is done, the query can then be computed. To process a query, a recursive process similar to the SPI algorithm is used. The queries are directed to the root clique and decomposed into queries for the clique's subtrees until a particular query can be answered at the clique at which it is directed. The algorithm and the computation are simple. The SEPI algorithm will be presented in this paper along with several examples.

Symbolic Probabilistic Inference with Continuous Variables

Research on Symbolic Probabilistic Inference (SPI) [2, 3] has provided an algorithm for resolving general queries in Bayesian networks. SPI applies the concept of dependency directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. Unlike traditional Bayesian network inferencing algorithms, SPI algorithm is goal directed, performing only those calculations that are required to respond to queries. Research to date on SPI applies to Bayesian networks with discrete-valued variables and does not address variables with continuous values. In this papers, we extend the SPI algorithm to handle Bayesian networks made up of continuous variables where the relationships between the variables are restricted to be ?linear gaussian?. We call this variation of the SPI algorithm, SPI Continuous (SPIC). SPIC modifies the three basic SPI operations: multiplication, summation, and substitution. However, SPIC retains the framework of the SPI algorithm, namely building the search tree and recursive query mechanism and therefore retains the goal-directed and incrementality features of SPI.