Particle filters are essential for state estimation in non-linear and non-Gaussian systems, with performance hinging on effective proposal distributions. This paper presents the implementation of Kalman Filter and No-U-Turn Sampler (NUTS) proposals within the Stone Soup Python framework. The Kalman Filter proposal offers computational efficiency for structured systems, while NUTS enables robust exploration of complex, highdimensional distributions. Benchmark evaluations demonstrate the complementary strengths of these methods, enhancing Stone Soup's capabilities for diverse state estimation challenges.

In this paper, we discuss the derivations, implementations and performance of target tracking algorithms for a single-target single-sensor system estimating the state, covariance and existence probability of a target. Given the target exists, we simulate measurements of the target with a given probability of detection, along with false measurements (clutter) parametrised by a clutter density. We evaluate the performance of the algorithms by computing the area under Receiver Operating Characteristic (ROC) curves against a range of clutter density values. We give particular attention to the effectiveness of correctly inferring the presence or absence of the target. We select the Integrated Probabilistic Data Association Filter (IPDAF) and the Integrated Expected Likelihood Particle Filter (IELPF) algorithms, with the IELPF implementing a near-optimal proposal which uses the current scan of measurements as well as a prior proposal for comparison. Simulation results indicate the performance of the IPDAF exceeds that of the preexisting particle filter implementing a prior proposal, but a novel particle filter using a near-optimal proposal and a modest number of particles outperforms the IPDAF.

Ahstract-This paper considers the problem of tracking a manoeuvring target when some of the measurements are delayed by the time taken to propagate through some medium. We are especially interested in bearing-only measurements, since it is possible to extract range information by fusing measurements which have negligible propagation delay (such as from electrooptical sensors) and measurements which have a propagation delay proportional to the range to the target (such as from acoustic sensors). This requires us to handle measurements which appear out of sequence, and with emission times unknown to the tracker. Unlike previous approaches, a particle filter is used, which handles out-of-sequence measurements by storing a history of hypothesised target states and measurement emission times for each particle. This allows new target states and times to be inserted into the trajectory of each target by interpolating between adjacent states in the history.

An assignment problem is considered with the constraint that the same hypothesis cannot be applied to more than one object. We desire efficiency without approximation. Multiple target tracking methods such as the joint probabilistic association filter (JPDAF) motivate us. Methods of solving this assignment problem involving enumerating all possible joint assignments is infeasible except for small problems. A recent approach circumvents this combinatorial explosion by representing the structure of the target hypotheses in a `net' which exploits redundancy in an ordered list of objects us to describe the problem. Here, we generalize this approach to process the objects in a tree structure this exploits conditional independence between subsets of the objects. This gives a substantial computational saving and allows us to consider scenarios which were previously impractical. In particular, we show the feasibility of using an exact JPDAF implementation to track 400 targets