In this paper, some recent results on the modified Riccati equation are studied. This modified Riccati equation has already been associated with tracking a target under measurement uncertainty. We consider the special case of tracking a target without clutter, but with a probability of detection of less than one. This special case
has received quite some attention recently, especially in relationship with Cramer Rao bounds, or equivalently expected performance. Furthermore, in some other recent works, new theoretical results on the modified Riccati equation have been derived. We will compare these results and point out their importance for performance
assessment and prediction in a target tracking context.
In this paper an efficient adaptive parameter control scheme for Multi Function Radar (MFR) is used. This scheme has been introduced in.5 The scheme has been designed in such a way that it meets constraints on specific quantities that are relevant for target tracking while minimizing the energy spent. It is shown here, that
this optimal scheme leads to a considerable variation of the realized detection probability, even within a single scenario. We also show that constraining or fixing the probability of detection to a certain predefined value leads to a considerable increase in the energy spent on the target. This holds even when one optimizes the fixed probability of detection. The bottom line message is that the detection probability is not a design parameter by itself, but merely the product of an optimal schedule.
In target tracking, the track filter is an important element. It is also quite important that it is implemented efficiently. This is even better seen if one thinks of it that a filter is running for each data association hypothesis and in a real multi target tracking application the number of hypotheses, that need to be updated every scan, may easily be in the order of thousands. A standard 'single model' building block for a track filter is the (Extended) Kalman Filter (EKF). Multiple model filters, such as the popular and widely used Interacting Multiple Model filter (IMM) or the recently developed Multiple Model Multiple Hypothesis filter (M3H), are based on banks of EKF's that run in parallel and interact according to an underlying Markov transition modeling assumption. It is well known that, in case of a single model filter, the standard Kalman Filter gains and covariances can be calculated off line, when the process noise covariance and the measurement noise covariance are known.
Unfortunately, this does not hold for the two types of multiple model filters, mentioned before. The main reason for this is that these multiple model filters interact. In this paper we investigate several methods to (partially) do the calculations off line and thus use less computations, while at the same time aiming at a minimal loss of
performance. We will compare such an approximate IMM or M3H filter with the full on line IMM or M3H filter, both in terms of computational load and performance.
In this paper we will give a general system setup, that allows the formulation of a wide range of Track Before Detect (TBD) problems. A general basic particle filter algorithm for this system is also provided. TBD is a technique, where tracks are produced directly on the basis of raw (radar) measurements, e.g. power or IQ data, without intermediate processing and decision making. The advantage over classical tracking is that the full information is integrated over time, this leads to a better detection and tracking performance, especially for weak targets. In this paper we look at the filtering and the detection aspect of TBD. We will formulate a detection result, that allows the user to implement any optimal detector in terms of the weights of a running particle filter. We will give a theoretical as well as a numerical (experimental) justification for this. Furthermore, we show that the TBD setup, that is chosen in this paper, allows a straightforward extension to the multi-target case. This easy extension is also due to the fact that the implementation of the solution is by means of a particle filter.
The problem of detecting whether or not a signal is present is often encountered. Several detection strategies lead to a likelihood ratio test against a threshold. In a simple setting explicit expressions for the likelihood can be obtained. However when the signal to be detected is generated by a nonlinear, non-Gaussian dynamical system it is in general impossible to obtain an expression for the probability of the signal under the hypothesis that it is present. Recently, so called particle filters have been proposed to solve nonlinear, non-Gaussian filtering problems. In this paper we show that the filtering solution obtained by a particle filter can be used to construct the likelihood ratio, needed to perform the likelihood ratio test for detection. Here we will show that different detection schemes can be used. These schemes have in common that they use the output of a particle filter for the purpose of detecting the possible presence of a target. Furthermore we will go into aspects that are of importance when actually building such a particle filter based detector.
In this paper we present a framework in which the general hybrid filtering or state estimation problem can be formulated. The problem of joint tracking and classification can be formulated in this framework as well as the problem of multiple model filtering with additional mode observations. In this formulation the state vector is decomposed into a continuous (kinematic) component and a discrete (mode and/or class) component. We also suppose that there are two types of measurements. Measurements that are related tot eh continuous part of the state (e.g. bearing and range measurements in a radar application) and measurements that are related to the discrete part of the state (e.g. radar cross section measurements). We will derive an optimal filter for this problem and will show how this filter can be implemented numerically.
In this paper a new method is presented to deal with multiple model filtering. The method is the so called Multiple Model Multiple Hypothesis Filter (MMMH filter). For each hypothesis a Kalman filter is running. This hypothesis represents a specific model mode sequence history. The proposed method has a high level of genericity and is highly flexible. The main feature is that the number of hypotheses that are maintained varies with the "difficulty" of a scenario. It is shown that the MMMH performs better than the widely used Interacting Multiple Model (IMM) filter.
In this paper we present a new method for multiple model filtering. This method is a combination of the IMM filter approach and the hybrid particle filter approach. The merging part of this IMM hybrid particle algorithm is able to deal with the model switching behavior, whereas the filtering part can deal with nonlinearities in the dynamics and measurements and possible non Gaussian noise within a certain mode.
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