In transportation networks, the majority of moving vehicles are route-based or trajectory-scheduled. Taking advantage of such predictive information generally produces more accurate dynamic models and better surveillance performance. This paper is concerned with the route-based dynamic modeling along with the route-aided tracking. First, the evolution of the positions across the route is formulated as a stationary Markov process from the characteristics of the route-based dynamics, which follows that the second- and third-order models of the straight-line route-based motions are constructed. This novel modeling strategy is in reverse to the conventional ones starting from the acceleration and its resultant dynamic models are easy to implement due to the linearity with respect to the system states. Second, an optimal initialization technique for route-aided tracking is proposed by utilizing the stationary process information sufficiently. Furthermore, an extension to the circular route-based dynamic modeling and a combinational modeling structure are also presented. Finally, in the context of aerial surveillance, numerical simulations are provided to show the effectiveness of the proposed dynamic modeling and to verify the theoretical results given in the paper.

Track-before-detect (TBD) in range-Doppler plane is of significance for Doppler radars. The existing methods suffer from the approximate motion models in range-Doppler plane and the inefficiency of energy integration. In this paper, an accurate evolution equation of target range and Doppler with respect to time is presented and a new pseudo-spectrum based TBD method is proposed to effectively integrate target energy and detect weak target in range-Doppler domain. According to the commonly assumed constant velocity motion in Cartesian coordinates, the evolution of range and Doppler is correctly described by a nonlinear function of target range-Doppler and the time invariant speed square. Consequently, a novel TBD method, which matches target speed instead of velocity in each direction, is proposed. Each original resolution cell in range-Doppler plane is predicted to the last frame of current processing batch according to the time evolution equation. Then, a pseudo-spectrum is constructed around the predicted position according to a point spread function. Multiframe accumulation is achieved by adding the sampling values of the pseudo-spectrum over several cells to the last frame. To match the unknown target speed square, a bank of pseudo-spectrum based speed square filter (PS-SSF) is presented. The target output envelopes in both range-Doppler and speed square domains are derived theoretically and a feasible parameter estimation method is proposed. Numerical simulation results demonstrate that the proposed PS-SSF method can not only achieve effective weak target detection in range-Doppler domain, but also produce precise parameter estimates of target range and Doppler, as well as target speed.

Conventional velocity-filtering-based track-beforedetect (VF-TBD) methods integrate the energy of a cell in a frame with that of the cell closest to the predicted target position in the last frame of the processing batch, assuming a certain target velocity. However, the target may not exactly be on the quantized cell and its echo envelope may occupy multiple adjacent cells. This often leads to significant energy loss and echo envelope degradation. In this paper, a novel VF-TBD method based on pseudo-spectrum (PS-VF-TBD) is presented to address this problem. For every cell, a pseudo-spectrum is constructed around the predicted position according to the assumed velocity using a truncated point spread function. Samples of the pseudospectrum on the cells that are located in the truncated spread area are added onto the last frame of the processing batch to integrate the target energy within multiple cells. Due to the use of the point spread model and the accurate sampling of the predicted spectrum, energy loss can be mitigated and the echo envelope well maintained. This approach simultaneously maximizes the signal-to-noise ratio (SNR) gain and enables improved parameter estimation utilizing the envelope characteristics. The procedure for pseudo-spectrum construction and multi-frame accumulation is derived in detail and the output SNR is analyzed theoretically. It is found that the proposed PS-VF-TBD can achieve an SNR gain greater than that by the conventional VF-TBD method. To deal with a target with unknown velocity, a bank of pseudospectrum- based velocity filters is proposed. The signal gain loss resulting from velocity mismatch is investigated and the μ-width of the envelope in the velocity domain is analyzed. Finally, a method for improved position and velocity estimation is presented. Simulation results demonstrate the superiority of the proposed method in terms of SNR gain, detection probability and estimation accuracy at the expense of increased computational complexity

Track-before-detect (TBD) of weak maneuvering targets in range-Doppler plane is investigated. The existing TBD methods suffer from performance degradation due to the use of approximate motion models in range-Doppler plane. In this paper, exact time evolving rules of target range and Doppler are presented for constant acceleration (CA) and coordinated turn (CT) motions in Cartesian coordinates, and two novel pseudo-spectrum based TBD approaches are proposed for effective detection of weak CA and CT targets in range-Doppler plane, respectively. In accordance with the common CA and CT motions in Cartesian coordinates, the accurate time evolution equations of range and Doppler are derived for CA and CT targets, respectively, which are nonlinear functions of range-Doppler and several invariable parameters. Then, the pseudo-spectrum based TBD of CA and CT targets in range-Doppler plane is performed by matching these invariants. Each range-Doppler cell is predicted according to the exact evolution equation. A pseudo-spectrum is constructed around the predicted position, and sample values of the pseudo-spectrum are added onto cells for energy integration. This eliminates performance loss caused by model mismatch and target output envelope can be well maintained. To deal with the unknown target parameters, two pseudo-spectrum based matched filter banks are proposed for CA and CT targets, respectively. Analysis and design of the filter banks are provided in detail. Simulations are conducted to evaluate the validity of the proposed methods in handling weak maneuvering targets.

Proportional navigation (PN) guidance laws have been commonly applied to homing missile systems guiding the missile to its target. When the target is stationary and its location is known a priori, the state of the missile is subjected to a destination constraint, which contains extra information on missile state that can help increase tracking performance. This article concerns with the constraint modeling and the state estimation with a destination constraint imposed by PN guidance law in 3-D space. Constraint models corresponding to three representative PN guidance laws: pure PN, true PN, and generalized PN, are presented using the state augmentation method, which stacks the states at the previous and current time steps in one state vector to express the constraint relationships. For cases where the destination information is noisy and the parameters of the guidance law, i.e., the navigation constant and the bias angle, are not known a priori, the unknown parameters are estimated along with the missile state in the state vector in an augmentation way. Based on the formulations of constraint models, the construction of pseudomeasurements is carried out. A constrained state estimation method is proposed by incorporating the pseudomeasurements into the nonlinear filtering process. In this method, a sequential process framework is employed and the cubature Kalman filter is used to handle the high-dimensional filtering problem and the strong nonlinearity involved in pseudomeasurements. Numerical experiments in three scenarios are performed to demonstrate the validity of the proposed models along with the estimation method.