Multi-frame Accumulation Research Articles

Dynamic Programming-Based Track-before-Detect Algorithm for Weak Maneuvering Targets in Range–Doppler Plane

This paper focuses on detecting and tracking maneuvering weak targets in the range–Doppler (RD) plane with the track-before-detect (TBD) algorithm based on dynamic programming (DP). Traditional DP-TBD algorithms integrate target detection and tracking in their framework while searching the paths provided by a predefined model of the kinematic properties within the constraints allowed. However, both the approximate motion model used in the RD plane and the model mismatch caused when the target undergoes a maneuver can degrade the TBD performance sharply. To address these issues, this paper accurately describes the evolution of the RD equation based on Constant Acceleration (CA) and Coordinated Turn (CT) motion models with the process noise in the Cartesian coordinate system, and it also employs a recursive method to estimate the parameters in the equations for efficient energy accumulation and path searches. Facing the situation that targets energy accumulation during the DP iteration process will lead to an expansion of the target energy accumulation process. This paper designs a more efficient Optimization Function (OF) to inhibit the expansion effect, improve the resolution of the nearby targets, and increase the detection probability of the weak targets simultaneously. In addition, to search the trajectory more efficiently and accurately, we improved the process of DP multi-frame accumulation, thus reducing the computation amount of large-scale searches. Finally, the effectiveness of the proposed method for CA and CT motion target detection and tracking is verified by many of the simulation experiments that were conducted in this paper.

Inertial information based star detection for airborne star sensor

Star sensors are among the most promising attitude measurement devices owing to their high accuracy. Insufficient star detection ability during daytime is a major issue in airborne applications because of the highly dynamic and strong sky background present. A star detection algorithm for a medium field-of-view star sensor combined with a zero-lock laser goniometer is proposed in this paper. The star sensor employs a high-frame-rate detector that shortens the exposure time to obtain an undistorted star spot under dynamic conditions. To improve the low signal-to-noise ratio of the star image influenced by the strong sky background, a technique for multi-frame image accumulation was introduced, prior to which attitude compensation for each star image frame was carried out by using the inertial information related to the reference frame measured by zero-lock laser gyro goniometers. Both simulations and laboratory experiments were conducted. The simulation results show that the proposed algorithm effectively enhances the stability of the star spot and signal-to-noise ratio of the star image. The experimental results demonstrate a fine star spot centroid extraction performance for the medium field of view star sensor with an extraction error of less than 0.2 pixels or 2 arc-second under four different types of one-dimensional angular motion after compensation. Based on this, the multi-frame accumulation of star images demonstrates little star spot dispersion compared with no compensation and exhibits a higher signal-to-noise ratio than a single-frame star image. In the real situation experiments, a K0 spectrum star with magnitude +3.0 was successfully observed under dynamic condition during daytime. The signal-to-noise ratio is up to 20, which is more than 5 times than that by the traditional method.

Pseudo-spectrum-based multi-sensor multi-frame detection in mixed coordinates

Multi-sensor track-before-detect (MS-TBD) can greatly enhance the weak target detection ability due to utilizing multi-frame (MF) data from multiple sensors. However, in the existing MS-TBD methods, when the resolutions of the MS are different, the target echoes obtained by the MS are arranged to the measurement space with unified resolution. This process may remove some valuable information of raw sensor data or introduce additional noise, which may lead to inadequate integration of the echo energy and degradation of the output envelope. For the sake of solving the issues mentioned above, a pseudo-spectrum (PS) method in mixed coordinates is investigated for TBD in MS systems. For each sensor, the conversion of each measurement cell's position from sensor coordinates to Cartesian coordinates is carried out and the prediction of that is conducted with an assumed velocity in Cartesian framework. Then the predicted position is converted back to global sensor coordinates, which takes one of the sensors as the origin. A PS is designed around the predicted global polar position and its samples are added to the integration frame for MF accumulation. This avoids additional spatial alignment and facilitates well-maintained target envelope, leading to effective energy integration and the improvement of estimation accuracy. The procedures of coordinate transformation and MF accumulation in multiple sensors are derived and the analysis of theoretical output SNR is provided. The effectiveness and the superiority of the proposed method is demonstrated by several simulations.

Multiframe track-before-detect method based on velocity filtering in mixed coordinates

In this paper, a velocity filtering based track-before-detect algorithm in mixed coordinates is presented to address the problem of integration loss caused by inaccurate motion model in polar coordinate sensors. Since the motion of a constant velocity (CV) target is better modeled in Cartesian coordinates, the search of measurements for integration in polar sensor coordinates is carried out according to the CV model in Cartesian coordinates instead of an approximate model in polar sensor coordinates. The position of each cell is converted into Cartesian coordinates and predicted according to an assumed velocity. Then, the predicted Cartesian position is converted back to polar sensor coordinates for multiframe accumulation. The use of the correct model improves integration effectiveness and consequently improves algorithm performance. To handle the weak target with unknown velocity, a velocity filter bank in mixed coordinates is presented. The influence of velocity mismatch on the performance of filter bank is analyzed, and an efficient strategy for filter bank design is proposed. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.

A 64 × 64 SPAD-Based Indirect Time-of-Flight Image Sensor With 2-Tap Analog Pulse Counters

This article presents a 64 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 64 indirect time-of-flight (iToF) image sensor with a depth range of 50 m, integrated into a 1P4M 110-nm CMOS process. The sensor is based on a single-photon avalanche diode (SPAD), the range-dependent phase delay of which is measured by compact analog time-gated pulse counters and then read out by column-parallel single-slope (SS) analog-to-digital converters (ADCs). We present two prototypes of iToF sensors that exploit one- or two-tap counters in the pixel. Compared to the one-tap sensor, the two-tap sensor achieves an improved fill factor of 26.3% with a pixel pitch of 32 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text {m}$ </tex-math></inline-formula> . This improvement is realized by using a retrograde deep n-well as guard-ring structure and two analog counters whose layout has been optimized. By utilizing two different demodulation frequencies of 1.56 and 50 MHz, the two-tap sensor achieves a large depth range of 50 m with a relative depth uncertainty of 0.22% and a high 3-D frame rate of 65 frames/s. When using an optical bandpass filter and multi-frame accumulation, the sensor shows a tolerance of 120-klx sunlight. Compared with the previous iToF benchmarks, the proposed SPAD-based iToF sensor demonstrates the largest depth range without compromising the relative depth uncertainty.

A Pseudo-Spectrum Approach for Weak Target Detection and Tracking

Conventional velocity-filtering-based track-before-detect (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 pseudo-spectrum 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 is 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 multiframe 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 pseudo-spectrum-based velocity filters is proposed. The signal gain loss resulting from velocity mismatch is investigated and the $\mu$ -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.

Pseudo-Spectrum Based Speed Square Filter for Track-Before-Detect in Range-Doppler Domain

Track-before-detect (TBD) in range-Doppler plane is of significance for Doppler radars. Existing methods suffer from approximate motion models in range-Doppler plane and 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 common constant velocity motion in Cartesian coordinates, the evolution of range and Doppler is correctly described by a nonlinear function of target range-Doppler and time invariant speed square. Consequently, a novel TBD method, which matches target speed instead of velocity in each direction, is proposed. Each cell in range-Doppler plane is predicted to the last frame 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 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 range and Doppler, as well as target speed.