Kalman Filter for Moving Object Tracking: Performance Analysis and Filter Design

This chapter presents Kalman filters for tracking moving objects and their efficient design strategy based on steady-state performance analysis. First, a dynamic/measurement model is defined for the tracking systems, assuming both position-only and position-velocity measurements. Then, problems with the Kalman filter design in tracking systems are summarized, and an efficient steady-state performance index proposed by the author [termed the root-mean-squared error index (the RMS index)] is introduced to resolve these concerns. The analytical relationship between the proposed RMS index and the covariance matrix of the process noise is shown, leading to a proposed design strategy that is based on this relationship. Theoretical performance analysis is conducted using the performance indices to show the optimality of the design strategy. Numerical simulations show the validity of the theoretical analyses and effectiveness of the proposed strategy in realistic situations. In addition, the optimal performance of the position-only-measured and position-velocity-measured systems is analyzed and compared. This comparison shows that the position-velocity-measured Kalman filter tracking is accurate when compared with the position-only-measured filter

Three-Dimensional Imaging Method Incorporating Range Points Migration and Doppler Velocity Estimation for UWB Millimeter-Wave Radar

High-resolution, short-range sensors that can be applied in optically challenging environments (e.g., in the presence of clouds, fog, and/or dark smog) are in high demand. Ultrawideband (UWB) millimeter-wave radars are one of the most promising devices for the above-mentioned applications. For target recognition using sensors, it is necessary to convert observational data into full 3-D images with both time efficiency and high accuracy. For such conversion algorithm, we have already proposed the range points migration (RPM) method. However, in the existence of multiple separated objects, this method suffers from inaccuracy and high computational cost due to dealing with many observed RPs. To address this issue, this letter introduces Doppler-based RPs clustering into the RPM method. The results from numerical simulations, assuming 140-GHz band millimeter radars, show that the addition of Doppler velocity into the RPM method results in more accurate 3-D images with reducing computational costs

Steady-State Performance Analysis of Tracking Filter Using LFM Waveforms and Range-Rate Measurement

The steady-state performance of a moving-object tracking filter is theoretically analyzed, assuming the simultaneous measurement of the range and range-rate (RRM system), and the use of linear frequency modulated (LFM) waveforms (RRM-LFM filter). An efficient analytical steady-state performance index, called an RMS index, is derived for the RRM-LFM filter to clarify the steady-state range prediction errors, theoretically. Using the derived RMS index, the optimal performance of the RRM-LFM filter is analyzed. The performance variation due to the use of LFM waveforms is clarified for the RRM tracking system. The theoretical performance analysis verifies that the measured range-rate significantly improves the tracking accuracy, compared to the conventional range-only measuring LFM tracking filter. Furthermore, the quantitative relationships among the measurement accuracy, degree of target maneuvering, and steady-state range prediction errors are clarified to validate the effectiveness of the RRM-LFM filter

Machine Learning-Based Classification of Human Behaviors and Falls in Restroom via Dual Doppler Radar Measurements

This study presents a radar-based remote measurement system for classification of human behaviors and falls in restrooms without privacy invasion. Our system uses a dual Doppler radar mounted onto a restroom ceiling and wall. Machine learning methods, including the convolutional neural network (CNN), long short-term memory, support vector machine, and random forest methods, are applied to the Doppler radar data to verify the model’s efficiency and features. Experimental results from 21 participants demonstrated the accurate classification of eight realistic behaviors, including falling. Using the Doppler spectrograms (time–velocity distribution) as the inputs, CNN showed the best results with an overall classification accuracy of 95.6% and 100% fall classification accuracy. We confirmed that these accuracies were better than those achieved by conventional restroom monitoring techniques using thermal sensors and radars. Furthermore, the comparison results of various machine learning methods and cases using each radar’s data show that the higher-order derivative parameters of acceleration and jerk, and the motion information in the horizontal direction are the efficient features for behavior classification in a restroom. These findings indicate that daily restroom monitoring using the proposed radar system accurately recognizes human behaviors and allows early detection of fall accidents

Optimal Steady-State Range Prediction Filter for Tracking with LFM Waveforms

This communication proposes a gain design method of an α - β filter with linear frequency-modulated (LFM) waveforms to achieve optimal range prediction (tracking) of maneuvering targets in steady-state. First, a steady-state root-mean-square (RMS) prediction error, called an RMS-index, is analytically derived for a constant-acceleration target. Next, a design method of the optimal gains that minimizes the derived RMS-index is proposed. Numerical analyses demonstrate the effectiveness of the proposed method, as well as producing a performance improvement over the conventional Kalman filter-based design method. Moreover, the theoretical relationship between range tracking performance and a coefficient for range-Doppler coupling of LFM waveforms is clarified. Numerical simulations using the proposed method demonstrate LFM radar tracking of maneuvering targets and prove the method’s effectiveness

Performance Analysis and Design Strategy for a Second-Order, Fixed-Gain, Position-Velocity-Measured (α-β-η-θ) Tracking Filter

We present a strategy for designing an α - β - η - θ filter, a fixed-gain moving-object tracking filter using position and velocity measurements. First, performance indices and stability conditions for the filter are analytically derived. Then, an optimal gain design strategy using these results is proposed and its relationship to the position-velocity-measured (PVM) Kalman filter is shown. Numerical analyses demonstrate the effectiveness of the proposed strategy, as well as a performance improvement over the traditional position-only-measured α - β filter. Moreover, we apply an α - β - η - θ filter designed using this strategy to ultra-wideband Doppler radar tracking in numerical simulations. We verify that the proposed strategy can easily design the gains for an α - β - η - θ filter based on the performance of the ultra-wideband Doppler radar and a rough approximation of the target’s acceleration. Moreover, its effectiveness in predicting the steady state performance in designing the position-velocity-measured Kalman filter is also demonstrated

Correct Stability Condition and Fundamental Performance Analysis of the <i>α</i>-<i>β</i>-<i>γ</i>-<i>δ</i> Filter

This paper theoretically analyzes the fundamental performance of a fourth-order steady-state moving object tracking filter, called an &#945; - &#946; - &#947; - &#948; filter. The &#945; - &#946; - &#947; - &#948; filter considers estimations of jerk (time-derivative of acceleration) in the motion of targets. First, regarding the stability conditions of the &#945; - &#946; - &#947; - &#948; filter, we prove that there are unstable cases even when the conventionally derived stability conditions are satisfied, and then we derive the correct stability conditions. Next, we analytically derive performance indices that indicate the steady-state errors for targets with typical motions. Based on the derived indices, the optimal performance of the &#945; - &#946; - &#947; - &#948; filter is theoretically analyzed and compared with that of the traditional second- and third-order steady-state tracking filters, i.e., &#945; - &#946; and &#945; - &#946; - &#947; filters. Numerical analyses and simulations are used to verify the advantages and disadvantages of the &#945; - &#946; - &#947; - &#948; filter over the above-mentioned filters. The practicality of the use of jerk for the tracking filtering problem is revealed in this paper

Performance Analysis and Design Strategy for a Second-Order, Fixed-Gain, Position-Velocity-Measured (α-β-η-θ) Tracking Filter

We present a strategy for designing an α - β - η - θ filter, a fixed-gain moving-object tracking filter using position and velocity measurements. First, performance indices and stability conditions for the filter are analytically derived. Then, an optimal gain design strategy using these results is proposed and its relationship to the position-velocity-measured (PVM) Kalman filter is shown. Numerical analyses demonstrate the effectiveness of the proposed strategy, as well as a performance improvement over the traditional position-only-measured α - β filter. Moreover, we apply an α - β - η - θ filter designed using this strategy to ultra-wideband Doppler radar tracking in numerical simulations. We verify that the proposed strategy can easily design the gains for an α - β - η - θ filter based on the performance of the ultra-wideband Doppler radar and a rough approximation of the target’s acceleration. Moreover, its effectiveness in predicting the steady state performance in designing the position-velocity-measured Kalman filter is also demonstrated