基于主動(dòng)波導(dǎo)不變量分布的改進(jìn)擴(kuò)展卡爾曼濾波跟蹤方法

孫同晶; 朱慶煜; 王治撰

doi:10.11999/JEIT240595

基于主動(dòng)波導(dǎo)不變量分布的改進(jìn)擴(kuò)展卡爾曼濾波跟蹤方法

doi: 10.11999/JEIT240595

孫同晶¹,
朱慶煜¹,
王治撰^{2, 3, ,}

1.
杭州電子科技大學(xué)自動(dòng)化學(xué)院杭州 310018
2.
上海交通大學(xué)船舶與海洋工程學(xué)院上海 200240
3.
水下測(cè)控技術(shù)國(guó)防科技重點(diǎn)實(shí)驗(yàn)室大連 116013

基金項(xiàng)目: 國(guó)家自然科學(xué)基金聯(lián)合基金(U22A2044)

詳細(xì)信息

作者簡(jiǎn)介:
孫同晶：女，博士，教授，研究方向?yàn)樾盘?hào)處理，信息融合，目標(biāo)定位和跟蹤

朱慶煜：男，碩士生，研究方向?yàn)樾盘?hào)處理和模式識(shí)別

王治撰：男，博士生，高級(jí)工程師，研究方向?yàn)樗履繕?biāo)回波特性和海洋環(huán)境特性研究

通訊作者:
王治撰　15142594278@163.com

中圖分類號(hào): TN011.6
計(jì)量
- 文章訪問數(shù): 193
- HTML全文瀏覽量: 45
- PDF下載量: 26
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2024-07-12
- 修回日期: 2024-12-04
- 網(wǎng)絡(luò)出版日期: 2024-12-07
- 刊出日期: 2025-01-31

Improved Extended Kalman Filter Tracking Method Based On Active Waveguide Invariant Distribution

1.
Department of Automation, Hangzhou Dian zi University, Hangzhou 310018, China
2.
School of ship and ocean engineering, Shanghai Jiao Tong University, Shanghai 200240, China
3.
Underwater Test and Control Technology Key Laboratory, Dalian 116013, China

Funds: The Joint Foundation of National Natural Science Foundation of China (U22A2044)

摘要

摘要: 在復(fù)雜的海洋環(huán)境中，目標(biāo)的可知信息受環(huán)境噪聲、混響等的干擾嚴(yán)重，導(dǎo)致目標(biāo)跟蹤效果較差，而從這些干擾中提取目標(biāo)的可利用特征及其困難。該文將目標(biāo)與環(huán)境的耦合特征融入目標(biāo)跟蹤算法中，提出了一種基于主動(dòng)波導(dǎo)不變量分布的改進(jìn)擴(kuò)展卡爾曼濾波跟蹤方法。首先基于淺海波導(dǎo)中目標(biāo)散射特性基本理論，推導(dǎo)了收發(fā)分置條件下的主動(dòng)波導(dǎo)不變量表征的數(shù)學(xué)模型，獲得了距離、頻率以及主動(dòng)波導(dǎo)不變量分布的約束關(guān)系；然后將該約束加入到擴(kuò)展卡爾曼濾波的狀態(tài)向量中，通過增加新的約束來(lái)提高目標(biāo)運(yùn)動(dòng)模型與真實(shí)目標(biāo)運(yùn)動(dòng)軌跡的契合度進(jìn)而提高目標(biāo)跟蹤的精度；最后通過仿真實(shí)驗(yàn)和實(shí)測(cè)數(shù)據(jù)驗(yàn)證了該方法的跟蹤性能，結(jié)果顯示：該方法較常規(guī)擴(kuò)展卡爾曼濾波跟蹤方法能夠更好地提高目標(biāo)跟蹤精度，仿真中結(jié)果的優(yōu)化率約能達(dá)到50%，實(shí)測(cè)數(shù)據(jù)處理結(jié)果的優(yōu)化率約在60%左右。
- 水下目標(biāo)跟蹤 /
- 擴(kuò)展卡爾曼濾波 /
- 淺海波導(dǎo) /
- 目標(biāo)干涉特性 /
- 主動(dòng)波導(dǎo)不變量
Abstract: Objective The complex and variable nature of the underwater environment presents significant challenges for the field of underwater target tracking. Factors such as environmental noise, interference, and reverberation can severely distort and obscure the signals emitted or reflected by underwater targets, complicating accurate detection and tracking efforts. Additionally, advancements in weak target signal technology add further complexity, as they necessitate sophisticated methods to enhance and interpret signals that may be lost amidst background noise. The challenges associated with underwater target tracking are multifaceted. One major issue is the interference that can compromise the integrity and reliability of target information. Another critical challenge lies in the difficulty of extracting useful feature information from the often chaotic underwater environment. Traditional tracking methods, which typically rely on basic signal processing techniques, frequently fall short in addressing these complexities. Underwater tracking technology serves as a cornerstone in several key fields, including marine science, military strategy, and marine resource development. Notably, effective underwater tracking is essential for monitoring, sonar detection, and the deployment of underwater weapons within the military sector. Considering the significance of underwater tracking technology, there is an urgent need for innovative methods to address the existing challenges. Therefore, this paper proposes a unified approach that views the target and environment as an integrated system, extracting coupled features—specifically, active waveguide invariants—and fusing these features into the motion model to enhance underwater tracking capabilities. Methods: This paper presents an enhanced extended Kalman filter tracking method, which is built upon the active waveguide invariant distribution. The mathematical model for active waveguide invariant representation is derived based on the foundational theory of target scattering characteristics in shallow water waveguides, with specific consideration of transmitter-receiver separation. This derivation establishes the constraint relationships among distance, frequency, and the active waveguide invariant distribution. These constraints are subsequently incorporated into the state vector of the extended Kalman filter to enhance the alignment between the target motion model and the actual trajectory, thereby improving tracking accuracy. The method includes image preprocessing steps such as filtering, edge detection, and edge smoothing, followed by the application of the Radon transform to extract essential parameters, including distance and frequency. The Radon transform is refined using threshold filtering to improve parameter extraction. The active waveguide invariant distribution is then computed, and the tracking performance of the method is validated through simulation experiments and real measurement data. The simulation setup involves a rigid ball as the target in a shallow water environment, modeled using a constant velocity assumption. Real measurement data is collected under similar conditions at the Xin’An River experimental site. For both simulations and real measurements, a steel ball model target and constant velocity model are employed, with equipment deployed on the same horizontal plane. Results and Discussions: First, the distribution of the constant of propagation within the active waveguide was obtained through simulation experiments. A comparison was made between the Invariant Distribution-Extended Kalman Filter (ID-EKF), the Extended Kalman Filter (EKF), and the Invariance Extended Kalman Filter (IEKF). In trajectory tracking, the ID-EKF demonstrated closer alignment to the true trajectory compared to both the EKF and IEKF. Additionally, in terms of the mean square error of the predicted posterior position, the ID-EKF exhibited a lower error rate. As indicated by the overall estimation accuracy, the ID-EKF achieved approximately 50% greater accuracy than the EKF and about 30% higher accuracy than the IEKF. Subsequently, the ID-EKF algorithm was validated in a real-world scenario using actual measurement data. The acoustic field interference stripes were obtained through the processing of received echo signals, and the distribution of the constant of propagation was extracted by manually selecting points and conducting a maximum search, followed by curve fitting using the joint edge curve fitting method. Results from Monte Carlo simulation experiments demonstrated a decreasing order of tracking accuracy for the ID-EKF, IEKF, and EKF, consistent with the simulation results. The overall estimation accuracy of the ID-EKF was approximately 60% higher than that of the EKF and about 40% superior to that of the IEKF. Conclusions: This paper presents a novel tracking method based on the extended Kalman filter, informed by the interference characteristics of target and environmental coupling in shallow water waveguides. The effectiveness of this method is substantiated through both theoretical simulation data and empirical lake measurement data. The active waveguide invariant distribution was derived using the Radon transform, which facilitated the implementation of the ID-EKF tracking. Results from both simulations and experiments reveal that the extracted active invariant value distribution manifests in two scenarios: either coinciding with 1 or exhibiting significant deviation from 1. When the extracted invariant value is markedly different from 1, the ID-EKF demonstrates a reduced tracking error and a more pronounced convergence relative to other tracking algorithms, highlighting the importance of precisely extracting this value to enhance the ID-EKF’s performance. Conversely, when the extracted value is close to 1, the tracking error of the ID-EKF aligns more closely with that of the IEKF algorithm. In both cases, it is evident that the extracted invariant value is pivotal in enhancing the accuracy of the tracking algorithm. Future research will prioritize the extraction of more accurate invariant values to facilitate the development of higher-precision tracking algorithms.
- Underwater target tracking /
- Extended Kalman filter /
- Shallow water waveguide /
- Target interference characteristic /
- The active waveguide invariant

HTML全文

圖 1 主動(dòng)聲吶工作模式

下載: 全尺寸圖片幻燈片

圖 2 仿真條紋與運(yùn)動(dòng)軌跡對(duì)比

下載: 全尺寸圖片幻燈片

圖 3 仿真工況

下載: 全尺寸圖片幻燈片

圖 4 基于仿真模型的目標(biāo)跟蹤實(shí)現(xiàn)流程

下載: 全尺寸圖片幻燈片

圖 5 仿真的聲場(chǎng)干涉條紋圖

下載: 全尺寸圖片幻燈片

圖 6 Radon變換過程

下載: 全尺寸圖片幻燈片

圖 7 主動(dòng)波導(dǎo)不變量分布圖

下載: 全尺寸圖片幻燈片

圖 8 仿真結(jié)果

下載: 全尺寸圖片幻燈片

圖 9 試驗(yàn)布放及工況

下載: 全尺寸圖片幻燈片

圖 10 聲場(chǎng)干涉條紋結(jié)果圖

下載: 全尺寸圖片幻燈片

圖 11 截取條紋圖的$\gamma $分布的提取過程

下載: 全尺寸圖片幻燈片

圖 12 試驗(yàn)結(jié)果

下載: 全尺寸圖片幻燈片

表 1 3種算法仿真的估計(jì)位置與真值誤差表(m)

算法	估計(jì)位置和真值偏差-均值	估計(jì)位置和真值偏差-峰值
EKF	0.19	0.25
IEKF	0.13	0.19
ID-EKF	0.09	0.13

下載: 導(dǎo)出CSV

表 2 算法仿真對(duì)比優(yōu)化表(%)

對(duì)比算法	均值優(yōu)化率	峰值優(yōu)化率
IEKF相對(duì)EKF	31.58	24.00
ID-EKF相對(duì)EKF	52.63	48.00
ID-EKF相對(duì)IEKF	30.77	31.58

下載: 導(dǎo)出CSV

表 3 測(cè)試參數(shù)及目標(biāo)

信號(hào)參數(shù)					目標(biāo)及其運(yùn)動(dòng)狀態(tài)
信號(hào)形式	頻率(kHz)	脈沖間隔(ms)	脈寬(ms)	采樣率(kHz)	球體目標(biāo)模型(1.2 m直徑)，由近及遠(yuǎn)運(yùn)動(dòng)
LFM	40～80	400	5	512	球體目標(biāo)模型(1.2 m直徑)，由近及遠(yuǎn)運(yùn)動(dòng)

下載: 導(dǎo)出CSV

表 4 3種算法試驗(yàn)的估計(jì)位置與真值誤差表(m)

算法	估計(jì)位置和真值偏差-均值	估計(jì)位置和真值偏差-峰值
EKF	0.195	0.256
IEKF	0.142	0.187
ID-EKF	0.079	0.095

下載: 導(dǎo)出CSV

表 5 算法試驗(yàn)對(duì)比優(yōu)化表(%)

算法對(duì)比	均值優(yōu)化率	峰值優(yōu)化率
IEKF相對(duì)EKF	27.179	26.953
ID-EKF相對(duì)EKF	59.487	62.891
ID-EKF相對(duì)IEKF	44.366	49.197

下載: 導(dǎo)出CSV

參考文獻(xiàn)(22)

[1]	郭戈, 王興凱, 徐慧樸. 基于聲吶圖像的水下目標(biāo)檢測(cè)、識(shí)別與跟蹤研究綜述[J]. 控制與決策, 2018, 33(5): 906–922. doi: 10.13195/j.kzyjc.2017.1678. GUO Ge, WANG Xingkai, and XU Huipu. Review on underwater target detection, recognition and tracking based on sonar image[J]. Control and Decision, 2018, 33(5): 906–922. doi: 10.13195/j.kzyjc.2017.1678.
[2]	KALMAN R E and BUCY R S. New results in linear filtering and prediction theory[J]. Journal of Basic Engineering, 1961, 83(1): 95–108. doi: 10.1115/1.3658902.
[3]	KALMAN R E. A new approach to linear filtering and prediction problems[J]. Journal of Basic Engineering, 1960, 82(1): 35–45. doi: 10.1115/1.3662552.
[4]	LI Tiancheng, SU Jinya, LIU Wei, et al. Approximate Gaussian conjugacy: Parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(12): 1913–1939. doi: 10.1631/FITEE.1700379.
[5]	周云, 胡錦楠, 趙瑜, 等. 基于卡爾曼濾波改進(jìn)壓縮感知算法的車輛目標(biāo)跟蹤[J]. 湖南大學(xué)學(xué)報(bào): 自然科學(xué)版, 2023, 50(1): 11–21. doi: 10.16339/j.cnki.hdxbzkb.2023002. ZHOU Yun, HU Jinnan, ZHAO Yu, et al. Vehicle target tracking based on Kalman filtering improved compressed sensing algorithm[J]. Journal of Hunan University: Natural Sciences, 2023, 50(1): 11–21. doi: 10.16339/j.cnki.hdxbzkb.2023002.
[6]	白冬杰. 車載毫米波雷達(dá)多目標(biāo)跟蹤算法研究[D]. [碩士論文], 北京交通大學(xué), 2019. BAI Dongjie. Research on multi-target tracking algorithm of vehicle-mounted millimeter-wave radar[D]. [Master dissertation], Beijing Jiaotong University, 2019.
[7]	吳葉麗, 行鴻彥, 侯天浩, 等. 基于改進(jìn)自適應(yīng)擴(kuò)展卡爾曼濾波的高精度姿態(tài)解算[J]. 探測(cè)與控制學(xué)報(bào), 2023, 45(6): 69–76. WU Yeli, XiNG Hongyan, HOU Tianhao, et al. An improved adaptive extended Kalman filter for high precision attitude solution[J]. Journal of Detection & Control, 2023, 45(6): 69–76.
[8]	成春彥, 李亞安. EKF和UKF算法在雙觀測(cè)站純方位目標(biāo)跟蹤中的應(yīng)用[J]. 水下無(wú)人系統(tǒng)學(xué)報(bào), 2023, 31(3): 388–397. doi: 10.11993/j.issn.2096-3920.202203014. CHENG Chunyan and LI Yaan. Applications of EKF and UKF algorithms in bearings-only target tracking with a double observation stations[J]. Journal of Unmanned Undersea Systems, 2023, 31(3): 388–397. doi: 10.11993/j.issn.2096-3920.202203014.
[9]	丁凱. 基于前視聲納的水下目標(biāo)跟蹤技術(shù)研究[D]. [碩士論文], 哈爾濱工程大學(xué), 2006. doi: 10.7666/d.y936424. DING Kai. Research on tracking of underwater object based on forward-looking sonar[D]. [Master dissertation], Harbin Engineering University, 2006. doi: 10.7666/d.y936424.
[10]	CHUPROV S D. Interference structure of a sound field in a layered ocean[M]. BREKHOVSKIKH L M and ANDREEVOI L B. Ocean Acoustics: Current State. Moscow: Nauka, 1982: 71–91.
[11]	BROOKS L A, KIDNER M R F, ZANDER A C, et al. Techniques for extraction of the waveguide invariant from interference patterns in spectrograms[C]. ACOUSTICS 2006, Christchurch, New Zealand, 2006: 445.
[12]	SELL A W and LEE CULVER R. Waveguide invariant analysis for modeling time-frequency striations in a range-dependent environment[J]. The Journal of the Acoustical Society of America, 2011, 129(S4): 2509. doi: 10.1121/1.3588287.
[13]	TURGUT A, ORR M, and ROUSEFF D. Broadband source localization using horizontal-beam acoustic intensity striations[J]. The Journal of the Acoustical Society of America, 2010, 127(1): 73–83. doi: 10.1121/1.3257211.
[14]	李永飛, 郭瑞明, 趙航芳. 淺海內(nèi)波環(huán)境下聲場(chǎng)干涉條紋的稀疏重建[J]. 物理學(xué)報(bào), 2023, 72(7): 074301. doi: 10.7498/aps.72.20221932. LI Yongfei, GUO Ruiming, and ZHAO Hangfang. Sparse reconstruction of acoustic interference fringes in shallow water and internal wave environment[J]. Acta Physica Sinica, 2023, 72(7): 074301. doi: 10.7498/aps.72.20221932.
[15]	余赟, 惠俊英, 殷敬偉, 等. 基于波導(dǎo)不變量的目標(biāo)運(yùn)動(dòng)參數(shù)估計(jì)及被動(dòng)測(cè)距[J]. 聲學(xué)學(xué)報(bào), 2011, 36(3): 258–264. doi: 10.15949/j.cnki.0371-0025.2011.03.015. YU Yun, HUI Junying, YIN Jingwei, et al. Moving target parameter estimation and passive ranging based on waveguide invariant theory[J]. Acta Acustica, 2011, 36(3): 258–264. doi: 10.15949/j.cnki.0371-0025.2011.03.015.
[16]	宋雪晶. 基于聲場(chǎng)干涉結(jié)構(gòu)的水聲目標(biāo)被動(dòng)定位技術(shù)[D]. [博士論文], 哈爾濱工程大學(xué), 2017. SONG Xuejing. Underwater acoustic target passive localization techniques based on acoustic field interference structure[D]. [Ph. D. dissertation], Harbin Engineering University, 2017.
[17]	QUIJANO J E, ZURK L M, and ROUSEFF D. Demonstration of the invariance principle for active sonar[J]. The Journal of the Acoustical Society of America, 2008, 123(3): 1329–1337. doi: 10.1121/1.2836763.
[18]	QUIJANO J E, CAMPBELL R L JR, OESTERLEIN T G, et al. Experimental observations of active invariance striations in a tank environment[J]. The Journal of the Acoustical Society of America, 2010, 128(2): 611–618. doi: 10.1121/1.3455813.
[19]	ZURK L M and ROUSEFF D. Striation-based beamforming for active sonar with a horizontal line array[J]. The Journal of the Acoustical Society of America, 2012, 132(4): EL264–EL270. doi: 10.1121/1.4748281.
[20]	HE Chensong, QUIJANO J E, and ZURK L M. Enhanced Kalman filter algorithm using the invariance principle[J]. IEEE Journal of Oceanic Engineering, 2009, 34(4): 575–585. doi: 10.1109/joe.2009.2028058.
[21]	芬恩·B·延森, 威廉·A·庫(kù)珀曼, 米切爾·B·波特, 等, 周利生, 王魯軍, 杜栓平, 譯. 計(jì)算海洋聲學(xué)[M]. 2版. 北京: 國(guó)防工業(yè)出版社, 2018: 54–57, 267–269. JENSEN F B, KUPERMAN W A, POTER M B, et al, ZHOU Lisheng, WANG Lujun, and DU Shuanping. translation. Computational Ocean Acoustics[M]. 2nd ed. Beijing: National Defense Industry Press, 2018: 54–57, 267–269.
[22]	林萌, 李翠華, 黃劍航. 基于Radon變換的運(yùn)動(dòng)模糊圖像參數(shù)估計(jì)[J]. 計(jì)算機(jī)技術(shù)與發(fā)展, 2008, 18(1): 33–36. doi: 10.3969/j.issn.1673-629X.2008.01.009. LIN Meng, LI Cuihua, and HUANG Jianhang. Parameters estimation of motion blurred images based on radon transform[J]. Computer Technology and Development, 2008, 18(1): 33–36. doi: 10.3969/j.issn.1673-629X.2008.01.009.