├── README.md ├── data └── data-1.txt ├── plots ├── Lidar.png └── Radar.png └── src ├── KF.py ├── datapoint.py ├── helpers.py ├── sensor_fusion.py └── tools.py /README.md: -------------------------------------------------------------------------------- 1 | # Object-Tracking-and-State-Prediction-with-Unscented-and-Extended-Kalman-Filters 2 | Radar and Lidar Sensor Fusion using Extended, and Unscented Kalman Filter for Object Tracking and State Prediction. 3 | 4 | # Understanding the data 5 | 6 | ``` 7 | [L(for lidar)] [m_x] [m_y] [t] [r_x] [r_y] [r_vx] [r_vy] 8 | [R(for radar)] [m_rho] [m_phi] [m_drho] [t] [r_px] [r_py] [r_vx] [r_vy] 9 | 10 | Where: 11 | (m_x, m_y) - measurements by the lidar 12 | (m_rho, m_phi, m_dho) - measurements by the radar in polar coordinates 13 | (t) - timestamp in unix/epoch time the measurements were taken 14 | (r_x, r_y, r_vx, r_vy) - the real ground truth state of the system 15 | 16 | Example: 17 | R 8.60363 0.0290616 -2.99903 1477010443399637 8.6 0.25 -3.00029 0 18 | L 8.45 0.25 1477010443349642 8.45 0.25 -3.00027 0 19 | ``` 20 | # Extended KF 21 | Since here for fusing Radar and Lidar data, we need to have Extended KF for working with Radar data since the position is obtained by converting the polar co-ordinates using non-linear equations to (x,y) position. 22 |
23 | Lidar data can be treated via simple Kalman Filter. 24 | 25 | # References: 26 |
27 | Helper methods and input data file adapted from https://github.com/mithi/Fusion-EKF-Python 28 | -------------------------------------------------------------------------------- /data/data-1.txt: -------------------------------------------------------------------------------- 1 | R 8.46642 0.0287602 -3.04035 1477010443399637 8.6 0.25 -3.00029 0 2 | L 8.44818 0.251553 1477010443449633 8.45 0.25 -3.00027 0 3 | R 8.57101 0.0282318 -0.0105258 1477010443499690 8.45 0.25 0 0 4 | L 8.45582 0.253997 1477010443549747 8.45 0.25 0 0 5 | R 8.42927 0.0301427 -1.85813 1477010443604698 8.35 0.25 -1.81979 0 6 | L 8.23962 0.24916 1477010443659650 8.25 0.25 -1.81978 0 7 | R 7.9351 0.0237437 -3.81077 1477010443709653 8.05 0.2 -3.99976 -0.99994 8 | L 7.84073 0.159858 1477010443759657 7.85 0.15 -3.99972 -0.99993 9 | R 7.61428 0.0204653 -3.22052 1477010443809660 7.7 0.15 -2.99982 0 10 | L 7.54016 0.159641 1477010443859663 7.55 0.15 -2.99982 0 11 | R 7.50876 0.0127032 -1.89765 1477010443914714 7.45 0.100001 -1.8165 -0.908239 12 | L 7.3426 0.0345312 1477010443969766 7.35 0.0500011 -1.81648 -0.90823 13 | R 7.20598 0.000683772 -2.79536 1477010444024741 7.2 9.49949e-07 -2.72851 -0.909507 14 | L 7.05406 -0.0533413 1477010444079717 7.05 -0.0499992 -2.72849 -0.909499 15 | R 6.74737 -0.0212224 -1.67069 1477010444134693 6.95 -0.15 -1.81898 -1.81898 16 | L 6.84972 -0.258748 1477010444189670 6.85 -0.25 -1.81896 -1.81897 17 | R 6.67866 -0.0519302 -2.02379 1477010444239651 6.75 -0.349999 -2.00076 -2.00075 18 | L 6.64329 -0.462604 1477010444289632 6.65 -0.449999 -2.00076 -2.00075 19 | R 6.63205 -0.0840904 -0.81497 1477010444339690 6.6 -0.549999 -0.998836 -1.99769 20 | L 6.56029 -0.650892 1477010444389748 6.55 -0.65 -0.99884 -1.99769 21 | R 6.46217 -0.130812 -0.356062 1477010444444769 6.5 -0.85 -0.908747 -3.63498 22 | L 6.45805 -1.05268 1477010444499791 6.45 -1.05 -0.908739 -3.63494 23 | R 6.49021 -0.179219 -1.23944 1477010444554767 6.35 -1.15 -1.81897 -1.81898 24 | L 6.25499 -1.25007 1477010444609744 6.25 -1.25 -1.81896 -1.81896 25 | R 6.59968 -0.226407 1.73835 1477010444664705 6.3 -1.45 0.909739 -3.63894 26 | L 6.36328 -1.65656 1477010444719667 6.35 -1.65 0.909727 -3.63891 27 | R 6.57796 -0.279439 -0.211523 1477010444769692 6.3 -1.8 -0.999494 -2.9985 28 | L 6.24641 -1.95075 1477010444819718 6.25 -1.95 -0.999489 -2.99847 29 | R 6.66141 -0.322252 1.75689 1477010444869719 6.3 -2.1 0.999984 -2.99994 30 | L 6.34644 -2.23829 1477010444919720 6.35 -2.25 0.999979 -2.99994 31 | R 6.76596 -0.36264 0.855484 1477010444974743 6.35 -2.4 0 -2.72613 32 | L 6.34927 -2.55175 1477010445029767 6.35 -2.55 0 -2.72611 33 | R 6.98232 -0.399959 1.89805 1477010445084742 6.4 -2.7 0.909499 -2.72851 34 | L 6.43257 -2.84245 1477010445139717 6.45 -2.85 0.909503 -2.72851 35 | R 7.12938 -0.43502 1.4149 1477010445189758 6.45 -3 0 -2.99754 36 | L 6.44119 -3.14955 1477010445239799 6.45 -3.15 0 -2.99754 37 | R 7.31886 -0.470836 2.21289 1477010445294720 6.5 -3.3 0.910402 -2.7312 38 | L 6.5453 -3.45745 1477010445349641 6.55 -3.45 0.910402 -2.7312 39 | R 7.5456 -0.49614 2.70911 1477010445404670 6.65 -3.6 1.81722 -2.72583 40 | L 6.76011 -3.75457 1477010445459700 6.75 -3.75 1.81721 -2.72581 41 | R 7.884 -0.521437 2.20619 1477010445514767 6.8 -3.9 0.907988 -2.72396 42 | L 6.85997 -4.05805 1477010445569835 6.85 -4.05 0.907976 -2.72393 43 | R 8.04387 -0.547179 2.23987 1477010445624820 6.9 -4.2 0.909334 -2.72801 44 | L 6.94332 -4.34473 1477010445679806 6.95 -4.35 0.90933 -2.72799 45 | R 8.3635 -0.567708 1.67528 1477010445734748 7 -4.45 0.910054 -1.8201 46 | L 7.04099 -4.55018 1477010445789690 7.05 -4.55 0.910054 -1.8201 47 | R 8.50541 -0.582556 2.23409 1477010445844738 7.1 -4.7 0.908302 -2.72489 48 | L 7.14735 -4.86125 1477010445899786 7.15 -4.85 0.908297 -2.72489 49 | R 8.88902 -0.604494 3.05765 1477010445954759 7.25 -5 1.81907 -2.72861 50 | L 7.30424 -5.15404 1477010446009732 7.35 -5.15 1.81907 -2.72861 51 | R 8.97814 -0.622421 2.42827 1477010446064786 7.4 -5.3 0.908194 -2.7246 52 | L 7.44737 -5.45308 1477010446119841 7.45 -5.45 0.90819 -2.72457 53 | R 9.4762 -0.63468 2.54048 1477010446174794 7.55 -5.55 1.81974 -1.81974 54 | L 7.64356 -5.66706 1477010446229748 7.65 -5.65 1.81972 -1.81972 55 | R 9.53172 -0.647271 2.40306 1477010446284703 7.7 -5.8 0.90983 -2.72951 56 | L 7.7342 -5.95374 1477010446339659 7.75 -5.95 0.909826 -2.72948 57 | R 9.89957 -0.659824 3.5853 1477010446389694 7.85 -6.1 1.9986 -2.9979 58 | L 7.95703 -6.24328 1477010446439730 7.95 -6.25 1.99858 -2.99787 59 | R 10.4099 -0.66785 2.53218 1477010446494754 8.05 -6.35 1.81738 -1.81739 60 | L 8.15891 -6.45335 1477010446549779 8.15 -6.45 1.81737 -1.81737 61 | R 10.3865 -0.678464 2.50771 1477010446604767 8.2 -6.6 0.909293 -2.72787 62 | L 8.25411 -6.74791 1477010446659755 8.25 -6.75 0.909293 -2.72787 63 | R 10.6843 -0.687607 2.70793 1477010446714702 8.35 -6.85 1.81994 -1.81993 64 | L 8.44494 -6.95805 1477010446769649 8.45 -6.95 1.81993 -1.81993 65 | R 10.9406 -0.696337 2.56416 1477010446819646 8.5 -7.1 1.00006 -3.00018 66 | L 8.54925 -7.24433 1477010446869643 8.55 -7.25 1.00006 -3.00018 67 | R 11.3727 -0.707378 3.44956 1477010446919691 8.65 -7.4 1.99807 -2.99712 68 | L 8.73559 -7.5421 1477010446969739 8.75 -7.55 1.99808 -2.99712 69 | R 11.7598 -0.716035 2.04742 1477010447024687 8.8 -7.65 0.909955 -1.8199 70 | L 8.84538 -7.75497 1477010447079636 8.85 -7.75 0.909946 -1.81988 71 | R 11.8789 -0.726017 2.80161 1477010447129681 8.9 -7.9 0.999086 -2.9973 72 | L 8.95966 -8.0381 1477010447179726 8.95 -8.05 0.999095 -2.9973 73 | R 11.9442 -0.735521 1.86678 1477010447234713 9 -8.15 0.909309 -1.8186 74 | L 9.05896 -8.24314 1477010447289701 9.05 -8.25 0.909301 -1.81859 75 | R 12.4893 -0.745345 2.79706 1477010447339681 9.1 -8.4 1.0004 -3.00119 76 | L 9.15332 -8.54857 1477010447389662 9.15 -8.55 1.00038 -3.00117 77 | R 12.6764 -0.755304 1.92258 1477010447444637 9.2 -8.65 0.909508 -1.819 78 | L 9.24541 -8.76863 1477010447499613 9.25 -8.75 0.9095 -1.81899 79 | R 13.0018 -0.765199 4.2891 1477010447549622 9.35 -8.95 1.99965 -3.99928 80 | L 9.44703 -9.15328 1477010447599631 9.45 -9.15 1.99964 -3.99928 81 | R 13.2646 -0.772362 2.209 1477010447649652 9.5 -9.25 0.999584 -1.99917 82 | L 9.54157 -9.35195 1477010447699673 9.55 -9.35 0.999584 -1.99917 83 | R 13.3655 -0.782802 2.24797 1477010447749669 9.55 -9.5 0 -3.00023 84 | L 9.54779 -9.64959 1477010447799666 9.55 -9.65 0 -3.0002 85 | R 13.8483 -0.794831 2.85181 1477010447849716 9.6 -9.8 0.999005 -2.997 86 | L 9.64606 -9.9341 1477010447899766 9.65 -9.95 0.998995 -2.997 87 | R 13.8368 -0.803954 1.95724 1477010447954720 9.7 -10.05 0.909855 -1.81969 88 | L 9.73801 -10.1396 1477010448009675 9.75 -10.15 0.909847 -1.81969 89 | R 14.4307 -0.812263 2.35389 1477010448059664 9.75 -10.3 0 -3.00065 90 | L 9.75524 -10.4732 1477010448109654 9.75 -10.45 0 -3.00063 91 | R 14.3135 -0.824455 2.63112 1477010448164710 9.8 -10.6 0.90817 -2.72451 92 | L 9.85048 -10.7526 1477010448219767 9.85 -10.75 0.908161 -2.72448 93 | R 14.7429 -0.835956 1.92166 1477010448274697 9.85 -10.9 0 -2.73074 94 | L 9.83614 -11.041 1477010448329628 9.85 -11.05 0 -2.73073 95 | R 14.8851 -0.848604 2.27417 1477010448379634 9.85 -11.2 0 -2.99965 96 | L 9.84568 -11.3496 1477010448429641 9.85 -11.35 0 -2.99961 97 | R 15.2094 -0.863774 2.26264 1477010448479667 9.85 -11.5 0 -2.99843 98 | L 9.83206 -11.6307 1477010448529693 9.85 -11.65 0 -2.99843 99 | R 15.413 -0.877244 0.866545 1477010448579678 9.8 -11.75 -1.0003 -2.00061 100 | L 9.74928 -11.8442 1477010448629664 9.75 -11.85 -1.00029 -2.00059 101 | R 15.4054 -0.88995 1.77828 1477010448679644 9.7 -12 -1.0004 -3.00119 102 | L 9.65354 -12.1497 1477010448729625 9.65 -12.15 -1.00039 -3.00116 103 | R 15.7547 -0.905673 1.01994 1477010448779630 9.6 -12.25 -0.999885 -1.99981 104 | L 9.54859 -12.3478 1477010448829636 9.55 -12.35 -0.999884 -1.99979 105 | R 15.5466 -0.922266 0.369379 1477010448879685 9.45 -12.45 -1.99803 -1.99805 106 | L 9.36086 -12.5501 1477010448929734 9.35 -12.55 -1.99804 -1.99804 107 | R 15.7759 -0.936847 0.912459 1477010448984693 9.3 -12.65 -0.909773 -1.81953 108 | L 9.22134 -12.7613 1477010449039652 9.25 -12.75 -0.909773 -1.81954 109 | R 15.9017 -0.95744 -0.700602 1477010449089745 9.05 -12.85 -3.99257 -1.99629 110 | L 8.84161 -12.9519 1477010449139839 8.85 -12.95 -3.99253 -1.99627 111 | R 15.6195 -0.978773 -0.291637 1477010449194745 8.75 -13 -1.8213 -0.910651 112 | L 8.66358 -13.0431 1477010449249651 8.65 -13.05 -1.8213 -0.910651 113 | R 15.6995 -0.995246 -0.795374 1477010449299701 8.5 -13.1 -2.997 -0.999005 114 | L 8.35763 -13.1557 1477010449349751 8.35 -13.15 -2.997 -0.998995 115 | R 15.5295 -1.0123 -1.48799 1477010449404748 8.2 -13.15 -2.72741 0 116 | L 8.03583 -13.1513 1477010449459745 8.05 -13.15 -2.72742 0 117 | R 15.2205 -1.03051 -1.3479 1477010449514693 7.9 -13.15 -2.72986 0 118 | L 7.76538 -13.1647 1477010449569641 7.75 -13.15 -2.72986 0 119 | R 15.3557 -1.04843 -0.489357 1477010449619676 7.6 -13.2 -2.9979 -0.999304 120 | L 7.44786 -13.2517 1477010449669711 7.45 -13.25 -2.9979 -0.999304 121 | R 14.9523 -1.06755 -1.47147 1477010449724687 7.3 -13.25 -2.72846 0 122 | L 7.16011 -13.2382 1477010449779664 7.15 -13.25 -2.72844 0 123 | R 14.6741 -1.08244 -2.33868 1477010449829700 7 -13.2 -2.99784 0.999284 124 | L 6.84891 -13.1493 1477010449879736 6.85 -13.15 -2.99784 0.999284 125 | R 14.8668 -1.09768 -2.01344 1477010449934724 6.7 -13.1 -2.72787 0.909275 126 | L 6.55759 -13.0679 1477010449989712 6.55 -13.05 -2.72787 0.909284 127 | R 14.5623 -1.11566 -1.26682 1477010450044722 6.4 -13.05 -2.72678 0 128 | L 6.26174 -13.0534 1477010450099732 6.25 -13.05 -2.72678 0 129 | R 14.3675 -1.1322 -1.86783 1477010450154684 6.1 -13 -2.72966 0.909888 130 | L 5.94198 -12.9494 1477010450209637 5.95 -12.95 -2.72963 0.90988 131 | R 14.0957 -1.14684 -3.18942 1477010450259674 5.8 -12.85 -2.99777 1.99851 132 | L 5.65107 -12.7365 1477010450309711 5.65 -12.75 -2.99778 1.99852 133 | R 13.7247 -1.15804 -1.68433 1477010450364717 5.55 -12.7 -1.81798 0.908995 134 | L 5.43839 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4.45 -11.05 0 1.81614 148 | L 4.45136 -10.93 1477010451169754 4.45 -10.95 0 1.81612 149 | R 11.6669 -1.1797 -2.64222 1477010451224789 4.45 -10.8 0 2.72555 150 | L 4.45788 -10.6457 1477010451279824 4.45 -10.65 0 2.72554 151 | R 11.4789 -1.17144 -2.50005 1477010451334789 4.45 -10.5 0 2.729 152 | L 4.44057 -10.3382 1477010451389755 4.45 -10.35 0 2.72898 153 | R 11.1898 -1.15508 -2.26227 1477010451444763 4.5 -10.2 0.908962 2.72687 154 | L 4.54925 -10.0439 1477010451499772 4.55 -10.05 0.908954 2.72685 155 | R 10.9942 -1.13588 -2.23426 1477010451554732 4.6 -9.9 0.909756 2.72927 156 | L 4.63755 -9.74952 1477010451609692 4.65 -9.75 0.909752 2.72926 157 | R 10.4986 -1.11645 -2.34038 1477010451664722 4.7 -9.6 0.90859 2.72578 158 | L 4.74589 -9.4609 1477010451719753 4.75 -9.45 0.908586 2.72576 159 | R 10.592 -1.09073 -1.62445 1477010451774708 4.85 -9.3 1.81967 2.72952 160 | L 4.94849 -9.13867 1477010451829663 4.95 -9.15 1.81967 2.72951 161 | R 10.2398 -1.06602 -1.22863 1477010451879669 5 -9.05 0.999884 1.99977 162 | L 5.04121 -8.94979 1477010451929676 5.05 -8.95 0.999874 1.99974 163 | R 10.3027 -1.04083 -1.33508 1477010451984680 5.15 -8.8 1.81805 2.72708 164 | L 5.26887 -8.63564 1477010452039685 5.25 -8.65 1.81803 2.72705 165 | R 10.116 -1.01021 -0.66468 1477010452089696 5.35 -8.55 1.99956 1.99957 166 | L 5.44864 -8.42738 1477010452139708 5.45 -8.45 1.99954 1.99954 167 | R 10.1164 -0.988358 -0.754614 1477010452194711 5.5 -8.35 0.909045 1.81807 168 | L 5.53862 -8.24357 1477010452249714 5.55 -8.25 0.909045 1.81808 169 | R 9.81408 -0.957431 -0.747175 1477010452304738 5.7 -8.1 2.72608 2.72608 170 | L 5.85094 -7.95601 1477010452359763 5.85 -7.95 2.72606 2.72606 171 | R 9.834 -0.9229 -0.425811 1477010452414768 5.95 -7.85 1.81801 1.81801 172 | L 6.05986 -7.73559 1477010452469773 6.05 -7.75 1.81802 1.81801 173 | R 9.79397 -0.893547 -0.362809 1477010452524779 6.15 -7.65 1.81798 1.81798 174 | L 6.25659 -7.54336 1477010452579785 6.25 -7.55 1.81798 1.81798 175 | R 9.82626 -0.862628 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1477010485279857 6.55 -3.45 0 -3.63613 787 | R 7.42685 -0.499304 2.20461 1477010485334822 6.6 -3.6 0.909673 -2.72901 788 | L 6.64571 -3.73674 1477010485389788 6.65 -3.75 0.909661 -2.72898 789 | R 7.73369 -0.519546 2.24171 1477010485444795 6.75 -3.85 1.81795 -1.81795 790 | L 6.85201 -3.93663 1477010485499803 6.85 -3.95 1.81793 -1.81793 791 | R 8.32239 -0.540957 2.69981 1477010485554749 6.9 -4.15 0.909979 -3.63994 792 | L 6.9548 -4.32855 1477010485609696 6.95 -4.35 0.909975 -3.6399 793 | R 8.30107 -0.565342 1.79442 1477010485664769 7 -4.45 0.907889 -1.81577 794 | L 7.05586 -4.55105 1477010485719843 7.05 -4.55 0.907881 -1.81576 795 | R 8.59318 -0.585948 2.51996 1477010485774801 7.1 -4.7 0.909789 -2.72935 796 | L 7.13261 -4.82718 1477010485829760 7.15 -4.85 0.909777 -2.72933 797 | R 8.84525 -0.603476 3.20216 1477010485884747 7.25 -5 1.81861 -2.72792 798 | L 7.34301 -5.14642 1477010485939735 7.35 -5.15 1.81859 -2.72789 799 | R 9.02066 -0.622827 2.45726 1477010485989735 7.4 -5.3 0.999994 -3 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1477010486744809 8.45 -7.1 1.81925 -2.72886 814 | L 8.54666 -7.24803 1477010486799777 8.55 -7.25 1.81924 -2.72886 815 | R 11.4023 -0.703311 2.66814 1477010486854698 8.65 -7.35 1.82079 -1.8208 816 | L 8.74711 -7.43338 1477010486909619 8.75 -7.45 1.8208 -1.8208 817 | R 11.4784 -0.712179 2.92582 1477010486959738 8.8 -7.6 0.997629 -2.99288 818 | L 8.84984 -7.75349 1477010487009857 8.85 -7.75 0.997629 -2.99288 819 | R 11.741 -0.726703 2.18954 1477010487064854 8.9 -7.9 0.909127 -2.72742 820 | L 8.94604 -8.07116 1477010487119852 8.95 -8.05 0.909127 -2.7274 821 | R 12.0578 -0.738017 1.97437 1477010487174826 9 -8.15 0.909524 -1.81903 822 | L 9.01893 -8.23506 1477010487229801 9.05 -8.25 0.909516 -1.81902 823 | R 12.3259 -0.7466 2.46112 1477010487284751 9.1 -8.4 0.909922 -2.72975 824 | L 9.1628 -8.53304 1477010487339701 9.15 -8.55 0.909913 -2.72976 825 | R 12.4872 -0.755033 3.12856 1477010487394740 9.25 -8.7 1.8169 -2.72535 826 | L 9.3508 -8.85468 1477010487449780 9.35 -8.85 1.81688 -2.72532 827 | R 12.9973 -0.761667 2.54796 1477010487504711 9.4 -9 0.910219 -2.73069 828 | L 9.45338 -9.162 1477010487559642 9.45 -9.15 0.910228 -2.73069 829 | R 13.3492 -0.7773 2.64735 1477010487609747 9.5 -9.3 0.997908 -2.99371 830 | L 9.56994 -9.45148 1477010487659852 9.55 -9.45 0.997908 -2.99372 831 | R 13.5895 -0.783535 1.80157 1477010487714799 9.6 -9.55 0.909971 -1.81993 832 | L 9.64603 -9.66938 1477010487769747 9.65 -9.65 0.909954 -1.81992 833 | R 13.7362 -0.793586 1.9961 1477010487824681 9.65 -9.8 0 -2.73054 834 | L 9.64842 -9.95866 1477010487879616 9.65 -9.95 0 -2.73053 835 | R 13.8624 -0.804437 2.82352 1477010487929707 9.7 -10.1 0.998187 -2.99456 836 | L 9.7516 -10.2483 1477010487979798 9.75 -10.25 0.998187 -2.99455 837 | R 14.2377 -0.814555 2.56532 1477010488034755 9.8 -10.4 0.909806 -2.7294 838 | L 9.8633 -10.5382 1477010488089713 9.85 -10.55 0.909797 -2.72938 839 | R 14.5453 -0.825759 1.93079 1477010488144715 9.85 -10.7 0 -2.72718 840 | L 9.84674 -10.8547 1477010488199718 9.85 -10.85 0 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9.15 -12.75 -1.99891 -1.9989 855 | R 15.7268 -0.954682 0.414822 1477010489004723 9.05 -12.85 -1.81839 -1.81839 856 | L 8.95936 -12.9426 1477010489059717 8.95 -12.95 -1.81838 -1.81838 857 | R 15.8476 -0.977762 -0.972751 1477010489114674 8.8 -13 -2.72942 -0.909806 858 | L 8.65422 -13.0444 1477010489169631 8.65 -13.05 -2.72941 -0.909806 859 | R 15.6101 -0.995616 -0.116796 1477010489219633 8.5 -13.15 -2.99987 -1.99991 860 | L 8.3436 -13.2381 1477010489269636 8.35 -13.25 -2.99984 -1.9999 861 | R 15.432 -1.01103 -1.74358 1477010489319687 8.25 -13.2 -1.99797 0.998985 862 | L 8.15674 -13.1486 1477010489369738 8.15 -13.15 -1.99797 0.998985 863 | R 15.4246 -1.02553 -0.658323 1477010489424683 8 -13.2 -2.73 -0.910004 864 | L 7.85314 -13.2533 1477010489479628 7.85 -13.25 -2.73 -0.910004 865 | R 15.1639 -1.04748 -1.86286 1477010489534731 7.65 -13.25 -3.62957 0 866 | L 7.45422 -13.2433 1477010489589835 7.45 -13.25 -3.62953 0 867 | R 15.1626 -1.06605 -1.33622 1477010489644778 7.3 -13.25 -2.7301 0 868 | L 7.13166 -13.2372 1477010489699722 7.15 -13.25 -2.73007 0 869 | R 14.8978 -1.08358 -1.4991 1477010489754727 7 -13.25 -2.72703 0 870 | L 6.84852 -13.2404 1477010489809733 6.85 -13.25 -2.727 0 871 | R 14.8615 -1.10225 -2.03746 1477010489864730 6.7 -13.2 -2.72742 0.909144 872 | L 6.55626 -13.1584 1477010489919727 6.55 -13.15 -2.72742 0.909144 873 | R 14.3946 -1.11583 -2.23409 1477010489974732 6.4 -13.1 -2.72703 0.908994 874 | L 6.25112 -13.0473 1477010490029738 6.25 -13.05 -2.727 0.908995 875 | R 14.3607 -1.13231 -1.93156 1477010490084683 6.1 -13 -2.73 0.910004 876 | L 5.95513 -12.9613 1477010490139629 5.95 -12.95 -2.72998 0.909996 877 | R 14.3815 -1.14857 -2.05973 1477010490189750 5.8 -12.9 -2.99275 0.99759 878 | L 5.6635 -12.8347 1477010490239871 5.65 -12.85 -2.99275 0.99758 879 | R 14.0268 -1.15873 -2.36004 1477010490294818 5.55 -12.75 -1.81993 1.81994 880 | L 5.45219 -12.6228 1477010490349765 5.45 -12.65 -1.81994 1.81994 881 | R 13.5149 -1.16708 -2.47916 1477010490404794 5.35 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| R 11.5336 -1.18409 -2.00293 1477010491174701 4.4 -10.8 0.9094 2.72823 896 | L 4.42489 -10.6572 1477010491229683 4.45 -10.65 0.909396 2.72819 897 | R 11.4356 -1.17086 -2.81654 1477010491279664 4.45 -10.5 0 3.00113 898 | L 4.44692 -10.3512 1477010491329645 4.45 -10.35 0 3.00113 899 | R 10.9254 -1.15506 -2.25117 1477010491379669 4.5 -10.2 0.999524 2.99855 900 | L 4.5556 -10.0446 1477010491429693 4.55 -10.05 0.999524 2.99856 901 | R 10.8604 -1.13609 -2.26342 1477010491479780 4.6 -9.9 0.998267 2.9948 902 | L 4.65841 -9.75093 1477010491529867 4.65 -9.75 0.998262 2.99479 903 | R 10.5329 -1.11857 -1.07221 1477010491584756 4.7 -9.65 0.910924 1.82187 904 | L 4.74425 -9.53907 1477010491639645 4.75 -9.55 0.910928 1.82186 905 | R 10.5106 -1.09824 -1.95487 1477010491694709 4.8 -9.4 0.908038 2.72411 906 | L 4.87523 -9.25457 1477010491749773 4.85 -9.25 0.908033 2.7241 907 | R 10.2807 -1.07104 -1.598 1477010491804763 4.95 -9.1 1.81851 2.72776 908 | L 5.04624 -8.96378 1477010491859753 5.05 -8.95 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-5.85 1.81844 1.81844 1192 | L 8.7543 -5.75242 1477010506969746 8.75 -5.75 1.81843 1.81843 1193 | R 10.6686 -0.565194 1.34315 1477010507024799 8.9 -5.65 2.72464 1.81643 1194 | L 9.06113 -5.54128 1477010507079852 9.05 -5.55 2.72465 1.81643 1195 | R 10.6386 -0.537333 0.800178 1477010507134822 9.15 -5.45 1.81916 1.81918 1196 | L 9.24452 -5.3352 1477010507189793 9.25 -5.35 1.81916 1.81916 1197 | R 10.6468 -0.515691 1.14332 1477010507244770 9.35 -5.3 1.81895 0.909466 1198 | L 9.43645 -5.25801 1477010507299747 9.45 -5.25 1.81894 0.90947 1199 | R 11.0213 -0.491273 0.378567 1477010507354696 9.55 -5.1 1.81986 2.72981 1200 | L 9.64908 -4.9531 1477010507409645 9.65 -4.95 1.81987 2.72981 1201 | R 10.8076 -0.462569 0.808191 1477010507464670 9.75 -4.85 1.81736 1.81735 1202 | L 9.86682 -4.74721 1477010507519695 9.85 -4.75 1.81736 1.81735 1203 | R 10.9769 -0.436747 0.773696 1477010507574699 9.95 -4.65 1.81806 1.81805 1204 | L 10.0706 -4.54316 1477010507629703 10.05 -4.55 1.81805 1.81805 1205 | R 11.3501 -0.410455 1.79691 1477010507684727 10.2 -4.45 2.72609 1.8174 1206 | L 10.3431 -4.35107 1477010507739752 10.35 -4.35 2.72606 1.81737 1207 | R 11.1934 -0.382691 -0.210545 1477010507794760 10.4 -4.2 0.908945 2.72688 1208 | L 10.4578 -4.07071 1477010507849768 10.45 -4.05 0.908953 2.72687 1209 | R 11.2679 -0.358104 1.20807 1477010507904742 10.55 -3.95 1.81903 1.81904 1210 | L 10.6424 -3.84126 1477010507959717 10.65 -3.85 1.81902 1.81903 1211 | R 11.2214 -0.330063 0.887286 1477010508014683 10.75 -3.7 1.81931 2.72896 1212 | L 10.8572 -3.53957 1477010508069649 10.85 -3.55 1.81931 2.72896 1213 | R 11.3235 -0.30085 0.302095 1477010508119661 10.9 -3.4 0.999745 2.99928 1214 | L 10.9372 -3.24816 1477010508169673 10.95 -3.25 0.999754 2.99928 1215 | R 11.3417 -0.277495 1.37716 1477010508224689 11.05 -3.15 1.81764 1.81765 1216 | L 11.135 -3.05697 1477010508279706 11.15 -3.05 1.81763 1.81764 1217 | R 11.5166 -0.252737 0.253884 1477010508334672 11.2 -2.9 0.909657 2.72896 1218 | L 11.2571 -2.74346 1477010508389639 11.25 -2.75 0.909648 2.72893 1219 | R 11.5547 -0.225803 -1.5427 1477010508439703 11.2 -2.6 -0.998725 2.99617 1220 | L 11.1393 -2.45312 1477010508489767 11.15 -2.45 -0.998725 2.99616 1221 | R 11.4655 -0.201037 0.457362 1477010508544784 11.2 -2.3 0.908813 2.72643 1222 | L 11.239 -2.16508 1477010508599802 11.25 -2.15 0.908805 2.7264 1223 | R 11.3365 -0.175531 0.442173 1477010508654756 11.3 -2 0.909855 2.72956 1224 | L 11.3424 -1.85113 1477010508709711 11.35 -1.85 0.909847 2.72953 1225 | -------------------------------------------------------------------------------- /plots/Lidar.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/srnand/Object-Tracking-and-State-Prediction-with-Unscented-and-Extended-Kalman-Filters/e51a52153a1ca2dfd26a2c7dfc9da126afa333b2/plots/Lidar.png -------------------------------------------------------------------------------- /plots/Radar.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/srnand/Object-Tracking-and-State-Prediction-with-Unscented-and-Extended-Kalman-Filters/e51a52153a1ca2dfd26a2c7dfc9da126afa333b2/plots/Radar.png -------------------------------------------------------------------------------- /src/KF.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | class KF(): 4 | def __init__(self,n): 5 | self.n = n 6 | self.I = np.matrix(np.eye(n)) 7 | self.x = None 8 | self.P = None 9 | self.F = None 10 | self.Q = None 11 | 12 | def predict(self): 13 | 14 | self.x = self.F * self.x 15 | self.P = self.F * self.P * self.F.T + self.Q 16 | 17 | def update(self, z, H, Hx, R): 18 | 19 | y = z - Hx 20 | PHt = self.P * H.T 21 | S = H * PHt + R 22 | K = PHt * (S.I) 23 | 24 | self.x = self.x + K * y 25 | self.P = (self.I - K * H) * self.P -------------------------------------------------------------------------------- /src/datapoint.py: -------------------------------------------------------------------------------- 1 | from tools import polar_to_cartesian 2 | import copy 3 | 4 | class DataPoint: 5 | """ 6 | A set of derived information from measurements of known sensors 7 | NOTE: Upon instantiation of a "radar" DataPoint, state variables are computed from raw data 8 | """ 9 | 10 | def __init__(self, d): 11 | self.timestamp = d['timestamp'] 12 | self.name = d['name'] 13 | self.all = d 14 | self.raw = [] 15 | self.data = [] 16 | 17 | if self.name == 'state': 18 | self.data = [d['x'], d['y'], d['vx'], d['vy']] 19 | self.raw = copy.deepcopy(self.data) 20 | 21 | elif self.name == 'lidar': 22 | self.data = [d['x'], d['y'], 0, 0] 23 | self.raw = [d['x'], d['y']] 24 | 25 | elif self.name == 'radar': 26 | x, y, vx, vy = polar_to_cartesian(d['rho'], d['phi'], d['drho']) 27 | self.data = [x, y, vx, vy] 28 | self.raw = [d['rho'], d['phi'], d['drho']] 29 | 30 | self.all['processed_data'] = self.data 31 | self.all['raw'] = self.raw 32 | 33 | def get_dict(self): 34 | return self.all 35 | 36 | def get_raw(self): 37 | return self.raw 38 | 39 | def get(self): 40 | return self.data 41 | 42 | def get_timestamp(self): 43 | return self.timestamp 44 | 45 | def get_name(self): 46 | return self.name -------------------------------------------------------------------------------- /src/helpers.py: -------------------------------------------------------------------------------- 1 | from datapoint import DataPoint 2 | from KF import KF 3 | 4 | def parse_data(file_path): 5 | """ 6 | Args: 7 | file_path 8 | - path to a text file with all data. 9 | - each line should have the following format: 10 | [SENSOR ID] [SENSOR RAW VALUES] [TIMESTAMP] [GROUND TRUTH VALUES] 11 | Whereas radar has three measurements (rho, phi, rhodot), lidar has two measurements (x, y). 12 | 13 | Specifically: 14 | 15 | For a row containing radar data, the columns are: 16 | sensor_type, rho_measured, phi_measured, rhodot_measured, timestamp, x_groundtruth, y_groundtruth, vx_groundtruth, vy_groundtruth 17 | 18 | For a row containing lidar data, the columns are: 19 | sensor_type, x_measured, y_measured, timestamp, x_groundtruth, y_groundtruth, vx_groundtruth, vy_groundtruth 20 | 21 | Example 1: 22 | line with three measurements from a radar sensor in polar coordinate 23 | followed by a timestamp in unix time 24 | followed by the the "ground truth" which is 25 | actual real position and velocity in cartesian coordinates (four state variables) 26 | 27 | R 8.46642 0.0287602 -3.04035 1477010443399637 8.6 0.25 -3.00029 0 28 | (R) (rho) (phi) (drho) (timestamp) (real x) (real y) (real vx) (real vy) 29 | 30 | Example 2: 31 | line with two measurements from a lidar sensor in cartesian coordinates 32 | followed by a timestamp in unix time 33 | followed by the the "ground truth" which is 34 | the actual real position and velocity in cartesian coordinates (four state variables) 35 | 36 | L 8.44818 0.251553 1477010443449633 8.45 0.25 -3.00027 0 37 | 38 | Returns: 39 | all_sensor_data, all_ground_truths 40 | - two lists of DataPoint() instances 41 | 42 | """ 43 | 44 | all_sensor_data = [] 45 | all_ground_truths = [] 46 | 47 | with open(file_path) as f: 48 | 49 | for line in f: 50 | data = line.split() 51 | 52 | if data[0] == 'L': 53 | 54 | sensor_data = DataPoint({ 55 | 'timestamp': int(data[3]), 56 | 'name': 'lidar', 57 | 'x': float(data[1]), 58 | 'y': float(data[2]) 59 | }) 60 | 61 | g = {'timestamp': int(data[3]), 62 | 'name': 'state', 63 | 'x': float(data[4]), 64 | 'y': float(data[5]), 65 | 'vx': float(data[6]), 66 | 'vy': float(data[7]) 67 | } 68 | 69 | ground_truth = DataPoint(g) 70 | 71 | elif data[0] == 'R': 72 | 73 | sensor_data = DataPoint({ 74 | 'timestamp': int(data[4]), 75 | 'name': 'radar', 76 | 'rho': float(data[1]), 77 | 'phi': float(data[2]), 78 | 'drho': float(data[3]) 79 | }) 80 | 81 | g = {'timestamp': int(data[4]), 82 | 'name': 'state', 83 | 'x': float(data[5]), 84 | 'y': float(data[6]), 85 | 'vx': float(data[7]), 86 | 'vy': float(data[8]) 87 | } 88 | ground_truth = DataPoint(g) 89 | 90 | all_sensor_data.append(sensor_data) 91 | all_ground_truths.append(ground_truth) 92 | 93 | return all_sensor_data, all_ground_truths 94 | 95 | 96 | def get_state_estimations(EKF, all_sensor_data): 97 | """ 98 | Calculates all state estimations given a FusionEKF instance() and sensor measurements 99 | 100 | Args: 101 | EKF - an instance of a FusionEKF() class 102 | all_sensor_data - a list of sensor measurements as a DataPoint() instance 103 | 104 | Returns: 105 | all_state_estimations 106 | - a list of all state estimations as predicted by the EKF instance 107 | - each state estimation is wrapped in DataPoint() instance 108 | """ 109 | 110 | all_state_estimations = [] 111 | 112 | for data in all_sensor_data: 113 | 114 | EKF.process(data) 115 | 116 | x = EKF.get() 117 | px, py, vx, vy = x[0, 0], x[1, 0], x[2, 0], x[3, 0] 118 | 119 | g = {'timestamp': data.get_timestamp(), 120 | 'name': 'state', 121 | 'x': px, 122 | 'y': py, 123 | 'vx': vx, 124 | 'vy': vy } 125 | 126 | state_estimation = DataPoint(g) 127 | all_state_estimations.append(state_estimation) 128 | 129 | return all_state_estimations 130 | 131 | def print_EKF_data(all_sensor_data, all_ground_truths, all_state_estimations, RMSE): 132 | """ 133 | Prints all relevant EKF data in a nice formal 134 | 135 | Args: 136 | all_sensor_data 137 | - a list of sensor measurements as DataPoint() instances 138 | all_state_estimations 139 | - a list of state estimations as DataPoint() instances 140 | all_ground_truths 141 | - a list of ground truths as DataPoint instances 142 | RMSE 143 | - a list of the four computed root-mean-square error of the four state variables considered 144 | 145 | Returns: None 146 | """ 147 | 148 | px, py, vx, vy = RMSE 149 | 150 | print("-----------------------------------------------------------") 151 | print('{:10s} | {:8.3f} | {:8.3f} | {:8.3f} | {:8.3f} |'.format("RMSE:", px, py, vx, vy)) 152 | print("-----------------------------------------------------------") 153 | print("NUMBER OF DATA POINTS:", len(all_sensor_data)) 154 | print("-----------------------------------------------------------") 155 | 156 | i = 1 157 | for s, p, t in zip(all_sensor_data, all_state_estimations, all_ground_truths): 158 | 159 | print("-----------------------------------------------------------") 160 | print("#", i, ":", s.get_timestamp()) 161 | print("-----------------------------------------------------------") 162 | 163 | if s.get_name() == 'lidar': 164 | x, y = s.get_raw() 165 | print('{:15s} | {:8.3f} | {:8.3f} |'.format("LIDAR:", x, y)) 166 | else: 167 | rho, phi, drho = s.get_raw() 168 | print('{:15s} | {:8.3f} | {:8.3f} | {:8.3f} |'.format("RADAR:", rho, phi, drho)) 169 | 170 | x, y, vx, vy = p.get() 171 | print('{:15s} | {:8.3f} | {:8.3f} | {:8.3f} | {:8.3f} |'.format("PREDICTION:", x, y, x, y)) 172 | 173 | x, y, vx, vy = t.get() 174 | print('{:15s} | {:8.3f} | {:8.3f} | {:8.3f} | {:8.3f} |'.format("TRUTH:", x, y, x, y)) 175 | 176 | i += 1 177 | -------------------------------------------------------------------------------- /src/sensor_fusion.py: -------------------------------------------------------------------------------- 1 | from KF import KF 2 | from datapoint import DataPoint 3 | from tools import calculate_jacobian, cartesian_to_polar, time_difference 4 | import numpy as np 5 | from tools import get_RMSE 6 | import matplotlib.pyplot as plt 7 | # from helpers import print_EKF_data 8 | 9 | def parse_data(file): 10 | sensor_data=[] 11 | true_data=[] 12 | 13 | with open(file, 'r') as dat: 14 | lines = dat.readlines() 15 | 16 | for line in lines: 17 | x= line.split() 18 | 19 | if x[0] == 'L': 20 | sensor_data_point = DataPoint({ 'timestamp': int(x[3]), 'name': 'lidar', 'x': float(x[1]), 'y': float(x[2])}) 21 | 22 | true_data_point = DataPoint({ 'timestamp': int(x[3]), 'name': 'state', 'x': float(x[4]), 'y': float(x[5]), 'vx': float(x[6]), 'vy': float(x[7])}) 23 | 24 | elif x[0] == 'R': 25 | sensor_data_point = DataPoint({ 'timestamp': int(x[4]), 'name': 'radar', 'rho': float(x[1]), 'phi': float(x[2]), 'drho': float(x[3])}) 26 | 27 | true_data_point = DataPoint({ 'timestamp': int(x[4]), 'name': 'state', 'x': float(x[5]), 'y': float(x[6]), 'vx': float(x[7]), 'vy': float(x[8])}) 28 | 29 | sensor_data.append(sensor_data_point) 30 | true_data.append(true_data_point) 31 | 32 | return sensor_data,true_data 33 | 34 | def start(data,kalmanFilter): 35 | global first_time 36 | timestamp = data.get_timestamp() 37 | x = np.matrix([data.get()]).T 38 | kalmanFilter.x=x 39 | kalmanFilter.P=P 40 | kalmanFilter.F=F 41 | kalmanFilter.Q=Q 42 | first_time=False 43 | return timestamp 44 | 45 | def updateQ(dt): 46 | 47 | dt2 = dt * dt 48 | dt3 = dt * dt2 49 | dt4 = dt * dt3 50 | 51 | x, y = a 52 | 53 | r11 = dt4 * x / 4 54 | r13 = dt3 * x / 2 55 | r22 = dt4 * y / 4 56 | r24 = dt3 * y / 2 57 | r31 = dt3 * x / 2 58 | r33 = dt2 * x 59 | r42 = dt3 * y / 2 60 | r44 = dt2 * y 61 | 62 | Q = np.matrix([[r11, 0, r13, 0],[0, r22, 0, r24],[r31, 0, r33, 0], [0, r42, 0, r44]]) 63 | 64 | return Q 65 | 66 | def kalman(data,kalmanFilter,timestamp): 67 | dt = time_difference(timestamp, data.get_timestamp()) 68 | timestamp = data.get_timestamp() 69 | 70 | kalmanFilter.F[0,2],kalmanFilter.F[1,3]=dt,dt 71 | kalmanFilter.Q = updateQ(dt) 72 | kalmanFilter.predict() 73 | 74 | z = np.matrix(data.get_raw()).T 75 | x = kalmanFilter.x 76 | 77 | if data.get_name() == 'radar': 78 | 79 | px, py, vx, vy = x[0, 0], x[1, 0], x[2, 0], x[3, 0] 80 | rho, phi, drho = cartesian_to_polar(px, py, vx, vy) 81 | H = calculate_jacobian(px, py, vx, vy) 82 | Hx = (np.matrix([[rho, phi, drho]])).T 83 | R = radar_R 84 | 85 | elif data.get_name() == 'lidar': 86 | 87 | H = lidar_H 88 | Hx = lidar_H * x 89 | R = lidar_R 90 | 91 | kalmanFilter.update(z, H, Hx, R) 92 | 93 | # if data.get_name() == 'lidar': 94 | # print x, kalmanFilter.x, "lidar" 95 | # elif data.get_name() == 'radar': 96 | # print x, kalmanFilter.x, "radar" 97 | 98 | return timestamp 99 | 100 | def run(sensor_data,kalmanFilter): 101 | 102 | state_estimations=[] 103 | for data in sensor_data: 104 | if first_time: 105 | timestamp = start(data,kalmanFilter) 106 | else: 107 | timestamp = kalman(data,kalmanFilter,timestamp) 108 | 109 | x = kalmanFilter.x 110 | 111 | px, py, vx, vy = x[0, 0], x[1, 0], x[2, 0], x[3, 0] 112 | 113 | g = {'timestamp': data.get_timestamp(), 114 | 'name': 'state', 115 | 'x': px, 116 | 'y': py, 117 | 'vx': vx, 118 | 'vy': vy } 119 | 120 | state_estimation = DataPoint(g) 121 | state_estimations.append(state_estimation) 122 | 123 | return state_estimations 124 | 125 | lidar_R = np.matrix([[0.01, 0], 126 | [0, 0.01]]) 127 | 128 | radar_R = np.matrix([[0.01, 0, 0], 129 | [0, 1.0e-6, 0], 130 | [0, 0, 0.01]]) 131 | 132 | lidar_H = np.matrix([[1, 0, 0, 0], 133 | [0, 1, 0, 0]]) 134 | 135 | P = np.matrix([[1, 0, 0, 0], 136 | [0, 1, 0, 0], 137 | [0, 0, 1000, 0], 138 | [0, 0, 0, 1000]]) 139 | 140 | Q = np.matrix(np.zeros([4, 4])) 141 | F = np.matrix(np.eye(4)) 142 | 143 | sensor_data,true_data = parse_data("data/data-1.txt") 144 | 145 | n = 4 146 | a = (5, 5) #accelerationNoise 147 | 148 | kalmanFilter = KF(n) 149 | 150 | first_time=True 151 | state_estimations=run(sensor_data,kalmanFilter) 152 | 153 | px, py, vx, vy = get_RMSE(state_estimations, true_data) 154 | 155 | # print_EKF_data(sensor_data, true_data, state_estimations, 156 | # RMSE = [px, py, vx, vy]) 157 | 158 | lidar_x_sensor=[] 159 | lidar_y_sensor=[] 160 | x_pred=[] 161 | y_pred=[] 162 | x_true=[] 163 | y_true=[] 164 | 165 | radar_r_sensor=[] 166 | radar_p_sensor=[] 167 | radar_d_sensor=[] 168 | 169 | i=0 170 | for s, p, t in zip(sensor_data, state_estimations, true_data): 171 | i+=1 172 | if i%4==0: 173 | continue 174 | if s.get_name() == 'lidar': 175 | x, y = s.get_raw() 176 | lidar_x_sensor.append(x) 177 | lidar_y_sensor.append(y) 178 | # x,y, vx, vy=p.get() 179 | # x_pred.append(x) 180 | # y_pred.append(y) 181 | 182 | # x,y, vx, vy=t.get() 183 | # x_true.append(x) 184 | # y_true.append(y) 185 | else: 186 | rho, phi, drho = s.get_raw() 187 | radar_r_sensor.append(rho) 188 | radar_p_sensor.append(phi) 189 | radar_d_sensor.append(drho) 190 | x,y, vx, vy=p.get() 191 | x_pred.append(x) 192 | y_pred.append(y) 193 | 194 | x,y, vx, vy=t.get() 195 | x_true.append(x) 196 | y_true.append(y) 197 | 198 | 199 | # plt.scatter(lidar_x_sensor,lidar_y_sensor,label="Sensor-Data",marker="o") 200 | plt.scatter(x_pred,y_pred,label="Predicted-Data",marker="*") 201 | plt.scatter(x_true,y_true,label="True-Data",marker=".") 202 | plt.legend() 203 | plt.text(10,-13,"Radar Data Plot") 204 | plt.show() 205 | 206 | 207 | 208 | 209 | -------------------------------------------------------------------------------- /src/tools.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from math import sin, cos, sqrt 3 | 4 | def cartesian_to_polar(x, y, vx, vy, THRESH = 0.0001): 5 | """ 6 | Converts 2d cartesian position and velocity coordinates to polar coordinates 7 | 8 | Args: 9 | x, y, vx, vy : floats - position and velocity components in cartesian respectively 10 | THRESH : float - minimum value of rho to return non-zero values 11 | 12 | Returns: 13 | rho, drho : floats - radius and velocity magnitude respectively 14 | phi : float - angle in radians 15 | """ 16 | 17 | rho = sqrt(x * x + y * y) 18 | phi = np.arctan2(y, x) 19 | 20 | 21 | if rho < THRESH: 22 | print("WARNING: in cartesian_to_polar(): d_squared < THRESH") 23 | rho, phi, drho = 0, 0, 0 24 | else: 25 | drho = (x * vx + y * vy) / rho 26 | 27 | return rho, phi, drho 28 | 29 | def polar_to_cartesian(rho, phi, drho): 30 | """ 31 | Converts 2D polar coordinates into cartesian coordinates 32 | 33 | Args: 34 | rho. drho : floats - radius magnitude and velocity magnitudes respectively 35 | phi : float - angle in radians 36 | 37 | Returns: 38 | x, y, vx, vy : floats - position and velocity components in cartesian respectively 39 | """ 40 | 41 | x, y = rho * cos(phi), rho * sin(phi) 42 | vx, vy = drho * cos(phi) , drho * sin(phi) 43 | 44 | return x, y, vx, vy 45 | 46 | def time_difference(t1, t2): 47 | """ 48 | Computes the time difference in microseconds (type: float) of two epoch times values in seconds (type: int) 49 | 50 | Args: 51 | t1 : int - previous epoch time in seconds 52 | t2 : int - current epoch time in seconds 53 | 54 | Returns: a float - the time difference in seconds 55 | """ 56 | return (t2 - t1) / 1000000.0 57 | 58 | 59 | def get_RMSE(predictions, truths): 60 | """ 61 | Computes the root mean square errors (RMSE) of the attributes of two lists of DataPoint() instances 62 | 63 | Args: 64 | predictions - a list of DataPoint() instances 65 | truths - a list of DataPoint() instances 66 | 67 | Returns: 68 | px, py, vx, vy - The RMSE of each respective DataPoint() attributes (type: float) 69 | """ 70 | pxs, pys, vxs, vys = [], [], [], [] 71 | 72 | for p, t in zip(predictions, truths): 73 | 74 | ppx, ppy, pvx, pvy = p.get() 75 | tpx, tpy, tvx, tvy = t.get() 76 | 77 | pxs += [(ppx - tpx) * (ppx - tpx)] 78 | pys += [(ppy - tpy) * (ppy - tpy)] 79 | vxs += [(pvx - tvx) * (pvx - tvx)] 80 | vys += [(pvy - tvy) * (pvy - tvy)] 81 | 82 | px, py = sqrt(np.mean(pxs)), sqrt(np.mean(pys)) 83 | vx, vy = sqrt(np.mean(vxs)), sqrt(np.mean(vys)) 84 | 85 | return px, py, vx, vy 86 | 87 | def calculate_jacobian(px, py, vx, vy, THRESH = 0.0001, ZERO_REPLACEMENT = 0.0001): 88 | """ 89 | Calculates the Jacobian given for four state variables 90 | 91 | Args: 92 | px, py, vx, vy : floats - four state variables in the system 93 | THRESH - minimum value of squared distance to return a non-zero matrix 94 | ZERO_REPLACEMENT - value to replace zero to avoid division by zero error 95 | 96 | Returns: 97 | H : the jacobian matrix expressed as a 4 x 4 numpy matrix with float values 98 | """ 99 | 100 | d_squared = px * px + py * py 101 | d = sqrt(d_squared) 102 | d_cubed = d_squared * d 103 | 104 | if d_squared < THRESH: 105 | 106 | print("WARNING: in calculate_jacobian(): d_squared < THRESH") 107 | H = np.matrix(np.zeros([3, 4])) 108 | 109 | else: 110 | 111 | r11 = px / d 112 | r12 = py / d 113 | r21 = -py / d_squared 114 | r22 = px / d_squared 115 | r31 = py * (vx * py - vy * px) / d_cubed 116 | r32 = px * (vy * px - vx * py) / d_cubed 117 | 118 | H = np.matrix([[r11, r12, 0, 0], 119 | [r21, r22, 0, 0], 120 | [r31, r32, r11, r12]]) 121 | 122 | return H --------------------------------------------------------------------------------