how to smooth this data by using KF filter i need matlab code.

No of samples SensVolt(in mV) 1 2453 2 2453 3 2453 4 2453 5 2607 6 2526 7 2606 8 2468 9 2463 10 2623 11 2544 12 2474 13 2487 14 2482 15 2507 16 2481 17 2578 18 2452 19 2465 20 2515 21 2619 22 2565 23 2440 24 2507 25 2477 26 2644 27 2576 28 2538 29 2423 30 2507 31 2512 32 2466 33 2624 34 2507 35 2430 36 2591 37 2485 38 2451 39 2606 40 2522 41 2494 42 2461 43 2463 44 2530 45 2415 46 2445 47 2644 48 2530 49 2526 50 2536 51 2523 52 2519 53 2512 54 2507 55 2561 56 2482 57 2407 58 2373 59 2478 60 2519 61 2537 62 2578 63 2515 64 2551 65 2485 66 2573 67 2492 68 2563 69 2530 70 2500 71 2521 72 2445 73 2515 74 2397 75 2531 76 2400 77 2464 78 2443 79 2426 80 2685 81 2513 82 2474 83 2486 84 2486 85 2494 86 2565 87 2442 88 2496 89 2507 90 2519 91 2488 92 2397 93 2467 94 2489 95 2548 96 2559 97 2479 98 2482 99 2503 100 2471 101 2379 102 2407 103 2459 104 2569 105 2457 106 2489 107 2478 108 2606 109 2442 110 2488 111 2436 112 2489 113 2518 114 2424 115 2509 116 2444 117 2481 118 2498 119 2431 120 2510 121 2493 122 2534 123 2460 124 2470 125 2522 126 2606 127 2452 128 2489 129 2534 130 2474 131 2474 132 2500 133 2562 134 2500 135 2496 136 2408 137 2524 138 2586 139 2505 140 2452 141 2569 142 2393 143 2436 144 2449 145 2439 146 2520 147 2592 148 2467 149 2492 150 2492 151 2458 152 2526 153 2491 154 2615 155 2428 156 2514 157 2466 158 2515 159 2498 160 2453 161 2508 162 2512 163 2529 164 2528 165 2416 166 2482 167 2515 168 2429 169 2556 170 2498 171 2469 172 2436 173 2483 174 2442 175 2574 176 2508 177 2536 178 2496 179 2482 180 2542 181 2511 182 2439 183 2513 184 2508 185 2483 186 2538 187 2538 188 2538 189 2538 190 2492 191 2489 192 2406 193 2434 194 2500 195 2443 196 2484 197 2481 198 2490 199 2573 200 2457 201 2510 202 2490 203 2385 204 2601 205 2508 206 2512 207 2579 208 2453 209 2640 210 2514 211 2578 212 2479 213 2546 214 2461 215 2583 216 2434 217 2405 218 2520 219 2458 220 2495 221 2482 222 2438 223 2525 224 2516 225 2519 226 2522 227 2474 228 2515 229 2594 230 2568 231 2494 232 2494 233 2520 234 2511 235 2456 236 2598 237 2428 238 2480 239 2391 240 2519 241 2526 242 2508 243 2526 244 2633 245 2520 246 2521 247 2467 248 2489 249 2382 250 2469 251 2550 252 2578 253 2519 254 2591 255 2488 256 2407 257 2483 258 2524 259 2537 260 2515 261 2473 262 2492 263 2494 264 2490 265 2400 266 2386 267 2478 268 2511 269 2495 270 2499 271 2544 272 2368 273 2589 274 2498 275 2600 276 2569 277 2510 278 2440 279 2513 280 2614 281 2601 282 2550 283 2500 284 2565 285 2544 286 2434 287 2589 288 2503 289 2486 290 2628 291 2497 292 2490 293 2623 294 2440 295 2566 296 2503 297 2510 298 2535 299 2518 300 2602 301 2475 302 2681 303 2559 304 2653 305 2482 306 2428 307 2468 308 2527 309 2474 310 2470 311 2469 312 2422 313 2511 314 2582 315 2526 316 2427 317 2524 318 2453 319 2389 320 2484 321 2382 322 2530 323 2480 324 2519 325 2532 326 2532 327 2532 328 2532 329 2502 330 2488 331 2439 332 2516 333 2468 334 2487 335 2540 336 2443 337 2488 338 2533 339 2453 340 2399 341 2573 342 2420 343 2461 344 2572 345 2492 346 2504 347 2484 348 2515 349 2513 350 2591 351 2505 352 2559 353 2486 354 2536 355 2511 356 2552 357 2599 358 2361 359 2471 360 2545 361 2480 362 2610 363 2537 364 2507 365 2495 366 2447 367 2461 368 2458 369 2506 370 2487 371 2612 372 2484 373 2445 374 2471 375 2471 376 2463 377 2560 378 2608 379 2523 380 2475 381 2447 382 2553 383 2470 384 2436 385 2449 386 2458 387 2480 388 2517 389 2656 390 2442 391 2513 392 2439 393 2405 394 2361 395 2431 396 2435 397 2515 398 2446 399 2459 400 2560 401 2527 402 2478 403 2555 404 2446 405 2431 406 2451 407 2533 408 2453 409 2479 410 2645 411 2523 412 2608 413 2435 414 2515 415 2446 416 2459 417 2560 418 2527 419 2478 420 2555 421 2446 422 2431 423 2451 424 2533 425 2453 426 2479 427 2645 428 2523 429 2608

how to smooth this data by using KF filter i need matlab code.

Answer 1

[Shlok]

Hi Teja,

I understand that you want to smooth your array of voltage measurements using a Kalman Filter. The Kalman Filter is a powerful tool for smoothing because it combines prior knowledge (prediction) with noisy measurements to produce an optimal estimate. The general approach to achieve this is to:

• Initialize the state estimate and error covariance.

% assuming SensVolt contains the voltage measurements

% Preallocate output
n = length(SensVolt);
x_est = zeros(1, n);  % Estimated signal
P = zeros(1, n);      % Error covariance

% Initialize Kalman filter parameters
Q = 1e-5;     % Process noise covariance
R = 1e-2;     % Measurement noise covariance
x_est(1) = SensVolt(1);  % Initial state estimate
P(1) = 1;     % Initial estimate error covariance

• At each sample, predict the next state based on the previous estimate.
• Update the estimate with the new measurement, balancing the uncertainty using the Kalman Gain.

for k = 2:n
    % Prediction
    x_pred = x_est(k-1);
    P_pred = P(k-1) + Q;

    % Kalman Gain
    K = P_pred / (P_pred + R);

    % Update
    x_est(k) = x_pred + K * (SensVolt(k) - x_pred);
    P(k) = (1 - K) * P_pred;
end

Hence, following these steps, you can smoothen out the array of sensor voltages effectively using a Kalman Filter.

To know more about Kalman Filter, refer to the following MathWorks documentation link:

https://www.mathworks.com/discovery/kalman-filter.html