如何从加速度计计算出正确的速度值

Question

如何从加速度计计算出正确的速度值

3

我需要计算iPhone在太空中的速度，例如冲击速度。
我的第一个问题是：使用这些过滤操作，加速度值accelerometer:didAccelerate是否正确：

gravity_x = acceleration.x * kFilteringFactor + gravity_x * (1.0 - kFilteringFactor);
gravity_y = acceleration.y * kFilteringFactor + gravity_y * (1.0 - kFilteringFactor);
gravity_z = acceleration.z * kFilteringFactor + gravity_z * (1.0 - kFilteringFactor);
float gravityNorm = sqrt(gravity_x * gravity_x + gravity_y * gravity_y + gravity_z * gravity_z);
accelX = acceleration.x - gravity_x / gravityNorm;
accelY = acceleration.y - gravity_y / gravityNorm;
accelZ = acceleration.z - gravity_z / gravityNorm;

这与使用CoreMotion的下面代码是相同的：
motionManager.deviceMotion.userAcceleration.x; motionManager.deviceMotion.userAcceleration.y; motionManager.deviceMotion.userAcceleration.z;?

接下来，根据同样的问题，我做了如下处理。

    const float accuracy=10;
    float accx = (float) ((int)  (accelX * accuracy))/ accuracy;
    float accy=  (float) ((int)  (accelY * accuracy))/ accuracy;
    float accz=  (float) ((int)  (accelZ * accuracy))/ accuracy;

对于进行数值四舍五入，我认为这样可以得到当前速度。

float dx = accx*9.81+prevX*9.81;
float dy = accy*9.81+prevY*9.81;
float dz = accz*9.81+prevZ*9.81;

speed_after_x = dx/2*myAccelerometer.updateInterval+speed_before_x;
speed_after_y = dy/2*myAccelerometer.updateInterval+speed_before_y;
speed_after_z = dz/2*myAccelerometer.updateInterval+speed_before_z;

根据iPhone加速度计的速度和距离
那么

    prevX=accx;
    prevY=accy;
    prevZ=accz;

    speed_before_x=speed_after_x;
    speed_before_y=speed_after_y;
    speed_before_z=speed_after_z;

最后，将速度计算为向量长度。

    float speed = sqrt(speed_after_x*speed_after_x+speed_after_y*speed_after_y+speed_after_z*speed_after_z);
    if (max_speed<speed)  max_speed = speed;

但速度值，也就是标签中包含的值，却总是在增加。我的意思是，如果我移动了设备然后停下来，速度值并不会变成0。难道加速度不会在0时自我补偿吗？

- Aft3rmath

这不是自己抵消了吗：((int) (accelX * accuracy)) / accuracy;。就像 ((10 * 100) / 100 == 10)。如果你的意图是将数字四舍五入然后转换回浮点数，那么有更好的方法来实现它。 - Diziet

准确度为10，以避免在设备保持时快速加速值的变化。 - Aft3rmath

是的，但将一个数字乘以同一个数字再除以该数字等同于什么都不做。 (A * B) / B = A. - Diziet

我不认为这就是速度不变为0的原因，无论如何，我必须使用acceleration.timestamp的差值，而不是完全等于updateInterval。 - Aft3rmath

哦，我知道了，这就是为什么这是一个注释而不是答案。 - Diziet

你为什么不使用核心动态？我认为它在>=ios4.0可用。 - Diziet

1个回答

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原文链接

- Diziet · Accepted Answer

以下是我编写的示例代码，我将在此处粘贴它：

//
//  ViewController.m
//  Acce
//
//  Created by Diziet on 14/05/2012.
//  Copyright (c) 2012 __MyCompanyName__. All rights reserved.
//

#import "ViewController.h"

@interface ViewController () {
    UIAccelerationValue gravX;
    UIAccelerationValue gravY;
    UIAccelerationValue gravZ;
    UIAccelerationValue prevVelocity;
    UIAccelerationValue prevAcce;
}

@property (strong) UIAccelerometer *sharedAcc;

@end

@implementation ViewController

@synthesize sharedAcc = _sharedAcc;

#define kAccelerometerFrequency        50.0 //Hz
#define kFilteringFactor 0.1

- (void)viewDidLoad
{
    [super viewDidLoad];
    // Do any additional setup after loading the view, typically from a nib.
    self.sharedAcc = [UIAccelerometer sharedAccelerometer];
    self.sharedAcc.delegate = self;
    self.sharedAcc.updateInterval = 1 / kAccelerometerFrequency; 

    gravX = gravY = gravZ = prevVelocity = prevAcce = 0.f;
}

- (void)viewDidUnload
{
    [super viewDidUnload];
    // Release any retained subviews of the main view.
}

- (BOOL)shouldAutorotateToInterfaceOrientation:(UIInterfaceOrientation)interfaceOrientation
{
    return (interfaceOrientation != UIInterfaceOrientationPortraitUpsideDown);
}

- (UIAccelerationValue)tendToZero:(UIAccelerationValue)value {
    if (value < 0) {
        return ceil(value);
    } else {
        return floor(value);
    }
}

#define kAccelerometerFrequency        50.0 //Hz
#define kFilteringFactor 0.1
- (void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration {
    gravX = (acceleration.x * kFilteringFactor) + (gravX * (1.0 - kFilteringFactor));
    gravY = (acceleration.y * kFilteringFactor) + (gravY * (1.0 - kFilteringFactor));
    gravZ = (acceleration.z * kFilteringFactor) + (gravZ * (1.0 - kFilteringFactor));

    UIAccelerationValue accelX = acceleration.x - ( (acceleration.x * kFilteringFactor) + (gravX * (1.0 - kFilteringFactor)) );

    UIAccelerationValue accelY = acceleration.y - ( (acceleration.y * kFilteringFactor) + (gravY * (1.0 - kFilteringFactor)) );
    UIAccelerationValue accelZ = acceleration.z - ( (acceleration.z * kFilteringFactor) + (gravZ * (1.0 - kFilteringFactor)) );
    accelX *= 9.81f;
    accelY *= 9.81f;
    accelZ *= 9.81f;
    accelX = [self tendToZero:accelX];
    accelY = [self tendToZero:accelY];
    accelZ = [self tendToZero:accelZ];

    UIAccelerationValue vector = sqrt(pow(accelX,2)+pow(accelY,2)+pow(accelZ, 2));
    UIAccelerationValue acce = vector - prevVelocity;
    UIAccelerationValue velocity = (((acce - prevAcce)/2) * (1/kAccelerometerFrequency)) + prevVelocity;

    NSLog(@"X %g Y %g Z %g, Vector %g, Velocity %g",accelX,accelY,accelZ,vector,velocity);

    prevAcce = acce;
    prevVelocity = velocity;
}

@end

它需要根据您的需求进行修改，尤其是因为我在之后只是抛弃了这些值。所得的值'velocity'被记录为'Velocity'，在加速事件停止后会回归到极小的负值，例如*10^-17。因此，在我看来，那就几乎相当于零了。您可能需要在其中进行一些四舍五入，甚至可能需要将这些值放大。我认为我无法将其提高到0.2或0.3，但我也不想把手机扔到房间的另一边(至少目前还没有这样做)。